Enter the area to paint and the coverage or spread rate shown on the can or data sheet. Thinning, waste and price are optional.
L
Enter the coverage or spread rate for one coat. The units of the can size and the price (L or kg) switch automatically to match the coverage unit.
Result and figure
Enter the area to paint and the paint's coverage (such as square feet per gallon) 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?
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How to Use
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Formulas and figures
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Symbols and terms
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Good to know before you start
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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)
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How to have ChatGPT do the calculation
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DataChef Features
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Related Features
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NumberChef Calculators List
What you can do on this page
- Enter the area to paint and either the coverage (ft² per gallon) or the spread rate (gallons or pounds per 100 ft²), and you get the amount of paint you need on the spot
- The result includes the number of coats (two coats, three coats and so on) and a waste percentage (paint left in rollers and trays, or spattered), and rounds up to whole cans
- Enter a thinning ratio (water or thinner added as a percentage of the paint) to also get how much to add and how much thinned paint you get
- You can switch to working backward: "how much area can I cover with the cans I have?" Handy for checking what leftover paint can do
- Enter the price per can (or per gallon or pound) for an estimated cost. A plain-language explanation of the formulas and copy-and-paste formulas for Excel, Google Sheets and Python are all on this page
Coverage, number of coats and thinning differ from paint to paint. Enter the values printed on your can or on the maker's product data sheet. To find the area of a wall, work out width × height on the rectangle area page and subtract windows and doors. For the outside of a whole house, use the exterior wall area page. By default this page works in ft² and gallons; switch "Units" above the calculator to Metric to use m² and liters.
What is this calculation used for?
DIY painting the walls of a room
For example, the four walls of a 12 × 10 ft room with an 8 ft ceiling (44 ft × 8 ft = 352 ft²), minus the window and door, are about 320 ft². With a paint that covers 350 sq ft per gallon, two coats take \(320 \times 2 \div 350 \approx 1.83\) gal, or about 2.01 gal with 10% waste. That is three 1-gallon cans, or 2 gallons plus 1 quart (2.25 gal).
How you combine can sizes changes the leftover a lot, so looking at the "cans before rounding up" value helps you buy with less waste.
Checking the paint quantity in an exterior painting quote
An exterior painting quote lists items such as "siding, 1,200 sq ft, two coats of [product]". If the product data sheet gives a spread rate of 300 sq ft per gallon on siding, the net amount is \(1200 \times 2 \div 300 = 8\) gal, or 8.8 gal with 10% waste: two 5-gallon buckets.
This lets you follow where the paint quantity and material cost in the quote come from. (A real quote also includes primer, scaffolding, masking and labor, so the paint amount alone cannot tell you whether the price is fair. Always check the spread rate and number of coats on the maker's data sheet.)
Recoating a roof or a porch floor
A roof soaks up coating and the slope causes more spatter, so it is common to allow more waste (10-15%). Coating 800 ft² of roof with an elastomeric roof coating at 1.5 gal per 100 ft² per coat, two coats, takes \(800 \times 2 \times 1.5 \div 100 = 24\) gal net, or 27.6 gal with 15% waste: six 5-gallon buckets.
Roof work is done at height, so for DIY put safety (ladders, fall protection and weather) first.
Staining a wood deck or fence
Penetrating wood stains usually give a range on the can, such as "150-300 sq ft per gallon (one coat)", and older, thirsty wood covers less area. Staining 150 ft² of deck floor and sides, two coats, at 150 sq ft per gallon (the low end, to be safe) takes 2 gal net, or 2.2 gal with 10% waste.
When the coverage is given as a range, entering the smaller value gives a safe estimate.
Checking how far the paint you have will go
If you have two 1-gallon cans left over from the last job, working backward tells you how much you can paint this time. With a paint that covers 350 sq ft per gallon, two coats and 10% waste, \(2 \div 1.1 \div (2 \div 350) \approx 318\) ft².
Paint that has been open for a long time may have thickened or lost quality, so check the can and the storage guidance on the can or from the maker before using it.
Formulas and figures
Turning coverage per gallon into a spread rate
Standard notation
(the usual math form)
\(q\)
\(=\)
\(1\)
\(\div\)
\(c\)
In words
(symbols replaced with words)
②
\(q\): spread rate (amount per ft², one coat)
\(=\)
\(1\)
\(\div\)
①
\(c\): coverage per gallon
The formula in words
①
Divide 1 by the
\(c\): coverage per gallon
to flip it into "how many gallons one square foot needs"
②
and you get the
\(q\): spread rate (amount per ft², one coat)
Quick example
For a latex paint whose can says "covers 350 sq ft per gallon (one coat)", the spread rate is
spread rate \(q\)
\(=\)
\(1\)
\(\div\)
coverage (350 ft²/gal)
\(1 \div 350 \approx 0.00286\ \mathrm{gal/ft^2}\ \ (0.286\ \mathrm{gal}\ \text{per}\ 100\ \mathrm{ft^2})\)
Key idea
Paint amounts are written in two ways. Cans usually show coverage, such as "covers 350-400 sq ft per gallon", while product data sheets often show a spread rate, the amount needed for a given area, such as "1.5 gal per 100 sq ft" for roof coatings.
This calculator accepts either and works internally with the spread rate \(q\), the amount per unit area per coat. When coverage is given, its reciprocal (1 divided by it) is the spread rate. Because the amount per single square foot is tiny, US data sheets and this calculator's US steps show it per 100 ft² (\(100 \div 350 \approx 0.286\) gal per 100 ft²). When the spread rate is given directly, that value is \(q\) and you do not need this formula.
Net amount of paint (no waste)
Figure
Standard notation
(the usual math form)
\(Q_0\)
\(=\)
\(S\)
\(\times\)
\(n\)
\(\times\)
\(q\)
In words
(symbols replaced with words)
④
\(Q_0\): net amount of paint
\(=\)
①
\(S\): area to paint
\(\times\)
②
\(n\): number of coats
\(\times\)
③
\(q\): spread rate (amount per ft², one coat)
The formula in words
①
Take the
\(S\): area to paint
②
multiply it by the
\(n\): number of coats
to get the total area painted
③
multiply by the
\(q\): spread rate (amount per ft², one coat)
④
and you get the
\(Q_0\): net amount of paint
Quick example
To give 400 ft² of walls two coats of the paint above (1/350 gal per ft²), the net amount is
net amount \(Q_0\)
\(=\)
area (400 ft²)
\(\times\)
coats (2)
\(\times\)
spread rate (1/350 gal/ft²)
\(400 \times 2 \times \tfrac{1}{350} = 800 \div 350 \approx 2.286\ \mathrm{gal}\)
Key idea
Two coats means painting the same surface twice, which is the same as painting twice the area. So multiply the area by the number of coats, then by the spread rate. For walls, the area is "perimeter × height" minus windows and doors; for the outside of a house, use the paintable area in the contractor's quote.
If the coverage (or spread rate) is given for thinned paint, this formula gives the amount of thinned paint. To get back to unthinned paint, divide by \(1 + d \div 100\) from the thinning formula below (the calculator does this automatically when you choose the basis).
Amount needed with waste
Figure
Standard notation
(the usual math form)
\(Q\)
\(=\)
\(Q_0\)
\(\times\)
\((\)
\(1\)
\(+\)
\(r\)
\(\div\)
\(100\)
\()\)
In words
(symbols replaced with words)
③
\(Q\): amount needed with waste
\(=\)
①
\(Q_0\): net amount of paint
\(\times\)
\((\)
\(1\)
\(+\)
②
\(r\): waste (%)
\(\div\)
\(100\)
\()\)
The formula in words
①
Take the
\(Q_0\): net amount of paint
②
multiply it by "1 +
\(r\): waste (%)
÷ 100" (the waste factor)
③
and you get the
\(Q\): amount needed with waste
Quick example
When the net amount is 2.286 gal and you allow 10% for waste, the amount needed is
amount needed \(Q\)
\(=\)
net amount (2.286 gal)
\(\times\)
\((\)
\(1\)
\(+\)
waste (10%)
\(\div\)
\(100\)
\()\)
\(2.286 \times (1 + 10 \div 100) = 2.286 \times 1.1 \approx 2.514\ \mathrm{gal}\)
Key idea
The exact calculated amount is never quite enough. Some paint dries in the roller or brush, some stays in the tray or can, some spatters, and a rough surface soaks up extra. This is called waste. How much depends on the tools, the surface and your experience, so you allow a set percentage on top of the net amount. 5-15% is common; allow more for rough surfaces (stucco, bare wood) or lots of brush work.
"10% more" is calculated as "× 1.1": the amount becomes 1.1 times the net amount.
Cans needed
Figure
Standard notation
(the usual math form)
\(B\)
\(=\)
\(\lceil\)
\(Q\)
\(\div\)
\(V\)
\(\rceil\)
In words
(symbols replaced with words)
④
\(B\): cans needed
\(=\)
③
\(\lceil\)
①
\(Q\): amount needed with waste
\(\div\)
②
\(V\): can size
\(\rceil\)
The formula in words
①
Take the
\(Q\): amount needed with waste
②
divide it by the
\(V\): can size
to see how many cans' worth it is
③
round up to a whole number (the symbol \(\lceil\ \rceil\) means "round up")
④
and you get the
\(B\): cans needed
Quick example
When you need 2.514 gal of paint sold in 1-gallon cans, the number of cans is
cans needed \(B\)
\(=\)
\(\lceil\)
amount (2.514 gal)
\(\div\)
can size (1 gal)
\(\rceil\)
\(2.514 \div 1 = 2.514\)
\(\lceil 2.514 \rceil = 3\)
Key idea
You can only buy whole cans, so if the division leaves a decimal, always round up (2.514 cans → 3 cans). Rounding to the nearest whole number or rounding down would leave you short. The symbol for rounding up is \(\lceil\ \rceil\) (the ceiling function). In the example you buy 3 gallons and use about 2.514, so about 0.486 gal is left over.
Enter the can size in the same unit as the coverage: in gallons for ft²/gal or gal/100 ft², and in pounds for lb/100 ft². To convert a can labeled in pounds to gallons, divide by the paint's weight per gallon (lb/gal, on the data sheet). You can also mix can sizes to cut the leftover: here, 2 gallons plus 2 quarts (2.5 gal) would be just short, so 2 gallons plus 3 quarts (2.75 gal) is enough.
Thinning (water or thinner to add, and the thinned amount)
Standard notation
(the usual math form)
\(D\)
\(=\)
\(Q\)
\(\times\)
\(d\)
\(\div\)
\(100\)
\(M\)
\(=\)
\(Q\)
\(\times\)
\((\)
\(1\)
\(+\)
\(d\)
\(\div\)
\(100\)
\()\)
In words
(symbols replaced with words)
③
\(D\): water or thinner to add
\(=\)
①
\(Q\): amount of unthinned paint
\(\times\)
②
\(d\): thinning ratio (%)
\(\div\)
\(100\)
④
\(M\): amount after thinning
\(=\)
\(Q\): amount of unthinned paint
\(\times\)
\((\)
\(1\)
\(+\)
\(d\): thinning ratio (%)
\(\div\)
\(100\)
\()\)
The formula in words
①
Take the
\(Q\): amount of unthinned paint
②
multiply it by the
\(d\): thinning ratio (%)
÷ 100
③
to get the
\(D\): water or thinner to add
, and the paint plus that (\(1 + d \div 100\) times the paint) is the
④
\(M\): amount after thinning
Quick example
To thin 2.514 gal of latex paint by 5% (adding water equal to 5% of the paint),
water to add \(D\)
\(=\)
paint (2.514 gal)
\(\times\)
thinning (5%)
\(\div\)
\(100\)
\(2.514 \times 5 \div 100 \approx 0.126\ \mathrm{gal}\ \ (\text{about}\ 16\ \mathrm{fl\,oz})\)
\(2.514 + 0.126 = 2.514 \times 1.05 = 2.64\ \mathrm{gal}\)
Key idea
On this page, the thinning ratio means "water or thinner added as a percentage of the paint". A 10% ratio means adding 1 gal of water to 10 gal of paint, for 11 gal in total. (It does not mean "10% of the final mix is water"; with that meaning you would add about 1.11 gal to 10 gal of paint, and the answer changes.) Maker instructions such as "thin up to 10% with water" are generally written in this "percent of the paint" sense.
If the coverage is given for unthinned paint, thinning does not change the number of cans. Thinning adjusts how easily the paint flows, and the amount of paint you need is set by the spread rate. Use this formula to know how much thinned paint you will have, or to convert coverage given "per gallon of thinned paint" back to unthinned paint. Stay within the maker's thinning limits: over-thinned paint leaves a thin film that does not perform well. Many latex wall paints are meant to be used without thinning when rolled or brushed.
Working backward: the area your cans will cover
Standard notation
(the usual math form)
\(S\)
\(=\)
\(B \times V\)
\(\div\)
\(\left(1 + \dfrac{r}{100}\right)\)
\(\div\)
\((\)
\(n\)
\(\times\)
\(q\)
\()\)
In words
(symbols replaced with words)
④
\(S\): area you can paint
\(=\)
①
paint on hand (cans \(B\) × can size \(V\))
\(\div\)
②
waste factor \(1 + r \div 100\)
\(\div\)
\((\)
③
\(n\): number of coats
\(\times\)
\(q\): spread rate
\()\)
The formula in words
①
Take the
paint on hand (cans \(B\) × can size \(V\))
②
divide it by the
waste factor \(1 + r \div 100\)
to get the amount you can really put on the wall
③
divide that by "
\(n\): number of coats
× spread rate \(q\)" (the paint that one square foot needs for \(n\) coats)
④
and you get the
\(S\): area you can paint
Quick example
With three 1-gallon cans (3 gal), 10% waste, two coats and a spread rate of 1/350 gal per ft², the area you can paint is
area \(S\)
\(=\)
on hand (3 cans × 1 gal = 3 gal)
\(\div\)
waste factor (1.1)
\(\div\)
\((\)
coats (2)
\(\times\)
spread rate (1/350 gal/ft²)
\()\)
\(3 \div 1.1 \approx 2.727\ \mathrm{gal}\)
\(2.727 \div \left(2 \times \tfrac{1}{350}\right) = 2.727 \times 175 \approx 477\ \mathrm{ft^2}\)
Key idea
This formula runs the "net amount", "with waste" and "cans" formulas backward. To find cans, you multiplied by the waste factor to increase the amount, so working backward you divide by it. Two coats need \(2 \times \tfrac{1}{350} = \tfrac{1}{175}\) gal per square foot, so dividing the usable paint by that gives the area.
Use it to see how far leftover paint will go, or to find "how many square feet will this one can cover?". The area for a single coat is the value with \(n = 1\) (about 955 ft² in the example).
Estimated cost
Standard notation
(the usual math form)
\(T\)
\(=\)
\(u\)
\(\times\)
\(B\)
In words
(symbols replaced with words)
③
\(T\): estimated cost
\(=\)
①
\(u\): unit price
\(\times\)
②
\(B\): number of cans
The formula in words
①
Take the
\(u\): unit price (price per can)
②
multiply it by the
\(B\): number of cans
③
and you get the
\(T\): estimated cost
Quick example
The cost of 3 gallons of paint at $35 a gallon is
estimated cost \(T\)
\(=\)
unit price ($35)
\(\times\)
cans (3)
\(35 \times 3 = 105\)
Key idea
Paint is bought by the can, so the cost is "price per can × number of cans". If the price is given per gallon or per pound (bulk pricing or a contractor's unit price), multiply by the amount needed with waste \(Q\) instead of the number of cans. This covers the paint only: primer, masking supplies and tools such as rollers, and for a contractor, scaffolding and labor, cost extra.
The basic method is to find the net amount as area × number of coats × spread rate (or area × coats ÷ coverage per gallon), increase it by the waste percentage, and divide by the can size, rounding up. The thinning ratio is "percent added to the paint", and if the coverage is for unthinned paint, thinning does not change the number of cans.
Symbols and terms
Symbols
| \(S\) | ess | The area to paint (ft²). For walls, "perimeter × height − windows and doors". When working backward, it is the area you can paint. |
| \(c\) | cee | The coverage per gallon (ft²/gal) - the value on the can such as "covers 350 sq ft per gallon". From "coverage". |
| \(q\) | cue | The spread rate (the amount per unit area for one coat; gallons or pounds per 100 ft² on US data sheets). From coverage per gallon, \(q = 1 \div c\). From "quantity". |
| \(n\) | en | The number of coats. 2 for two finish coats. From "number". |
| \(Q_0\) | cue zero | The net amount of paint (unthinned, no waste). It is found with \(Q_0 = S \times n \times q\). The subscript 0 means "the amount before waste". |
| \(r\) | ar | The waste percentage (%) - extra for paint left in tools and containers or spattered. From "rate". |
| \(Q\) | capital cue | The amount needed with waste (unthinned). It is found with \(Q = Q_0 \times (1 + r \div 100)\). |
| \(V\) | vee | The size of one can (gal or lb). From "volume". |
| \(B\) | bee | The number of cans needed, or the number of cans on hand. It is found with \(B = \lceil Q \div V \rceil\). |
| \(d\) | dee | The thinning ratio (%) - water or thinner added as a percentage of the paint. From "dilution". |
| \(D\) | capital dee | The amount of water or thinner to add. It is found with \(D = Q \times d \div 100\). |
| \(M\) | em | The amount after thinning. It is found with \(M = Q + D = Q \times (1 + d \div 100)\). From "mixture". |
| \(u\) | you | The unit price of the paint (per can, or per gallon or pound). From "unit price". |
| \(T\) | tee | The estimated cost (paint only). From "total". |
| \(\lceil x \rceil\) | ceiling of x | The symbol for rounding up to a whole number (the ceiling function). (Example - \(\lceil 2.514 \rceil = 3\), \(\lceil 3 \rceil = 3\)) |
Terms
| spread rate | The amount of paint used to cover a unit of area once. Data sheets often give a range (such as "1 to 1.5 gal per 100 sq ft"), and the real amount changes with how absorbent the surface is and how the paint is applied. Using the middle or the higher end of the range gives a safe estimate. |
| coverage | The area one gallon (or one can) of paint covers (ft²/gal). It is the usual way cans show it, and it is the reciprocal of the spread rate. US interior paint cans typically say 350-400 sq ft per gallon for one coat. If a value is given for two coats, enter 1 as the number of coats, or double it to get the one-coat value. |
| area to paint | The size of the surface you paint, also called the paintable area. For walls, subtract windows and doors from perimeter × height. For exterior painting, the amount of paint depends on this area, not on the home's floor area. |
| number of coats | How many times you paint the same surface. Two finish coats over a primer is standard for most walls; the primer is a different product, so count only the finish coats here. The maker's instructions say how many coats are needed. |
| thinning ratio | Water or thinner added as a percentage of the paint (%). This page uses the definition "10% of 10 gal of paint = 1 gal of water". Each paint has a range set by the maker, and thinning beyond it weakens the paint film. |
| thinning | Making paint runnier with water or thinner. Latex (water-based) paint is thinned with water, and oil-based (solvent) paint with mineral spirits or the recommended thinner. It is done to balance how easily the paint flows against how thick the film is. |
| unthinned paint | The paint as it comes in the can, before any water or thinner is added. Coverage and can sizes refer to unthinned paint. |
| waste percentage | The percentage added to the net amount for paint left in rollers, brushes and trays, spatter, and extra soaked up by the surface. 5-15% is common, depending on the tools and the surface. |
| rounding up | Raising a number with a decimal part to the next whole number. Paint is sold only in whole cans, so the number of cans is always rounded up. |
| reciprocal | 1 divided by a number. The reciprocal of 350 is \(1 \div 350 \approx 0.00286\). It turns "350 sq ft per gallon" into "about 0.00286 gallon per sq ft". |
| weight per gallon | How much one gallon of paint weighs (lb/gal), listed on the data sheet. Most paints are heavier than water (about 8.3 lb/gal); to turn a container labeled in pounds into gallons, divide by this weight. |
| paint film | The thin layer paint leaves on the surface once it dries. The paint's performance (durability, water resistance, color) depends on the film thickness, so over-thinning or spreading too thin makes the film too thin. |
| masking | Covering what you do not want painted (windows, floors, furniture) with painter's tape, plastic or drop cloths. The cost of tape and sheeting is not included in the paint cost on this page. |
| primer | The first coat, a primer or sealer that helps the finish paint stick and stops the surface from soaking up paint. It is a different product from the finish paint, so calculate it separately. |
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 a rectangle and units of area (Grade 3) |
|
| Multiplying and dividing decimals (Grades 5–6) |
|
| Percents (Grade 6) |
|
| Unit rates (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 turn coverage per gallon into a spread rate
| Coverage (ft²/gal) | 350 |
| Spread rate (gal per 100 ft²) | =100/B1 |
Table to find the net amount of paint
| Area to paint (ft²) | 400 |
| Number of coats | 2 |
| Coverage (ft²/gal) | 350 |
| Net amount of paint (gal) | =B1*B2/B3 |
Table to find the amount needed with waste
| Net amount of paint (gal) | 2.286 |
| Waste (%) | 10 |
| Amount needed with waste (gal) | =B1*(1+B2/100) |
Table to find the cans needed
| Amount needed with waste (gal) | 2.514 |
| Can size (gal) | 1 |
| Cans needed | =ROUNDUP(B1/B2,0) |
Table to find the thinning amounts
| Amount of unthinned paint (gal) | 2.514 |
| Thinning ratio (%) | 5 |
| Water or thinner to add (gal) | =B1*B2/100 |
| Amount after thinning (gal) | =B1*(1+B2/100) |
Table to work backward: the area your cans will cover
| Cans on hand | 3 |
| Can size (gal) | 1 |
| Waste (%) | 10 |
| Number of coats | 2 |
| Coverage (ft²/gal) | 350 |
| Area you can paint (ft²) | =B1*B2/(1+B3/100)/B4*B5 |
Table to find the estimated cost
| Unit price ($ per can) | 35 |
| Number of cans | 3 |
| Estimated cost ($) | =B1*B2 |
After pasting, the upper rows of column B are your inputs and the last row is calculated automatically.
"ROUNDUP(value, 0)" rounds up to a whole number (the ⌈ ⌉ in the formulas). The tables use the coverage in ft²/gal from the can directly (dividing by the coverage is the same as multiplying by the spread rate).
B2 in the first table is about 0.286, B4 in the second is about 2.286, B3 in the third is about 2.514, B3 in the fourth is 3, the fifth gives about 0.126 and 2.64, B6 in the sixth is about 477.27, and B3 in the seventh is 105.
Just replace the numbers in column B with your own.
"ROUNDUP(value, 0)" rounds up to a whole number (the ⌈ ⌉ in the formulas). The tables use the coverage in ft²/gal from the can directly (dividing by the coverage is the same as multiplying by the spread rate).
B2 in the first table is about 0.286, B4 in the second is about 2.286, B3 in the third is about 2.514, B3 in the fourth is 3, the fifth gives about 0.126 and 2.64, B6 in the sixth is about 477.27, and B3 in the seventh is 105.
Just replace the numbers in column B with your own.
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 turn coverage per gallon into a spread rate
| Coverage (ft²/gal) | 350 |
| Spread rate (gal per 100 ft²) | =100/B1 |
Table to find the net amount of paint
| Area to paint (ft²) | 400 |
| Number of coats | 2 |
| Coverage (ft²/gal) | 350 |
| Net amount of paint (gal) | =B1*B2/B3 |
Table to find the amount needed with waste
| Net amount of paint (gal) | 2.286 |
| Waste (%) | 10 |
| Amount needed with waste (gal) | =B1*(1+B2/100) |
Table to find the cans needed
| Amount needed with waste (gal) | 2.514 |
| Can size (gal) | 1 |
| Cans needed | =ROUNDUP(B1/B2,0) |
Table to find the thinning amounts
| Amount of unthinned paint (gal) | 2.514 |
| Thinning ratio (%) | 5 |
| Water or thinner to add (gal) | =B1*B2/100 |
| Amount after thinning (gal) | =B1*(1+B2/100) |
Table to work backward: the area your cans will cover
| Cans on hand | 3 |
| Can size (gal) | 1 |
| Waste (%) | 10 |
| Number of coats | 2 |
| Coverage (ft²/gal) | 350 |
| Area you can paint (ft²) | =B1*B2/(1+B3/100)/B4*B5 |
Table to find the estimated cost
| Unit price ($ per can) | 35 |
| Number of cans | 3 |
| Estimated cost ($) | =B1*B2 |
The same formulas as in Excel (including the ROUNDUP function) work as is. Copy the whole table, paste it into cell A1, and replace the numbers in column B with your own.
How to calculate it in Python
import math
area_ft2 = 400 # area to paint (ft2)
coverage_ft2_per_gal = 350 # coverage per gallon (ft2/gal). For a spread rate (gal per ft2), put it in q directly
coats = 2 # number of coats
loss_rate = 10 # waste (%)
dilution_rate = 5 # thinning (% of the paint)
can_size = 1 # can size (gal)
price_per_can = 35 # price per can ($)
q = 1 / coverage_ft2_per_gal # spread rate (gal per ft2, one coat)
net_quantity = area_ft2 * coats * q # net amount of paint (gal)
required_quantity = net_quantity * (1 + loss_rate / 100) # amount needed with waste (gal)
cans_needed = math.ceil(required_quantity / can_size) # cans needed (round up)
diluent = required_quantity * dilution_rate / 100 # water or thinner to add (gal)
mixed = required_quantity + diluent # amount after thinning (gal)
cost = cans_needed * price_per_can # estimated cost ($)
# working backward: the area the cans on hand will cover
have_cans = 3
paintable_area = have_cans * can_size / (1 + loss_rate / 100) / (coats * q)
print(f"Spread rate: {q:.6f} gal/ft2 ({q * 100:.3f} gal per 100 ft2)")
print(f"Net amount of paint: {net_quantity:.3f} gal")
print(f"Amount needed with waste: {required_quantity:.3f} gal")
print(f"Cans needed: {cans_needed} (before rounding up {required_quantity / can_size:.3f})")
print(f"Water or thinner to add: {diluent:.3f} gal, amount after thinning: {mixed:.3f} gal")
print(f"Estimated cost: ${cost:,.2f}")
print(f"Area {have_cans} cans will cover: {paintable_area:.2f} ft2")
Runs with the standard library only. math.ceil() rounds up (the ⌈ ⌉ in the formulas). Replace the area, coverage, coats and price at the top with your own numbers and run it. For a product given as a spread rate (such as 1.5 gal per 100 ft², which is 0.015 gal per ft²), put that value in q directly and enter the can size in the same unit.
How to write it in LaTeX and other math languages (copy and paste)
Turning coverage per gallon into a spread rate
q = 1 ÷ c
q = \frac{1}{c}
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<mi>q</mi>
<mo>=</mo>
<mfrac><mn>1</mn><mi>c</mi></mfrac>
</mrow>
</math>
q = 1 / c
1/c
q := 1/c;
q = 1/c;
q = 1/c
Net amount of paint (no waste)
Q₀ = S × n × q
Q_0 = S \times n \times q
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<msub><mi>Q</mi><mn>0</mn></msub>
<mo>=</mo>
<mi>S</mi><mo>×</mo><mi>n</mi><mo>×</mo><mi>q</mi>
</mrow>
</math>
Q_0 = S xx n xx q
s*n*q
Q0 := S*n*q;
Q0 = S*n*q;
Q_0 = S × n × q
Amount needed with waste
Q = Q₀ × (1 + r ÷ 100)
Q = Q_0 \left(1 + \frac{r}{100}\right)
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<mi>Q</mi>
<mo>=</mo>
<msub><mi>Q</mi><mn>0</mn></msub>
<mo>⁢</mo>
<mrow><mo>(</mo><mn>1</mn><mo>+</mo><mfrac><mi>r</mi><mn>100</mn></mfrac><mo>)</mo></mrow>
</mrow>
</math>
Q = Q_0 (1 + r / 100)
q0*(1 + r/100)
Q := Q0*(1 + r/100);
Q = Q0*(1 + r/100);
Q = Q_0 (1 + r/100)
Cans needed
B = ⌈Q ÷ V⌉
B = \left\lceil \frac{Q}{V} \right\rceil
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<mi>B</mi>
<mo>=</mo>
<mo>⌈</mo>
<mfrac><mi>Q</mi><mi>V</mi></mfrac>
<mo>⌉</mo>
</mrow>
</math>
B = |~ Q / V ~|
Ceiling[q/v]
B := ceil(Q/V);
B = ceil(Q/V);
B = ⌈Q/V⌉
Thinning (water or thinner to add, and the thinned amount)
D = Q × d ÷ 100, M = Q × (1 + d ÷ 100)
D = Q \times \frac{d}{100},\quad M = Q \left(1 + \frac{d}{100}\right)
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<mi>D</mi>
<mo>=</mo>
<mi>Q</mi><mo>×</mo><mfrac><mi>d</mi><mn>100</mn></mfrac>
<mo>,</mo>
<mi>M</mi>
<mo>=</mo>
<mi>Q</mi>
<mo>⁢</mo>
<mrow><mo>(</mo><mn>1</mn><mo>+</mo><mfrac><mi>d</mi><mn>100</mn></mfrac><mo>)</mo></mrow>
</mrow>
</math>
D = Q xx d / 100, M = Q (1 + d / 100)
{q*d/100, q*(1 + d/100)}
Dw := Q*d/100; M := Q*(1 + d/100);
D = Q*d/100; M = Q*(1 + d/100);
D = Q × d/100, M = Q (1 + d/100)
Working backward: the area your cans will cover
S = B × V ÷ (1 + r ÷ 100) ÷ (n × q)
S = \frac{B \times V}{\left(1 + \dfrac{r}{100}\right) \times n \times q}
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<mi>S</mi>
<mo>=</mo>
<mfrac>
<mrow><mi>B</mi><mo>×</mo><mi>V</mi></mrow>
<mrow><mrow><mo>(</mo><mn>1</mn><mo>+</mo><mfrac><mi>r</mi><mn>100</mn></mfrac><mo>)</mo></mrow><mo>×</mo><mi>n</mi><mo>×</mo><mi>q</mi></mrow>
</mfrac>
</mrow>
</math>
S = (B xx V) / ((1 + r / 100) xx n xx q)
b*v/((1 + r/100)*n*q)
S := B*V/((1 + r/100)*n*q);
S = B*V/((1 + r/100)*n*q);
S = (B × V)/((1 + r/100) × n × q)
Estimated cost
T = u × B
T = u \times B
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<mi>T</mi>
<mo>=</mo>
<mi>u</mi>
<mo>×</mo>
<mi>B</mi>
</mrow>
</math>
T = u * B
u*b
T := u*B;
T = u*B;
T = u × B
How to have ChatGPT do the calculation
You are a quantity calculation assistant for painting. 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 giving 400 sq ft of walls two coats of a latex paint that covers 350 sq ft per gallon (one coat). The waste allowance is 10%, the paint is thinned 5% with water (as a percentage of the paint), and it is sold in 1-gallon cans. Find each of the following: 1. The spread rate (amount per sq ft for one coat, 1 ÷ coverage), also shown per 100 sq ft 2. The net amount of paint (area × coats × spread rate) 3. The amount needed with waste (net amount × (1 + waste/100)) 4. The number of cans needed (amount ÷ can size, rounded up) and the value before rounding up 5. The amount of water to add (amount × thinning/100) and the amount after thinning 6. The area that three 1-gallon cans will cover (3 ÷ (1 + waste/100) ÷ (coats × spread rate)) Show the formulas you used and the numbers from the execution result.
How to Use
-
1Enter your numbersType the numbers you want to calculate with into the input fields
-
2CalculatePress the "Calculate" button
-
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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