Enter the side length of the cube. You get the volume (side × side × side) and, for input in cm, the volume converted to liters (L) and m³.
Enter 0 or a positive number for the side length, without units (for 10 cm, enter "10").
Result and figure
Enter the side length in the field 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 side length, and you get the volume of the cube (volume = side × side × side) right away
- Unit conversions are shown at the same time (for input in inches, US gallons and cubic feet). Switch "Units" to Metric to get liters and m³ for input in cm
- The result is also shown as a 3D figure (drag it with the mouse to turn it around)
- A plain-language explanation of the formulas and copy-and-paste formulas for Excel, Google Sheets and Python are all on this page
Enter the side length as a number only, without units. The answer is in your input unit cubed (in³ for inches, ft³ for feet). Other solids, such as rectangular boxes and cylinders, have their own pages.
What is this calculation used for?
Comparing the capacity of storage bins (home and moving)
Storage totes are often sold by capacity in gallons, such as "18-gallon tote". A cube-shaped box 16 in on each side has a volume of \(16 \times 16 \times 16 = 4096\,\mathrm{in^3}\), and dividing by 231 gives about 17.7 gallons.
Convert your own boxes or the space you want to fill to gallons with this formula, and you can compare them directly with the capacity listed in stores and online.
Estimating the water and weight of a cube aquarium (fish tanks and pets)
Fill a cube aquarium 12 in on each side, and the water volume is \(12 \times 12 \times 12 = 1728\,\mathrm{in^3} = 1\,\mathrm{ft^3}\), about 7.48 gallons. Water weighs about 8.34 lb per gallon, so the water alone is about 62 lb.
How much water conditioner to add depends on the gallons, and checking whether your stand can hold it takes the weight. This formula is the starting point for both.
Working out the volume of a shipping box (online selling and shipping)
Many carriers charge by the actual weight or the "dimensional weight" (a weight worked out from the volume), whichever is greater. A cube-shaped box 12 in on each side has a volume of \(12^3 = 1728\,\mathrm{in^3}\). With the divisor of 139 used by major US carriers, the dimensional weight is \(1728 \div 139 \approx 12.4\) lb, which they round up to 13 lb (divisors vary by carrier and service).
Light, bulky packages are hit hardest by dimensional weight, so working out the volume before you ship gives you a good idea of the cost.
Turning the amount of soil or concrete into order units (DIY and gardening)
Planters, raised beds and post holes that are close to a cube can be estimated with this formula too. A hole 18 in (1.5 ft) on each side is \(1.5 \times 1.5 \times 1.5 = 3.375\,\mathrm{ft^3}\).
Bagged soil is sold by the cubic foot (such as 1.5 ft³ bags) and ready-mix concrete and gravel by the cubic yard, so find the volume first and then convert it to bags (\(3.375 \div 1.5 = 2.25\), so 3 bags) or to an order (\(3.375 \div 27 = 0.125\) yd³).
Planning space for emergency drinking water (emergency preparedness)
A common guideline for storing drinking water is 1 gallon per person per day. A cube-shaped water container 8 in on each side holds \(8 \times 8 \times 8 = 512\,\mathrm{in^3}\), or about 2.2 gallons, which is about 2 days for one person.
The volume also tells you it will weigh about 18.5 lb when full (water is about 8.34 lb per gallon). You can check both the storage space and how heavy it is to carry before you buy.
Formulas and figures
Volume of a cube
Figure
Standard notation
(the usual math form)
\(V\)
\(=\)
\(a\)
\(3\)
In words
(symbols replaced with words)
③
\(V\): volume of the cube
\(=\)
①
\(a\): side length
②
cubed (the length used 3 times)
The formula in words
①
Take the
\(a\): side length
②
and
cube it (multiply the length by itself 3 times)
③
and you get the
\(V\): volume of the cube
Quick example
The volume of a cube-shaped box 10 in on each side is
\(V\): volume of the cube
\(=\)
side length (10 in)
cubed
\(10 \times 10 \times 10 = 1000\,\mathrm{in^3}\)
Key idea
Why does multiplying 3 times give the volume? Volume counts how many cubes with 1-inch sides (1 in³ each) fit inside. A cube 10 in on each side holds small 1 in³ cubes 10 across, 10 deep and 10 high with no gaps, for \(10 \times 10 \times 10 = 1000\) in all. So its volume is 1000 in³.
The area of a square uses the side twice (\(a^2\)); the volume of a cube uses it three times (\(a^3\)). Going from flat (2D) to solid (3D) adds one more multiplication. This formula is also why raising a number to the third power is called "cubing" it.
Converting volume units (in³ → gal)
Figure
Standard notation
(the usual math form)
\(V_{\mathrm{gal}}\)
\(=\)
\(V_{\mathrm{in^3}}\)
\(\div\)
\(231\)
In words
(symbols replaced with words)
③
\(V_{\mathrm{gal}}\): volume in gallons
\(=\)
①
\(V_{\mathrm{in^3}}\): volume in in³
\(\div\)
②
\(231\): in³ in 1 gallon
The formula in words
①
Take the
\(V_{\mathrm{in^3}}\): volume in in³
②
divide it by
\(231\): in³ in 1 gallon
③
and you get the
\(V_{\mathrm{gal}}\): volume in gallons
Quick example
The volume of a box 10 in on each side, 1000 in³, in gallons is
volume in gallons
\(=\)
volume in in³ (1000)
\(\div\)
in³ in 1 gallon (231)
\(1000 \div 231 \approx 4.33\,\mathrm{gal}\)
Key idea
A US liquid gallon is defined as exactly 231 in³. That is the volume of a cube about 6.14 in on each side (\(6.14 \times 6.14 \times 6.14 \approx 231\)).
So to change in³ to gallons, just divide by 231. To go from gallons back to in³, multiply by 231. It also follows that 1 ft³ = 1728 in³ is \(1728 \div 231 \approx 7.48\) gallons. (In metric, 1 liter is exactly a cube 10 cm on each side, 1000 cm³.)
Converting volume units (in³ → ft³)
Figure
Standard notation
(the usual math form)
\(V_{\mathrm{ft^3}}\)
\(=\)
\(V_{\mathrm{in^3}}\)
\(\div\)
\(1728\)
In words
(symbols replaced with words)
③
\(V_{\mathrm{ft^3}}\): volume in ft³
\(=\)
①
\(V_{\mathrm{in^3}}\): volume in in³
\(\div\)
②
\(1728\): in³ in 1 ft³
The formula in words
①
Take the
\(V_{\mathrm{in^3}}\): volume in in³
②
divide it by
\(1728\): in³ in 1 ft³
③
and you get the
\(V_{\mathrm{ft^3}}\): volume in ft³
Quick example
The volume of a cube 12 in (= 1 ft) on each side, 1728 in³, in ft³ is
volume in ft³
\(=\)
volume in in³ (1728)
\(\div\)
in³ in 1 ft³ (1728)
\(1728 \div 1728 = 1\,\mathrm{ft^3}\)
Key idea
A volume conversion factor is the length conversion factor cubed. Since \(1\,\mathrm{ft} = 12\,\mathrm{in}\), \(1\,\mathrm{ft^3} = 12\,\mathrm{in} \times 12\,\mathrm{in} \times 12\,\mathrm{in} = 1728\,\mathrm{in^3}\). For area the factor was 12 squared, 144; for volume it is 12 cubed, 1728. It is easy to mistakenly use 12 or 144, so be careful.
The same idea gives \(1\,\mathrm{yd^3} = 3 \times 3 \times 3 = 27\,\mathrm{ft^3}\), which you need when ordering concrete, gravel or mulch by the cubic yard.
The volume of a cube is "side × side × side" (the side cubed). The answer is in your input unit cubed (in³ for inches). To convert, divide in³ by 231 for US gallons, or by 1728 for ft³.
Symbols and terms
Symbols
| \(V\) | vee | A symbol often used for volume, from the first letter of "volume". On this page it is the volume of the cube. |
| \(a\) | a | The side length of the cube. All 12 edges of a cube are the same length, so one letter is enough. |
| \(a^3\) | a cubed (a to the third power) | The number \(a\) multiplied by itself 3 times (\(a \times a \times a\)). The small 3 at the upper right is an exponent that tells you to use the number 3 times in a multiplication. |
| \(\mathrm{in^3}\) | cubic inches | A unit of volume. A cube with 1-inch sides has a volume of 1 in³. It is also written "cu in". |
| \(\mathrm{ft^3}\) | cubic feet | A unit of volume. A cube with 1-foot sides has a volume of 1 ft³. \(1\,\mathrm{ft^3} = 1728\,\mathrm{in^3} \approx 7.48\,\mathrm{gal}\). |
| \(\mathrm{gal}\) | gallon | A unit of volume (capacity). The US liquid gallon is exactly \(231\,\mathrm{in^3}\) (about 3.785 L). It is the familiar unit on milk jugs and at the gas pump. |
Terms
| cube | A solid whose faces are all squares of the same size. It has 6 faces, 12 edges and 8 vertices, and every edge is the same length. Dice and a Rubik's Cube are everyday examples. |
| volume | The amount of space a solid takes up, as a number. It is measured by how many unit cubes (such as 1 in³) fit inside. |
| cubed | Multiplying a number by itself 3 times, also called "to the third power". The name comes from this very formula for the volume of a cube. |
| capacity | How much a container can hold. It is measured the same way as volume, using the inside measurements of the container. Gallons, quarts and fluid ounces (or liters and milliliters) are common units. |
| unit conversion | Writing the same amount in a different unit. For volume, the key point is that the length factor cubed is the volume factor (1 ft = 12 in, so 1 ft³ = 1728 in³). |
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.
| Multiplication (Grades 3–4) |
|
| Cubes and rectangular prisms (Grades 1–5) |
|
| What volume is, and its units (Grade 5) |
|
| Multiplying decimals (Grades 5–6) |
|
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 volume of a cube
| Side length | 10 |
| Volume of the cube | =B1^3 |
Table to convert in³ to gallons
| Volume in in³ | 1000 |
| Volume in gallons | =B1/231 |
Table to convert in³ to ft³
| Volume in in³ | 1728 |
| Volume in ft³ | =B1/1728 |
After pasting, column A has the item names and column B the numbers. The upper row is your input, and the formula in the last row calculates from it automatically.
"B1" in a formula stands for "the number in that cell". "^" is a power (how many times to multiply) and "/" is division. "=B1^3" cubes the side, that is, side × side × side.
In the first table, for example, B2 shows 10 × 10 × 10 = 1000 (in³ if you entered inches). The second table shows about 4.33 (gal) in B2, and the third shows 1 (ft³). Just replace the input with your own length.
"B1" in a formula stands for "the number in that cell". "^" is a power (how many times to multiply) and "/" is division. "=B1^3" cubes the side, that is, side × side × side.
In the first table, for example, B2 shows 10 × 10 × 10 = 1000 (in³ if you entered inches). The second table shows about 4.33 (gal) in B2, and the third shows 1 (ft³). Just replace the input with your own length.
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 volume of a cube
| Side length | 10 |
| Volume of the cube | =B1^3 |
Table to convert in³ to gallons
| Volume in in³ | 1000 |
| Volume in gallons | =B1/231 |
Table to convert in³ to ft³
| Volume in in³ | 1728 |
| Volume in ft³ | =B1/1728 |
The same formulas as in Excel work as is. Copy the whole table, paste it into cell A1, and replace the input with your own length.
How to calculate it in Python
a = 10 # side length (inches in this example)
volume = a ** 3 # volume of the cube (input unit cubed; in3 in this example)
volume_gal = volume / 231 # for input in inches, the volume in US gallons
print(f"Volume of the cube: {volume} in3")
print(f"In gallons: {volume_gal} gal")
Runs with the standard library only. "**" is a power (a ** 3 multiplies a by itself 3 times) and "/" is division. Change the side length at the top and run it (this example is for input in inches; to get ft³, divide by 1728).
How to write it in LaTeX and other math languages (copy and paste)
Volume of a cube
V = a³
V = a^{3}
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<mi>V</mi>
<mo>=</mo>
<msup><mi>a</mi><mn>3</mn></msup>
</mrow>
</math>
V = a^3
a^3
V := a^3;
V = a^3;
V = a^3
Converting volume units (in³ → gal)
V[gal] = V[in³] ÷ 231
V_{\mathrm{gal}} = V_{\mathrm{in^3}} \div 231
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<msub><mi>V</mi><mi>gal</mi></msub>
<mo>=</mo>
<msub><mi>V</mi><mrow><msup><mi>in</mi><mn>3</mn></msup></mrow></msub>
<mo>÷</mo>
<mn>231</mn>
</mrow>
</math>
V_(gal) = V_(in^3) -: 231
vIn3/231
vGal := vIn3/231;
v_gal = v_in3/231;
V(gal) = V(in³)/231
Converting volume units (in³ → ft³)
V[ft³] = V[in³] ÷ 1728
V_{\mathrm{ft^3}} = V_{\mathrm{in^3}} \div 1728
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<msub><mi>V</mi><mrow><msup><mi>ft</mi><mn>3</mn></msup></mrow></msub>
<mo>=</mo>
<msub><mi>V</mi><mrow><msup><mi>in</mi><mn>3</mn></msup></mrow></msub>
<mo>÷</mo>
<mn>1728</mn>
</mrow>
</math>
V_(ft^3) = V_(in^3) -: 1728
vIn3/1728
vFt3 := vIn3/1728;
v_ft3 = v_in3/1728;
V(ft³) = V(in³)/1728
How to have ChatGPT do the calculation
You are a math calculation assistant. 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). A cube-shaped box is 10 in on each side. Find each of the following: 1. The volume of this cube in in³ 2. That volume in US gallons (1 gal = 231 in³) 3. That volume 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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Related Features
Area of a Rectangle Calculator (Length × Width)
Calculates the area of a square or rectangle (the 2D version). Area goes with squaring, volume with cubing
Exponent Calculator (Powers, a to the nth Power)
Calculates powers (a to the nth power), such as the "cubed" in the volume of a cube
Nth Root Calculator (Square Root, Cube Root, nth Root)
Calculates the cube root (∛) you use to work back from the volume to the side length of a cube
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