Choose the shape of the space, enter its size and depth, and choose the material. The waste factor and the price can be left blank (then no waste is added and no cost is calculated).
Choosing a material fills in a typical bulk density. If the bag says something like "25 L (about 12 kg)", enter the value calculated from it (kg ÷ L) for a more accurate result. Choosing a pot size fills in typical top and bottom diameters and depth, so adjust them to your actual pot.
Result and figure
Enter the size and depth of your bed (or the size of your planter or pot) in the fields on the left and press "Calculate". The result will appear here.
Table of Contents
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What you can do on this page
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What is this calculation used for?
-
How to Use
-
Formulas and figures
-
Symbols and terms
-
Good to know before you start
-
How to calculate it in Excel
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How to calculate it in Google Sheets
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How to calculate it in Python
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How to write it in LaTeX and other math languages (copy and paste)
-
How to have ChatGPT do the calculation
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DataChef Features
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Related Features
-
NumberChef Calculators List
What you can do on this page
- Enter the size of a bed or garden (length × width, a total area, or the diameter of a round bed) and the depth in inches, and you get the amount of soil, sand or potting mix you need in cubic feet and cubic yards on the spot
- For planters (inside length × width × depth) and pots (choose a pot size to fill in typical top and bottom diameters and depth), you get the soil per container and the total for several
- Choose the material (potting mix, topsoil, akadama, kanuma, leaf mold, decomposed granite, river sand, fill sand or lawn topdressing) to fill in a typical bulk density (lb/ft³) and convert the amount to pounds. You can change the bulk density yourself
- Enter the bag size, such as 1.5 ft³ or 40 lb, to get the number of bags rounded up, along with the bags before rounding, the amount you buy and the amount left over. A waste factor (%) for settling after watering and for compaction follows "amount needed = net amount × (1 + waste factor)"
- You can also work backward: "what area will my bags cover", "how deep will they fill" and "how many planters or pots will they fill". Enter a price (per bag, ft³, lb or yd³) to get the cost. A plain-language explanation of the formulas and copy-and-paste formulas for Excel, Google Sheets and Python are all on this page
The amount, weight and number of bags are estimates. Bulk density varies a lot with the type of soil, the particle size and how moist it is, and the contents of bagged products (ft³ or lb) differ by product, so check the label too. The soil for a given pot size is for a pot of standard shape and changes with the height of the pot and how much it narrows at the bottom. For gravel and crushed stone laid loose (driveways, over landscape fabric and so on), use the "Gravel Calculator" page. This page is for soil, sand and potting mix for beds, gardens, planters, lawn topdressing and fill.
What is this calculation used for?
Filling a raised bed or refreshing garden soil
Raised beds are a popular way to grow vegetables, and a 4 ft × 8 ft bed is a classic size. Filled 8 in deep with potting mix, the net amount is \(32 \times 8 \div 12 \approx 21.33\) ft³; with a 10% waste factor it is about 23.47 ft³, or \(\lceil 23.47 \div 1.5 \rceil = 16\) bags of 1.5 ft³.
Each extra inch of depth adds about 2.67 ft³, so decide how deep to fill first, then work out the bags, and you will know how many trips and how much budget you need. That is almost a cubic yard (0.87 yd³), so for several beds, bulk delivery by the cubic yard is often cheaper. If you mix in compost, reduce the potting mix by that amount.
Potting mix for patio or balcony planters
A 24-inch planter may be about 22 in × 8 in inside the rim, but it narrows toward the bottom. Using the size halfway down (20 in × 7 in) and a soil depth of 6 in gives \(20 \times 7 \times 6 \div 1728 \approx 0.486\) ft³ per planter, about half of a 1 ft³ bag. Three planters take about 1.46 ft³, or about 1.53 ft³ with a 5% waste factor, which is 2 bags of 1 ft³ or 2 bags of 1.5 ft³.
Potting mix costs a different amount per cubic foot depending on the bag size, so working out how much each planter needs first helps you choose the bag size and count with the least waste. The weight is shown too, as a guide to how much your balcony can hold or how much you can carry at once.
Repotting (estimating soil from the pot size)
When repotting houseplants or flowers, people usually move up one or two sizes, and pots are named by the top diameter in inches. A 6-inch pot of standard shape holds about 0.047 ft³ of soil and an 8-inch pot about 0.11 ft³. Repotting four plants into 8-inch pots takes about \(0.113 \times 4 \approx 0.45\) ft³, so one 1 ft³ bag is enough, with about 0.55 ft³ left over.
You can save the leftover for the next repotting. Use the backward mode to check "how many 6-inch pots will one 1 ft³ bag fill" and see how many plants you can repot with the soil you have. The actual soil depends on the pot shape and any drainage layer, so treat the values from the pot size as a guide and use your own measurements if you have them.
Topdressing a lawn (thin but wide)
Lawns are topdressed once or twice a year with a thin layer of sand or soil to level bumps and protect the roots. The layer is thin, about 1/4 in, but it covers the whole lawn: for 1,000 ft², the net amount is \(1000 \times 0.25 \div 12 \approx 20.83\) ft³ (about 0.77 yd³). At a bulk density of 94 lb/ft³ that is about 1,958 lb, or \(\lceil 1958 \div 50 \rceil = 40\) bags of 50 lb.
"It is so thin, a little will do" often leaves you short. Remember that even 1/4 in takes about 2 ft³ (roughly 200 lb) per 100 ft². Sand is usually sold by weight or by the cubic yard, so the calculation uses bags sold by weight.
Fill and backfill (ordering decomposed granite or fill by the truckload)
To improve drainage in a yard or to backfill after pipe work or planting a tree, people use decomposed granite, fill sand or fill dirt. Raising a 10 ft × 10 ft area by 4 in takes a net 33.33 ft³; with a 20% waste factor for compaction it is 40 ft³ (about 1.48 yd³), weighing about 3,760 lb (nearly 2 tons). That would be 94 bags of 40 lb, so at this scale bulk delivery by the cubic yard is the usual choice.
Suppliers ask "how many yards?", so you can give them the yd³ value directly. To estimate the cost with a price per cubic yard, set the price unit to "per yd³" (delivery fees are extra).
Blending your own mix
Gardeners often mix their own soil by volume, such as "3 parts potting mix to 1 part compost". If you need 24 ft³ in total, that is \(24 \times \tfrac{3}{4} = 18\) ft³ of potting mix and \(24 \times \tfrac{1}{4} = 6\) ft³ of compost, and each is divided by its own bag size to get the number of bags.
Mix ratios are by volume, so dividing the cubic feet from this page by the ratio gives the amount of each material. Materials differ a lot in weight (leaf mold about 19 lb/ft³, topsoil about 69), so measure by volume, not by weight.
Checking the quantities in a landscaping quote
A landscaping quote may list "topsoil, 243 sq ft at 4 in, 3 cu yd". Area × depth gives \(243 \times 4 \div 12 \div 27 = 3\) yd³, so you can ask the contractor whether any difference from the quoted amount is a waste factor or a deeper layer.
Knowing where the quantities come from lets you separate the material cost (quantity × unit price) from labor and hauling, and makes comparing quotes easier (in a real job, soil conditions and how much it is compacted can increase the amount needed, so the quantity alone does not tell you whether the price is fair).
Formulas and figures
Area of a bed or garden (rectangle or circle)
Standard notation
(the usual math form)
\(S\)
\(=\)
\(l\)
\(\times\)
\(w\)
\(S\)
\(=\)
\(\pi\)
\(\times\)
\(\left(\dfrac{d}{2}\right)\)
\(2\)
In words
(symbols replaced with words)
③
\(S\): area (rectangle)
\(=\)
①
\(l\): length
\(\times\)
②
\(w\): width
⑥
\(S\): area (circle)
\(=\)
\(\pi\)
\(\times\)
④
half the diameter \(d\) (the radius)
⑤
squared
The formula in words
①
Take the
\(l\): length
②
multiply it by the
\(w\): width
③
to get the
\(S\): area of a rectangle
④
Take
half the diameter \(d\) (the radius)
⑤
squared
and multiply by \(\pi\) (about 3.14)
⑥
to get the
\(S\): area of a circle
Quick example
The areas of an 8 ft × 4 ft raised bed and of a round bed 4 ft across are
\(S\): area (rectangle)
\(=\)
length (8 ft)
\(\times\)
width (4 ft)
\(8 \times 4 = 32\,\mathrm{ft^2}\)
\(\pi \times \left(\dfrac{4}{2}\right)^{2} = 3.14 \times 4 \approx 12.57\,\mathrm{ft^2}\)
Key idea
The area is how much ground you will cover with soil, the starting point for the amount of soil. If you have several beds of the same size, multiply the area of one bed by the number of beds, or enter the total ft² as a total area. For a round bed or the ring around a tree, measure the diameter; the area is half the diameter (the radius) squared, times pi.
For planters and pots, the calculation starts from the soil per container instead of an area (the third formula below).
Soil for a bed or garden (net amount)
Figure
Standard notation
(the usual math form)
\(V\)
\(=\)
\(S\)
\(\times\)
\(t\)
\(\div\)
\(12\)
In words
(symbols replaced with words)
③
\(V\): net amount (ft³)
\(=\)
①
\(S\): area (ft²)
\(\times\)
②
\(t\): depth (in)
\(\div\)
\(12\)
The formula in words
①
Take the
\(S\): area (ft²)
②
multiply it by the
\(t\): depth (in)
and divide by 12 to turn "ft² × in" into cubic feet
③
to get the
\(V\): net amount (ft³)
Quick example
The net amount of soil to fill a 32 ft² raised bed 8 in deep is
\(V\): net amount
\(=\)
area (32 ft²)
\(\times\)
depth (8 in)
\(\div\)
\(12\)
\(32 \times 8 \div 12 \approx 21.33\,\mathrm{ft^3}\)
\(21.33\,\mathrm{ft^3} \div 27 \approx 0.79\,\mathrm{yd^3}\)
Key idea
The amount of soil is a volume, "area × depth". The area is in square feet and the depth in inches, so "ft² × in" has to be turned into cubic feet. A depth of 1 in is \(\tfrac{1}{12}\) ft, so 1 ft² × 1 in is \(\tfrac{1}{12}\) ft³. That is why "ft² × in ÷ 12" gives cubic feet.
Bagged potting mix and garden soil are labeled in cubic feet, so this page works mainly in cubic feet and also shows cubic yards, the unit for bulk delivery by truck. 1 yd³ = 3 ft × 3 ft × 3 ft = 27 ft³. This is the net amount for an exact fill. In practice, soil settles after watering and so on, so the fourth formula adds a waste factor.
Soil per planter or pot
Figure
Standard notation
(the usual math form)
\(V_1\)
\(=\)
\(a\)
\(\times\)
\(b\)
\(\times\)
\(t\)
\(\div\)
\(1728\)
\(V_1\)
\(=\)
\(\pi\)
\(\times\)
\(t\)
\(\div\)
\(3\)
\(\times\)
\(\left(R^2 + R R_{\mathrm{b}} + R_{\mathrm{b}}^2\right)\)
\(\div\)
\(1728\)
In words
(symbols replaced with words)
④
\(V_1\): soil per planter (ft³)
\(=\)
①
\(a\): inside length (in)
\(\times\)
②
\(b\): inside width (in)
\(\times\)
③
\(t\): soil depth (in)
\(\div\)
\(1728\)
⑦
\(V_1\): soil per pot (ft³)
\(=\)
\(\pi\)
\(\times\)
⑤
\(t\): soil depth (in)
\(\div\)
\(3\)
\(\times\)
⑥
\(R^2 + R R_{\mathrm{b}} + R_{\mathrm{b}}^2\) from the top radius \(R\) and the bottom radius \(R_{\mathrm{b}}\)
\(\div\)
\(1728\)
The formula in words
①
Take the
\(a\): inside length (in)
②
multiply it by the
\(b\): inside width (in)
③
and the
\(t\): soil depth (in)
and divide by 1728 to turn cubic inches into cubic feet
④
to get the
\(V_1\): soil per planter (ft³)
⑤
A pot is wide at the top and narrow at the bottom (a frustum), so take \(\pi\) times the
\(t\): soil depth (in)
divided by 3,
⑥
multiply by
\(R^2 + R R_{\mathrm{b}} + R_{\mathrm{b}}^2\) from the top radius \(R\) and the bottom radius \(R_{\mathrm{b}}\)
and divide by 1728 to turn cubic inches into cubic feet
⑦
to get the
\(V_1\): soil per pot (ft³)
Quick example
The soil per container for a 24-inch planter (inside 20 in × 7 in halfway down) filled 6 in deep, and for an 8-inch pot (top 8 in, bottom 5.2 in) filled 5.6 in deep, is
\(V_1\): soil per container
\(=\)
length (20 in)
\(\times\)
width (7 in)
\(\times\)
depth (6 in)
\(\div\)
\(1728\)
\(20 \times 7 \times 6 \div 1728 = 840 \div 1728 \approx 0.486\,\mathrm{ft^3}\)
\(R = 8 \div 2 = 4,\quad R_{\mathrm{b}} = 5.2 \div 2 = 2.6\)
\(4^{2} + 4 \times 2.6 + 2.6^{2} = 16 + 10.4 + 6.76 = 33.16\)
\(3.14 \times 5.6 \div 3 \times 33.16 \div 1728 \approx 0.112\,\mathrm{ft^3}\)
Key idea
A planter is box-shaped, so its soil is the volume of a rectangular prism, "length × width × depth". Measured in inches, the answer is in cubic inches, and 1 ft³ = 12 × 12 × 12 = 1,728 in³, so divide by 1728 to get cubic feet. A 24-inch planter may measure about 22 in × 8 in inside the rim, but it narrows toward the bottom, and the soil depth without headspace is only about 5–6 in. Using the width halfway down (about 20 in × 7 in) gives about 0.49 ft³, close to half of a 1 ft³ bag. Multiplying the rim size by the full height of the container gives 20% or more too much.
A pot is wide at the top and narrow at the bottom (a frustum), so its volume formula uses both the top radius \(R\) and the bottom radius \(R_{\mathrm{b}}\). Treating it as a cylinder with \(\pi R^2 t\) gives too much, by the amount the pot narrows. Strictly, the soil surface sits a little below the rim, where the radius is slightly smaller than half the top diameter, so this formula also comes out slightly high (a little extra is the safer side, since you will not need to buy more).
In the US, pots are named by the top diameter in inches. For a standard pot, the height is about the same as the top diameter; leaving about 1 in of headspace, the soil depth is about 70% of the top diameter and the bottom diameter about 65% of it, and this page fills in those values as a guide. With them, a 6-inch pot holds about 0.047 ft³, an 8-inch pot about 0.11 ft³ and a 12-inch pot about 0.38 ft³. Pot heights and shapes vary, so measure your pot or use the volume printed on it if there is one.
Amount needed with waste (volume)
Figure
Standard notation
(the usual math form)
\(V'\)
\(=\)
\(V\)
\(\times\)
\(\left(1 +\right.\)
\(\dfrac{r}{100}\)
\(\left.\right)\)
In words
(symbols replaced with words)
③
\(V'\): amount with waste
\(=\)
①
\(V\): net amount
\(\times\)
\(\left(1 +\right.\)
②
\(r\): waste factor (%) ÷ 100
\(\left.\right)\)
The formula in words
①
Take the
\(V\): net amount
②
multiply it by
"1 + waste factor \(r\) ÷ 100"
(1.1 for a 10% waste factor)
③
to get the
\(V'\): amount with waste
Quick example
Adding a 10% waste factor for settling after watering to a net amount of 21.33 ft³ gives
\(V'\): amount with waste
\(=\)
net amount (21.33 ft³)
\(\times\)
\(\left(1 +\right.\)
waste factor (10%) ÷ 100
\(\left.\right)\)
\(21.33 \times \left(1 + \dfrac{10}{100}\right) = 21.33 \times 1.1 \approx 23.47\,\mathrm{ft^3}\)
Key idea
Soil fresh from the bag is fluffy and full of air. It settles when watered and packs down when walked on, so its apparent volume shrinks. There are also spills when emptying bags and adjustments for compost or amendments you mix in, so buying exactly the net amount often leaves you short. The usual practice is to buy "net amount × (1 + waste factor)": commonly 10–20% for beds, gardens and fill, and 5–10% for planters and pots.
Light, fluffy potting mix and leaf mold settle the most, and heavy materials such as decomposed granite and sand, tamped as fill, pack down the most. Set the waste factor to 0 to calculate with the net amount as is. For planters and pots, the net amount \(V\) is "soil per container \(V_1\) × number of containers".
Converting the amount to weight (lb)
Standard notation
(the usual math form)
\(W\)
\(=\)
\(V'\)
\(\times\)
\(\rho\)
In words
(symbols replaced with words)
③
\(W\): weight (lb)
\(=\)
①
\(V'\): amount with waste (ft³)
\(\times\)
②
\(\rho\): bulk density (lb/ft³)
The formula in words
①
Take the
\(V'\): amount with waste (ft³)
②
multiply it by the
\(\rho\): bulk density (lb/ft³)
③
to get the
\(W\): weight (lb)
Quick example
The weight of 23.47 ft³ of potting mix (bulk density 31 lb/ft³) is
\(W\): weight
\(=\)
amount (23.47 ft³)
\(\times\)
bulk density (31 lb/ft³)
\(23.47 \times 31 \approx 727.5\,\mathrm{lb}\)
Key idea
Potting mix is mostly sold by volume, but topsoil, sand and similar materials are often sold by weight, such as 40 lb or 50 lb bags, and bulk deliveries are ordered in cubic yards (or tons), so you often need to go between volume and weight. The bridge is the bulk density (lb/ft³), "how many pounds one cubic foot weighs as bagged".
Typical values are about 31 for potting mix, 19 for leaf mold, 25 for kanuma, 44 for akadama, 69 for topsoil, and about 94 for decomposed granite, river sand, fill sand and sandy topdressing. But soil gets heavier when wet and changes with particle size. Decomposed granite and sand in particular range from about 80–95 lb/ft³ dry to 105–110 lb/ft³ after rain, so when you order bulk by truck, check the quantity by volume (cubic yards), not by weight. Bagged, dry topsoil can also be lighter, around 45–55 lb/ft³. If a bag says "1.5 cu ft (about 40 lb)", then 40 ÷ 1.5 ≈ 27 lb/ft³ is the bulk density of that product. The weight also tells you how much your car can carry or your deck or balcony can hold.
Number of bags (rounded up)
Figure
Standard notation
(the usual math form)
\(B\)
\(=\)
\(\lceil\)
\(V'\)
\(\div\)
\(k\)
\(\rceil\)
\(B\)
\(=\)
\(\lceil\)
\(W\)
\(\div\)
\(k\)
\(\rceil\)
In words
(symbols replaced with words)
④
\(B\): bags needed (bags sold by volume)
\(=\)
③
\(\lceil\)
①
\(V'\): amount with waste (ft³)
\(\div\)
②
\(k\): bag size (ft³)
\(\rceil\)
⑦
\(B\): bags needed (bags sold by weight)
\(=\)
\(\lceil\)
⑤
\(W\): weight (lb)
\(\div\)
⑥
\(k\): bag size (lb)
\(\rceil\)
The formula in words
①
Take the
\(V'\): amount with waste (ft³)
②
divide it by the
\(k\): bag size (ft³)
to see how many bags' worth it is
③
round up to the next whole number (the symbol \(\lceil\ \rceil\) means "round up")
④
and you get the
\(B\): bags needed
⑤
For bags sold by weight, take the
\(W\): weight (lb)
⑥
divide it by the
\(k\): bag size (lb)
and round up
⑦
to get the
\(B\): bags needed for bags sold by weight
Quick example
The number of 1.5 ft³ bags of potting mix needed for 23.47 ft³ is
\(B\): bags needed
\(=\)
\(\lceil\)
amount (23.47 ft³)
\(\div\)
bag size (1.5 ft³)
\(\rceil\)
\(23.47 \div 1.5 \approx 15.64\)
\(\lceil 15.64 \rceil = 16\)
Key idea
Bags come only whole, so if the division leaves a decimal, always round up (15.64 bags → 16). Rounding to the nearest or rounding down would leave you short. The symbol for rounding up is \(\lceil\ \rceil\) (the ceiling function). You buy 16 × 1.5 = 24 ft³, so 24 − 23.47 ≈ 0.53 ft³ is left over.
Bags labeled by weight, such as "40 lb" topsoil or sand, are divided by weight, not volume. Convert the amount with waste \(V'\) to the weight \(W\) with the bulk density, then divide by the pounds per bag and round up. When the same soil comes in several bag sizes, such as 1, 1.5 and 2 ft³, bigger bags tend to leave more over but are often cheaper per cubic foot, so compare the number of bags and the leftover before you decide. For large amounts (about 1 yd³ or more), bulk delivery by the cubic yard is often cheaper than bags.
Estimated cost
Standard notation
(the usual math form)
\(T\)
\(=\)
\(u\)
\(\times\)
\(Q\)
In words
(symbols replaced with words)
③
\(T\): estimated cost
\(=\)
①
\(u\): unit price
\(\times\)
②
\(Q\): quantity
The formula in words
①
Take the
\(u\): unit price (per bag, ft³, lb or yd³)
②
multiply it by the
\(Q\): quantity (bags, volume or weight, to match the price)
③
to get the
\(T\): estimated cost
Quick example
The material cost of 16 bags of potting mix at $12 a bag is
\(T\): estimated cost
\(=\)
unit price ($12 per bag)
\(\times\)
quantity (16 bags)
\(12 \times 16 = 192\)
Key idea
The key is to match the units of the price and the quantity. For a price per bag, multiply by the rounded-up number of bags \(B\). For a price per cubic foot, multiply by the amount with waste \(V'\) (ft³); per pound, by the weight with waste \(W\); per cubic yard, by the amount with waste divided by 27. With bags you pay for the rounded-up part (the leftover) too, so for large amounts, such as filling raised beds or bringing in fill, bulk delivery by the cubic yard can be cheaper. Fertilizer, compost, delivery fees and hauling are extra.
Working backward (area, depth or containers from the bags you have)
Standard notation
(the usual math form)
\(V_{\mathrm{use}}\)
\(=\)
\(n\)
\(\times\)
\(k\)
\(\div\)
\(\left(1 +\right.\)
\(\dfrac{r}{100}\)
\(\left.\right)\)
\(S\)
\(=\)
\(V_{\mathrm{use}}\)
\(\div\)
\((\)
\(t\)
\(\div 12\)
\()\)
\(t\)
\(=\)
\(V_{\mathrm{use}}\)
\(\div\)
\((\)
\(S\)
\(\div 12\)
\()\)
\(N\)
\(=\)
\(\lfloor\)
\(V_{\mathrm{use}}\)
\(\div\)
\(V_1\)
\(\rfloor\)
In words
(symbols replaced with words)
④
\(V_{\mathrm{use}}\): usable amount (ft³)
\(=\)
①
\(n\): bags you have
\(\times\)
②
\(k\): bag size (ft³)
\(\div\)
\(\left(1 +\right.\)
③
\(r\): waste factor ÷ 100
\(\left.\right)\)
⑥
\(S\): area it will cover (ft²)
\(=\)
\(V_{\mathrm{use}}\): usable amount
\(\div\)
\((\)
⑤
\(t\): depth (in)
\(\div 12\)
\()\)
⑧
\(t\): depth it will fill (in)
\(=\)
\(V_{\mathrm{use}}\): usable amount
\(\div\)
\((\)
⑦
\(S\): area (ft²)
\(\div 12\)
\()\)
⑩
\(N\): containers it will fill
\(=\)
\(\lfloor\)
\(V_{\mathrm{use}}\): usable amount
\(\div\)
⑨
\(V_1\): soil per container (ft³)
\(\rfloor\)
The formula in words
①
Take the
\(n\): bags you have
②
multiply it by the
\(k\): bag size (ft³)
to get the amount you have (for bags sold by weight, also divide by the bulk density \(\rho\) to get ft³),
③
divide it by
1 + waste factor \(r\) ÷ 100
to take out the waste
④
to get the
\(V_{\mathrm{use}}\): usable amount
⑤
Divide the usable amount by the
\(t\): depth ÷ 12
⑥
to get the
\(S\): area it will cover
⑦
Divide the usable amount by the
\(S\): area ÷ 12
⑧
to get the
\(t\): depth it will fill
⑨
Divide the usable amount by the
\(V_1\): soil per container
and round down (the symbol \(\lfloor\ \rfloor\) means "round down")
⑩
to get the
\(N\): containers it will fill
Quick example
The area three 1.5 ft³ bags of potting mix will cover 8 in deep with a 10% waste factor, and the number of 6-inch pots (0.0475 ft³ each) one 1 ft³ bag will fill with no waste, are
\(3 \times 1.5 = 4.5\,\mathrm{ft^3}\)
\(4.5 \div 1.1 \approx 4.09\,\mathrm{ft^3}\)
\(4.09 \div (8 \div 12) \approx 6.14\,\mathrm{ft^2}\)
\(1 \div 0.0475 \approx 21.06 \quad \lfloor 21.06 \rfloor = 21\)
Key idea
Working backward just follows the formulas the other way. Multiply the bags by the bag size to get the amount you have (for bags sold by weight, divide by the bulk density to get ft³), and take out the waste to get the usable amount. Then, from "amount = area × depth ÷ 12", setting the depth gives the area, and setting the area gives the depth. For planters and pots, divide the usable amount by the soil per container and round down to get how many you can fill (the part left over is not enough for one more container, so round down; rounding up would leave you short of soil).
Use it to check "how many more planters can I fill with the leftover mix?" or "how deep will these bags fill my bed?"
To find the soil, sand or potting mix you need, get the cubic feet from "area (ft²) × depth (in) ÷ 12" (for planters and pots, soil per container × number of containers), add the waste factor, then divide by the bag size and round up. Use the volume as is for bags sold by cubic feet, or convert to pounds with the bulk density (lb/ft³) for bags sold by weight. Divide by 27 for cubic yards for bulk delivery. A pot is a frustum, wider at the top than at the bottom, and its volume comes from the top and bottom radii.
Symbols and terms
Symbols
| \(S\) | S | The area of the bed or garden (ft²), set by length × width, a total area or a diameter (for a circle). A common letter for area, said to come from "square" or "surface". |
| \(l\), \(w\) | l, w | The length and width of a rectangle (ft), from "length" and "width". |
| \(d\) | d | The diameter of a round bed (ft), from "diameter". The radius is \(d \div 2\). |
| \(\pi\) | pi | Pi, about 3.14. It appears in the area of a circle ("radius × radius × pi") and in the volume of a frustum. |
| \(t\) | t | The soil depth (in), from "thickness". For beds, "area × depth ÷ 12" gives cubic feet; for planters and pots, "in³ ÷ 1728" gives cubic feet. |
| \(V\) | V | The net amount (ft³), from "volume". For beds, \(V = S \times t \div 12\); for planters and pots, \(V = V_1 \times\) number of containers. 27 ft³ = 1 yd³. |
| \(a\), \(b\) | a, b | The inside length and width of a planter (in), measured inside where the soil goes. |
| \(R\) | R | Half the top diameter of a pot (the inside diameter at the rim), which is the top radius (in), from "radius". |
| \(R_{\mathrm{b}}\) | R sub b | Half the bottom diameter of a pot, which is the bottom radius (in). The b stands for "bottom". For a standard pot, about 65% of \(R\). |
| \(V_1\) | V sub 1 | The soil per planter or pot (ft³). The 1 means "for one container". For a planter, \(a \times b \times t \div 1728\); for a pot, the frustum volume formula. |
| \(r\) | r | The waste factor (%), from "rate". The share added to the net amount for settling, compaction and spills; 10 means 10% more (1.1 times). A different quantity from the pot radius \(R\) (capital). |
| \(V'\) | V prime | The amount with waste (ft³). Found with \(V' = V \times (1 + r \div 100)\). The mark "\(\prime\)" means "a slightly changed version of \(V\)", read "prime". |
| \(\rho\) | rho | The bulk density (lb/ft³), a Greek letter often used for density. If a 1.5 ft³ bag weighs about 40 lb, it is \(40 \div 1.5 \approx 27\). |
| \(W\) | W | The weight of the amount needed with waste (lb), from "weight". Found with \(W = V' \times \rho\). |
| \(k\) | k | The bag size: in ft³ for bags sold by volume (such as 1.5 ft³ bags) or in lb for bags sold by weight (such as 40 lb bags). |
| \(B\) | B | The number of bags needed, from "bag". Found with \(B = \lceil V' \div k \rceil\) (by volume) or \(\lceil W \div k \rceil\) (by weight). |
| \(n\) | n | The number of bags you have, when working backward, from "number". |
| \(V_{\mathrm{use}}\) | V sub use | The part of the soil you have that you can actually use after taking out the waste (ft³). |
| \(N\) | N | The number of planters or pots you can fill, when working backward. Found with \(N = \lfloor V_{\mathrm{use}} \div V_1 \rfloor\). |
| \(u\) | u | The unit price (per bag, ft³, lb or yd³), from "unit price". |
| \(Q\) | Q | The quantity that matches the price unit (bags, volume or weight), from "quantity". |
| \(T\) | T | The estimated cost (materials only, without fertilizer, delivery and so on), from "total". |
| \(\lceil x \rceil\) | ceiling of x | The ceiling function: rounds up to the next whole number. (Examples: \(\lceil 15.64 \rceil = 16\), \(\lceil 16 \rceil = 16\)) |
| \(\lfloor x \rfloor\) | floor of x | The floor function: rounds down to a whole number. (Example: \(\lfloor 21.06 \rfloor = 21\)) Used for "containers it will fill" when working backward. |
Terms
| bulk density | The weight per unit of volume of loose material such as soil, including the gaps and air between the particles (lb/ft³ or kg/L). It is much lower than the density of the mineral particles themselves (about 2.5–2.7 times water). Typical values are about 31 lb/ft³ for potting mix, 44 for akadama and 94 for decomposed granite or sand (about 80–95 dry and 105–110 wet). |
| specific gravity | How many times heavier a material is than the same volume of water. Water is 1, and 1 ft³ of water weighs about 62.4 lb, so a specific gravity of 1 is about 62.4 lb/ft³. |
| cubic yard | The volume of a cube 1 yd (3 ft) on each side, 27 ft³. The unit for ordering topsoil, fill or mulch in bulk by truck. |
| waste factor | The share added to the net amount for settling after watering, compaction and spills (%). 10–20% is common for beds and fill, and 5–10% for planters and pots. |
| potting mix | A ready-to-use mix for containers, usually made of peat or coir, bark, perlite and fertilizer. It is light (about 31 lb/ft³) and sold by volume, such as 1, 1.5 and 2 ft³ bags. |
| topsoil | The dark upper layer of soil, the basic soil for yards and gardens. It holds water well and is used to replace bed soil and as fill. |
| akadama | A granular clay soil from Japan, dried into hard grains. It has no fertilizer and is a basic soil for bonsai, usually mixed with other materials. |
| kanuma | A light, yellowish, granular soil from the Kanuma area of Japan. It drains well and is acidic, and is used for azaleas, rhododendrons, blueberries and bonsai. |
| leaf mold | Decomposed fallen leaves used as a soil amendment. Very light (about 19 lb/ft³), mixed into soil to loosen it. |
| decomposed granite | Granite weathered into sandy, gritty soil (often called DG). It drains well and is used for paths, as a base under yards, for fill, backfill and topdressing. Sold in bags by weight or in bulk by the cubic yard. |
| topdressing | A thin layer (about 1/4 in) of sand or soil spread over a lawn to protect the roots and level bumps. It is thin but covers a large area, so the amount adds up. |
| fill dirt | Soil added on top of the ground to raise it, for example to build up a bed or improve drainage in a yard. Decomposed granite or fill sand is often used, with a larger waste factor for compaction. |
| pot size | How pots are named. In the US, by the top diameter in inches (a 6-inch pot is about 6 in across); in metric countries, by the top diameter in cm. |
| frustum | A cone with its tip cut off parallel to the base. A pot wider at the top than at the bottom has this shape. Its volume is "pi × height ÷ 3 × (top radius² + top radius × bottom radius + bottom radius²)", found by taking a small cone away from a large one. |
| headspace | The gap of about 1 in left between the rim of a pot and the soil surface, where water collects before it soaks in. The soil depth is shallower than the pot by this amount. |
| drainage layer | Coarse material such as pumice or gravel placed at the bottom of a pot. It takes up room, so there is less soil. Many growers now skip it and use a pot with drainage holes instead. |
| rounding up | Changing a value with a decimal part to the next whole number. Bags come only whole, so always round up the number of bags. |
| rounding down | Dropping the decimal part to get a whole number. For "how many pots can I fill with the soil I have", the part that is not enough for one more pot is dropped, so round down. |
| pi | The number of times the circumference of a circle goes around its diameter, about 3.14. The area of a circle is "radius × radius × pi". |
Good to know before you start
Here is what helps you use the calculation on this page with real understanding, not just by pressing the button.
| Area of rectangles and circles (Grades 3–7) |
|
| Volume of a rectangular prism (Grade 5) |
|
| Converting units of length and volume (Grades 4–6) |
|
| Volume of cones and frustums (Grade 8 and up) |
|
| Weight and density (Grades 5–8) |
|
| Percentages and ratios (Grades 6–7) |
|
| Rounding (Grades 3–4) |
|
How to calculate it in Excel
Copy the whole table below and paste it into cell A1 in Excel. It works as is.
Table to find the area of a bed (rectangle)
| Length (ft) | 8 |
| Width (ft) | 4 |
| Area (ft²) | =B1*B2 |
Table to find the area of a bed (circle)
| Diameter (ft) | 4 |
| Area (ft²) | =PI()*(B1/2)^2 |
Table to find the soil for a bed
| Area (ft²) | 32 |
| Depth (in) | 8 |
| Net amount (ft³) | =B1*B2/12 |
Table to find the soil per planter
| Inside length (in) | 20 |
| Inside width (in) | 7 |
| Soil depth (in) | 6 |
| Soil per planter (ft³) | =B1*B2*B3/1728 |
Table to find the soil per pot
| Top diameter (in) | 8 |
| Bottom diameter (in) | 5.2 |
| Soil depth (in) | 5.6 |
| Soil per pot (ft³) | =PI()*B3/3*((B1/2)^2+(B1/2)*(B2/2)+(B2/2)^2)/1728 |
Table to find the amount needed with waste (volume)
| Net amount (ft³) | 21.33 |
| Waste factor (%) | 10 |
| Amount with waste (ft³) | =B1*(1+B2/100) |
Table to find the weight (lb)
| Amount with waste (ft³) | 23.47 |
| Bulk density (lb/ft³) | 31 |
| Weight (lb) | =B1*B2 |
Table to find the number of bags
| Amount with waste (ft³) or weight (lb) | 23.47 |
| Bag size (ft³ or lb) | 1.5 |
| Bags needed | =ROUNDUP(B1/B2,0) |
Table to find the estimated cost
| Unit price ($) | 12 |
| Quantity (bags, ft³, lb or yd³) | 16 |
| Estimated cost ($) | =B1*B2 |
Table to work backward (area, depth or containers from the bags you have)
| Bags you have | 3 |
| Bag size (ft³) | 1.5 |
| Waste factor (%) | 10 |
| Depth (in) | 8 |
| Usable amount (ft³) | =B1*B2/(1+B3/100) |
| Area it will cover (ft²) | =B5/(B4/12) |
| Area (ft², to find the depth) | 32 |
| Depth it will fill (in) | =B5/B7*12 |
| Soil per container (ft³, to find the number) | 0.0475 |
| Containers it will fill | =ROUNDDOWN(B5/B9,0) |
After pasting, the upper rows in column B are your inputs and the last rows are calculated automatically.
"ROUNDUP(value, 0)" rounds up to a whole number (the ⌈ ⌉ in the formulas), and "ROUNDDOWN(value, 0)" rounds down (the ⌊ ⌋). "PI()" is pi.
The third table turns "ft² × in" into cubic feet with "/12" (B3 shows about 21.33). B4 in the fourth table shows about 0.486, B4 in the fifth about 0.113, B3 in the sixth about 23.46, B3 in the seventh about 727.6 and B3 in the eighth 16 bags.
For bags sold by weight, enter the weight (lb) from the seventh table in B1 of the eighth table, and the pounds per bag in B2.
In the last table, B6 is the area it will cover (about 6.14 ft²), B8 is "how deep it will fill the area in B7" (about 1.53 in), and B10 is "how many containers of the size in B9 it will fill" (86).
"ROUNDUP(value, 0)" rounds up to a whole number (the ⌈ ⌉ in the formulas), and "ROUNDDOWN(value, 0)" rounds down (the ⌊ ⌋). "PI()" is pi.
The third table turns "ft² × in" into cubic feet with "/12" (B3 shows about 21.33). B4 in the fourth table shows about 0.486, B4 in the fifth about 0.113, B3 in the sixth about 23.46, B3 in the seventh about 727.6 and B3 in the eighth 16 bags.
For bags sold by weight, enter the weight (lb) from the seventh table in B1 of the eighth table, and the pounds per bag in B2.
In the last table, B6 is the area it will cover (about 6.14 ft²), B8 is "how deep it will fill the area in B7" (about 1.53 in), and B10 is "how many containers of the size in B9 it will fill" (86).
How to calculate it in Google Sheets
Copy the whole table below and paste it into cell A1 in Google Sheets. It works as is.
Table to find the area of a bed (rectangle)
| Length (ft) | 8 |
| Width (ft) | 4 |
| Area (ft²) | =B1*B2 |
Table to find the area of a bed (circle)
| Diameter (ft) | 4 |
| Area (ft²) | =PI()*(B1/2)^2 |
Table to find the soil for a bed
| Area (ft²) | 32 |
| Depth (in) | 8 |
| Net amount (ft³) | =B1*B2/12 |
Table to find the soil per planter
| Inside length (in) | 20 |
| Inside width (in) | 7 |
| Soil depth (in) | 6 |
| Soil per planter (ft³) | =B1*B2*B3/1728 |
Table to find the soil per pot
| Top diameter (in) | 8 |
| Bottom diameter (in) | 5.2 |
| Soil depth (in) | 5.6 |
| Soil per pot (ft³) | =PI()*B3/3*((B1/2)^2+(B1/2)*(B2/2)+(B2/2)^2)/1728 |
Table to find the amount needed with waste (volume)
| Net amount (ft³) | 21.33 |
| Waste factor (%) | 10 |
| Amount with waste (ft³) | =B1*(1+B2/100) |
Table to find the weight (lb)
| Amount with waste (ft³) | 23.47 |
| Bulk density (lb/ft³) | 31 |
| Weight (lb) | =B1*B2 |
Table to find the number of bags
| Amount with waste (ft³) or weight (lb) | 23.47 |
| Bag size (ft³ or lb) | 1.5 |
| Bags needed | =ROUNDUP(B1/B2,0) |
Table to find the estimated cost
| Unit price ($) | 12 |
| Quantity (bags, ft³, lb or yd³) | 16 |
| Estimated cost ($) | =B1*B2 |
Table to work backward (area, depth or containers from the bags you have)
| Bags you have | 3 |
| Bag size (ft³) | 1.5 |
| Waste factor (%) | 10 |
| Depth (in) | 8 |
| Usable amount (ft³) | =B1*B2/(1+B3/100) |
| Area it will cover (ft²) | =B5/(B4/12) |
| Area (ft², to find the depth) | 32 |
| Depth it will fill (in) | =B5/B7*12 |
| Soil per container (ft³, to find the number) | 0.0475 |
| Containers it will fill | =ROUNDDOWN(B5/B9,0) |
The same formulas as in Excel (including ROUNDUP, ROUNDDOWN and PI) work as is. Copy the whole table, paste it into cell A1, and replace the numbers in column B with your own.
How to calculate it in Python
import math
length_ft = 8 # bed length (ft)
width_ft = 4 # bed width (ft)
depth_in = 8 # soil depth (in)
density_lb_per_ft3 = 31 # bulk density (lb/ft³). About 31 for potting mix, 19 leaf mold, 44 akadama, 69 topsoil, 94 decomposed granite
waste_percent = 10 # waste factor (%) for settling and compaction; 0 for none
bag_ft3 = 1.5 # bag size (ft³)
price_per_bag = 12 # price per bag ($)
area_ft2 = length_ft * width_ft # area (ft²)
volume_ft3 = area_ft2 * depth_in / 12 # net amount (ft³); ft² × in ÷ 12 = ft³
required_ft3 = volume_ft3 * (1 + waste_percent / 100) # amount with waste (ft³)
weight_lb = required_ft3 * density_lb_per_ft3 # weight (lb)
bags_needed = math.ceil(required_ft3 / bag_ft3) # bags needed (rounded up)
cost = bags_needed * price_per_bag # estimated cost ($)
print(f"Area: {area_ft2} ft²")
print(f"Net amount: {volume_ft3:.2f} ft³ ({volume_ft3 / 27:.2f} yd³)")
print(f"Amount with waste: {required_ft3:.2f} ft³")
print(f"Weight: {weight_lb:.1f} lb")
print(f"Bags needed: {bags_needed}")
print(f"Estimated cost: ${cost:,.2f}")
# soil per pot (frustum): 8-inch pot = top 8 in, bottom 5.2 in, soil depth 5.6 in
top_in, bottom_in, pot_depth_in = 8, 5.2, 5.6
big_r, small_r = top_in / 2, bottom_in / 2
pot_ft3 = math.pi * pot_depth_in / 3 * (big_r ** 2 + big_r * small_r + small_r ** 2) / 1728
print(f"Soil per 8-inch pot: {pot_ft3:.3f} ft³")
# working backward: area three 1.5 ft³ bags cover 8 in deep with 10% waste
have_bags = 3
usable_ft3 = have_bags * bag_ft3 / (1 + 10 / 100)
coverable_area_ft2 = usable_ft3 / (8 / 12)
print(f"Area {have_bags} bags cover 8 in deep: {coverable_area_ft2:.2f} ft²")
print(f"8-inch pots one 1 ft³ bag will fill: {math.floor(1 / pot_ft3)}")
Runs with the standard library only. math.ceil() rounds up (the ⌈ ⌉ in the formulas) and math.floor() rounds down (the ⌊ ⌋). Replace the sizes, bulk density and bag size at the top with your own numbers and run it. For bags sold by weight, divide weight_lb by the pounds per bag instead of required_ft3.
How to write it in LaTeX and other math languages (copy and paste)
Area of a bed or garden (rectangle or circle)
S = l × w, S = π × (d ÷ 2)²
S = l \times w,\quad S = \pi \left(\frac{d}{2}\right)^{2}
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<mi>S</mi><mo>=</mo><mi>l</mi><mo>×</mo><mi>w</mi>
<mo>,</mo>
<mi>S</mi><mo>=</mo><mi>π</mi>
<msup>
<mrow><mo>(</mo><mfrac><mi>d</mi><mn>2</mn></mfrac><mo>)</mo></mrow>
<mn>2</mn>
</msup>
</mrow>
</math>
S = l * w, S = pi * (d/2)^2
{l*w, Pi*(d/2)^2}
S := l*w; S := Pi*(d/2)^2;
S = l*w; S = pi*(d/2)^2;
S = l × w, S = π (d/2)^2
Soil for a bed or garden (net amount)
V = S × t ÷ 12
V = \frac{S \times t}{12}
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<mi>V</mi><mo>=</mo>
<mfrac><mrow><mi>S</mi><mo>×</mo><mi>t</mi></mrow><mn>12</mn></mfrac>
</mrow>
</math>
V = S * t / 12
s*t/12
V := S*t/12;
V = S*t/12;
V = S × t/12
Soil per planter or pot
V₁ = a × b × t ÷ 1728, V₁ = π × t ÷ 3 × (R² + R·Rb + Rb²) ÷ 1728
V_1 = \frac{a \times b \times t}{1728},\quad V_1 = \frac{\pi t \left(R^2 + R R_{\mathrm{b}} + R_{\mathrm{b}}^2\right)}{3 \times 1728}
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<msub><mi>V</mi><mn>1</mn></msub><mo>=</mo>
<mfrac><mrow><mi>a</mi><mo>×</mo><mi>b</mi><mo>×</mo><mi>t</mi></mrow><mn>1728</mn></mfrac>
<mo>,</mo>
<msub><mi>V</mi><mn>1</mn></msub><mo>=</mo>
<mfrac>
<mrow><mi>π</mi><mi>t</mi><mrow><mo>(</mo><msup><mi>R</mi><mn>2</mn></msup><mo>+</mo><mi>R</mi><msub><mi>R</mi><mi>b</mi></msub><mo>+</mo><msubsup><mi>R</mi><mi>b</mi><mn>2</mn></msubsup><mo>)</mo></mrow></mrow>
<mrow><mn>3</mn><mo>×</mo><mn>1728</mn></mrow>
</mfrac>
</mrow>
</math>
V_1 = (a * b * t) / 1728, V_1 = (pi * t * (R^2 + R*R_b + R_b^2)) / (3 * 1728)
{a*b*t/1728, Pi*t*(R^2 + R*Rb + Rb^2)/5184}
V1 := a*b*t/1728; V1 := Pi*t*(R^2 + R*Rb + Rb^2)/5184;
V1 = a*b*t/1728; V1 = pi*t*(R^2 + R*Rb + Rb^2)/5184;
V_1 = (a × b × t)/1728, V_1 = (π t (R^2 + R R_b + R_b^2))/(3 × 1728)
Amount needed with waste (volume)
V' = V × (1 + r ÷ 100)
V' = V \left(1 + \frac{r}{100}\right)
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<msup><mi>V</mi><mo>′</mo></msup><mo>=</mo><mi>V</mi>
<mrow><mo>(</mo><mn>1</mn><mo>+</mo><mfrac><mi>r</mi><mn>100</mn></mfrac><mo>)</mo></mrow>
</mrow>
</math>
V' = V * (1 + r/100)
v*(1 + r/100)
Vp := V*(1 + r/100);
Vp = V*(1 + r/100);
V' = V (1 + r/100)
Converting the amount to weight (lb)
W = V' × ρ
W = V' \times \rho
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<mi>W</mi><mo>=</mo>
<msup><mi>V</mi><mo>′</mo></msup>
<mo>×</mo><mi>ρ</mi>
</mrow>
</math>
W = V' * rho
vp*rho
W := Vp*rho;
W = Vp*rho;
W = V' × ρ
Number of bags (rounded up)
B = ⌈V' ÷ k⌉ (by volume), B = ⌈W ÷ k⌉ (by weight)
B = \left\lceil \frac{V'}{k} \right\rceil,\quad B = \left\lceil \frac{W}{k} \right\rceil
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<mi>B</mi><mo>=</mo>
<mo>⌈</mo><mfrac><msup><mi>V</mi><mo>′</mo></msup><mi>k</mi></mfrac><mo>⌉</mo>
<mo>,</mo>
<mi>B</mi><mo>=</mo>
<mo>⌈</mo><mfrac><mi>W</mi><mi>k</mi></mfrac><mo>⌉</mo>
</mrow>
</math>
B = |~ V' / k ~|, B = |~ W / k ~|
{Ceiling[vp/k], Ceiling[w/k]}
B := ceil(Vp/k); B := ceil(W/k);
B = ceil(Vp/k); B = ceil(W/k);
B = ⌈V'/k⌉, B = ⌈W/k⌉
Estimated cost
T = u × Q
T = u \times Q
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<mi>T</mi><mo>=</mo><mi>u</mi><mo>×</mo><mi>Q</mi>
</mrow>
</math>
T = u * Q
u*q
T := u*Q;
T = u*Q;
T = u × Q
Working backward (area, depth or containers from the bags you have)
V_use = n × k ÷ (1 + r ÷ 100), S = V_use ÷ (t ÷ 12), t = V_use ÷ (S ÷ 12), N = ⌊V_use ÷ V₁⌋
V_{\mathrm{use}} = \frac{n \times k}{1 + \frac{r}{100}},\quad S = \frac{12\,V_{\mathrm{use}}}{t},\quad t = \frac{12\,V_{\mathrm{use}}}{S},\quad N = \left\lfloor \frac{V_{\mathrm{use}}}{V_1} \right\rfloor
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<msub><mi>V</mi><mi>use</mi></msub><mo>=</mo>
<mfrac>
<mrow><mi>n</mi><mo>×</mo><mi>k</mi></mrow>
<mrow><mn>1</mn><mo>+</mo><mfrac><mi>r</mi><mn>100</mn></mfrac></mrow>
</mfrac>
<mo>,</mo>
<mi>S</mi><mo>=</mo><mfrac><mrow><mn>12</mn><msub><mi>V</mi><mi>use</mi></msub></mrow><mi>t</mi></mfrac>
<mo>,</mo>
<mi>t</mi><mo>=</mo><mfrac><mrow><mn>12</mn><msub><mi>V</mi><mi>use</mi></msub></mrow><mi>S</mi></mfrac>
<mo>,</mo>
<mi>N</mi><mo>=</mo><mo>⌊</mo><mfrac><msub><mi>V</mi><mi>use</mi></msub><msub><mi>V</mi><mn>1</mn></msub></mfrac><mo>⌋</mo>
</mrow>
</math>
V_use = (n * k) / (1 + r/100), S = 12 V_use / t, t = 12 V_use / S, N = |__ V_use / V_1 __|
vuse = n*k/(1 + r/100); {12*vuse/t, 12*vuse/s, Floor[vuse/v1]}
Vuse := n*k/(1 + r/100); S_cover := 12*Vuse/t; t_fill := 12*Vuse/S; N_fill := floor(Vuse/V1);
Vuse = n*k/(1 + r/100); S_cover = 12*Vuse/t; t_fill = 12*Vuse/S; N_fill = floor(Vuse/V1);
V_use = (n × k)/(1 + r/100), S = 12 V_use/t, t = 12 V_use/S, N = ⌊V_use/V_1⌋
How to have ChatGPT do the calculation
You are a quantity calculation assistant for gardening and landscaping. Do the following calculation by actually running Python code, and base your answer only on the numbers from the execution result (do not answer by mental math or guessing). I am filling an 8 ft × 4 ft raised bed 8 in deep with potting mix (bulk density 31 lb/ft³). I allow a 10% waste factor for settling after watering. Find each of the following: 1. The area (ft²) 2. The net amount (ft³ and yd³) and the amount with the 10% waste factor (ft³) 3. The weight of the amount with waste, using the bulk density (lb) 4. The number of 1.5 ft³ bags to buy (rounded up), the amount bought (bags × 1.5 ft³) and the amount left over 5. If I only have three 1.5 ft³ bags of the same mix, the area they will cover 8 in deep with a 10% waste factor (ft²) 6. The soil per pot for an 8-inch pot, treated as a frustum with a top diameter of 8 in, a bottom diameter of 5.2 in and a soil depth of 5.6 in (ft³) Show the formulas you used and the numbers from the execution result.
How to Use
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1Enter your numbersType the numbers you want to calculate with into the input fields
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2CalculatePress the "Calculate" button
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3Check the resultThe result appears on the spot. The same page also explains the idea behind the calculation and the formula
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