Rectangular Prism Volume Calculator (Length × Width × Height)

Enter the length, width and height of the box. The volume (length × width × height) is shown, along with conversions to liters (L) and cubic meters (m³).

Units

Length

Width

Height

Use the same unit for all three and enter only numbers greater than 0 (numbers only, no units. For 30 cm, enter "30").

Result and figure

Enter the length, width and height in the fields on the left and press "Calculate". The result will appear here.

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What you can do on this page
What is this calculation used for?
How to Use
Formulas and figures
Symbols and terms
- Symbols
- Terms
Good to know before you start
How to calculate it in Excel
How to calculate it in Google Sheets
How to calculate it in Python
How to write it in LaTeX and other math languages (copy and paste)
How to have ChatGPT do the calculation
DataChef Features
Related Features
NumberChef Calculators List

What you can do on this page

Enter the three lengths (length, width and height), and the volume of the rectangular prism (volume = length × width × height) is calculated on the spot
The result also shows the volume in other units: US gallons and cubic feet if you enter inches, and US gallons if you enter feet. Switch "Units" to Metric to get liters and cubic meters instead
The result is also drawn as a 3D shape. Drag it with the mouse to turn it around and check its shape and size
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 length, width and height in the same unit (all in inches, or all in feet). Which side you call the length or the width does not change the answer. The volumes of other solids, such as cubes, cylinders and spheres, have their own pages.

What is this calculation used for?

Finding how much water an aquarium holds (fish and pets)

A standard 10-gallon aquarium is 20 in long, 10 in wide and 12 in tall. Its volume is \(20 \times 10 \times 12 = 2400\,\mathrm{in^3}\), which is \(2400 \div 231 \approx 10.4\) gallons (in practice you do not fill it to the brim, so it holds a little less water).
Heater wattage, filter capacity and how many fish you can keep are all rated "per gallon", so choosing an aquarium starts with this calculation.

Comparing the water in a bath and a shower (home and savings)

If the inside of a bathtub is 50 in long and 22 in wide and you fill it 12 in deep, the water is \(50 \times 22 \times 12 = 13200\,\mathrm{in^3}\), or about \(13200 \div 231 \approx 57\) gallons (real tubs have sloped sides, so it is a little less).
A US showerhead uses at most 2.5 gallons per minute, so a 10-minute shower uses about 25 gallons or less. Comparing a bath with a shower, like many ways to save water, starts with a volume calculation.

Calculating the dimensional weight of a package (shipping)

Carriers charge not only by actual weight but also by "dimensional weight". A common formula is "length × width × height (in inches) ÷ 139". A box 24 in by 16 in by 12 in has a volume of \(24 \times 16 \times 12 = 4608\,\mathrm{in^3}\), so its dimensional weight is \(4608 \div 139 \approx 33.2\) lb, which is rounded up to 34 lb.
The lighter and bulkier a package is, the more its volume matters, so this calculation is used every day in shipping.

Estimating the soil for a raised garden bed (gardening)

To fill a raised bed that is 8 ft long, 4 ft wide and 1 ft deep, you need \(8 \times 4 \times 1 = 32\,\mathrm{ft^3}\) of soil.
Bagged soil is sold by volume, such as 2 cubic feet per bag, so \(32 \div 2 = 16\) bags will do. For a bulk delivery, which is sold by the cubic yard, it is \(32 \div 27 \approx 1.2\) yd³. This calculation helps you avoid buying too much or too little.

Using the volume of a room to choose fans and air purifiers (home and appliances)

A room that is 12 ft long and 10 ft wide with an 8 ft ceiling holds \(12 \times 10 \times 8 = 960\,\mathrm{ft^3}\) of air.
Fans and air purifiers are rated in cubic feet per minute (CFM). A fan that moves 80 CFM takes \(960 \div 80 = 12\) minutes to move the same amount of air as the whole room, so knowing the room volume lets you read these numbers.

Formulas and figures

Volume of a rectangular prism

Figure

Standard notation (the usual math form)

\(V\) \(=\) \(l\) \(\times\) \(w\) \(\times\) \(h\)

In words (symbols replaced with words)

④ \(V\): volume \(=\) ① \(l\): length \(\times\) ② \(w\): width \(\times\) ③ \(h\): height

The formula in words

① Take the \(l\): length

② multiply it by the \(w\): width

③ multiply that by the \(h\): height

④ and you get the \(V\): volume

Quick example

The volume of a box that is 5 in long, 8 in wide and 4 in tall is

\(V\): volume \(=\) length (5 in) \(\times\) width (8 in) \(\times\) height (4 in)

\(5 \times 8 \times 4 = 160\,\mathrm{in^3}\)

Key idea

Why do three multiplications give the volume? Volume counts how many unit cubes fit inside, here cubes that are 1 inch on each side (1 in³). In a box 5 in long, 8 in wide and 4 in tall, the bottom layer holds \(5 \times 8 = 40\) of these cubes, and there are 4 layers stacked up, so there are \(40 \times 4 = 160\) cubes in all. That is 160 in³. Always use the same unit for the length, width and height. If all three are in inches, the answer is in cubic inches (in³); if all three are in feet, it is in cubic feet (ft³).

Base area × height (volume of a prism)

Figure

Standard notation (the usual math form)

\(V\) \(=\) \(S\) \(\times\) \(h\)

In words (symbols replaced with words)

③ \(V\): volume \(=\) ① \(S\): area of the base \(\times\) ② \(h\): height

The formula in words

① Take the \(S\): area of the base

② multiply it by the \(h\): height

③ and you get the \(V\): volume

Quick example

The volume of a box that is 5 in long and 8 in wide (base area 40 in²) and 4 in tall is

\(V\): volume \(=\) area of the base (40 in²) \(\times\) height (4 in)

\(5 \times 8 = 40\,\mathrm{in^2}\)

\(40 \times 4 = 160\,\mathrm{in^3}\)

Key idea

The "length × width" part is exactly the area of the rectangle at the bottom (the area of the base). So the volume of a rectangular prism can also be read as "area of the base × height". Many US textbooks write this as \(V = Bh\), with \(B\) for the area of the base. The nice thing about this view is that it works even when the base is not a rectangle. Whether the base is a triangle or a circle, the volume of any prism or cylinder is "area of the base × height". The box formula is the simplest case of this rule.

Converting volume units (in³ to 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 \(1728\): cubic inches in 1 ft³

The formula in words

① Take the \(V_{\mathrm{in^3}}\): volume in in³

② divide it by \(1728\): cubic inches in 1 ft³

③ and you get the \(V_{\mathrm{ft^3}}\): volume in ft³

Quick example

A 10-gallon aquarium that is 20 in by 10 in and 12 in tall holds 2400 in³. In cubic feet, that is

volume in ft³ \(=\) volume in in³ (2400) \(\div\) cubic inches in 1 ft³ (1728)

\(2400 \div 1728 \approx 1.39\,\mathrm{ft^3}\)

Key idea

\(1\,\mathrm{ft^3}\) is the space inside a cube that is 1 foot (12 inches) on each side, so it holds \(12 \times 12 \times 12 = 1728\,\mathrm{in^3}\). That is why you divide cubic inches by 1728 to get cubic feet. For liquids, 1 US gallon is \(231\,\mathrm{in^3}\), so the same tank holds \(2400 \div 231 \approx 10.4\) gallons, which is why it is sold as a 10-gallon tank. The conversion factor for volume is the length factor cubed. Since 1 yd = 3 ft, \(1\,\mathrm{yd^3} = 3 \times 3 \times 3 = 27\,\mathrm{ft^3}\). A common mistake is to multiply by 3 or by 9 instead of 27.

The volume of a rectangular prism is length × width × height. Since length × width is the area of the base, it can also be read as "area of the base × height", a view that works for every prism and cylinder. To convert cubic inches to cubic feet, divide by 1728; to get US gallons, divide by 231.

Symbols and terms

Symbols

\(V\)	vee	The usual symbol for volume, from the first letter of "volume".
\(l\)	ell	The length of the box, from the first letter of "length".
\(w\)	double-u	The width of the box, from the first letter of "width".
\(h\)	aitch	The height of the box, from the first letter of "height".
\(S\)	ess	The area of the base (the rectangle at the bottom). On this page, \(S = l \times w\). Many US textbooks use \(B\) for the same thing.
\(\mathrm{in^3}\)	cubic inches	A unit of volume. A cube that is 1 inch on each side has a volume of 1 in³. Do not mix it up with in² (square inches), which is a unit of area.
\(\mathrm{ft^3}\)	cubic feet	A unit of volume. A cube that is 1 foot on each side has a volume of 1 ft³. \(1\,\mathrm{ft^3} = 1728\,\mathrm{in^3} \approx 7.48\) gallons, and \(1\,\mathrm{yd^3} = 27\,\mathrm{ft^3}\).
\(\mathrm{gal}\)	gallons	A unit for amounts of liquid such as water. 1 US gallon is exactly \(231\,\mathrm{in^3}\) (about 3.785 liters), and 1 gallon = 4 quarts.

Terms

rectangular prism	A box shape whose 6 faces are all rectangles (some may be squares). Tissue boxes, bricks and fish tanks are all rectangular prisms, the most common solid around us.
cube	A solid whose 6 faces are all identical squares, the shape of a die. It is a special rectangular prism whose length, width and height are all equal.
volume	The amount of space a solid takes up, given as a number. It is measured by how many unit cubes, such as 1-inch cubes (1 in³), fit inside.
area of the base	The area of the bottom face of a solid. For a rectangular prism, it is the area of the bottom rectangle (length × width). "Area of the base × height" is the basic way to find the volume of a prism or cylinder.
prism	A solid made by stacking a polygon straight up without changing its shape. A rectangular prism is a prism whose base is a rectangle.
unit conversion	Writing the same amount in a different unit. For volume, the key point is that the volume factor is the length factor cubed (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)	Knowing the times tables and multiplying three numbers in order, such as 3 × 4 × 5
Rectangular prisms and cubes (Grades 4–5)	Telling a rectangular prism (a box whose 6 faces are rectangles) from a cube (a die shape whose 6 faces are squares) Pointing out the length, width and height on a drawing of a box
What volume is and its units (Grade 5)	Knowing that volume can be counted as the number of unit cubes, such as 1-inch cubes (1 in³), that fit inside Reading and writing units such as in³ and ft³, and knowing that \(1\,\mathrm{ft^3} = 1728\,\mathrm{in^3}\) Knowing that 1 US gallon is \(231\,\mathrm{in^3}\)
Multiplying decimals (Grades 5–6)	Multiplying decimals such as \(3.5 \times 2.5\) (used when lengths are measured in feet, like 3.5 ft)

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 rectangular prism

Length (in)	10
Width (in)	20
Height (in)	12
Volume (in³)	=B1B2B3

Table to find it as "area of the base × height"

Length (in)	10
Width (in)	20
Height (in)	12
Area of the base (in²)	=B1*B2
Volume (in³)	=B4*B3

Table to convert cubic inches to cubic feet

Volume in in³	2400
Volume in ft³	=B1/1728

After pasting, column A holds the labels and column B holds the numbers. The upper rows are your inputs, and the formulas in the lower rows calculate automatically from them.
In a formula, "B1" and "B2" mean "use the number in that cell", "*" is multiplication and "/" is division.
In the first table, for example, B4 shows 10 × 20 × 12 = 2400 (in³, since the inputs are in inches). The second table shows the same 2400 in B5, and the third table shows about 1.39 (ft³) in B2. To get US gallons instead, change "/1728" to "/231" (about 10.39 gallons). Just replace the input numbers with your own lengths.

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 rectangular prism

Length (in)	10
Width (in)	20
Height (in)	12
Volume (in³)	=B1B2B3

Table to find it as "area of the base × height"

Length (in)	10
Width (in)	20
Height (in)	12
Area of the base (in²)	=B1*B2
Volume (in³)	=B4*B3

Table to convert cubic inches to cubic feet

Volume in in³	2400
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 numbers with your own lengths.

How to calculate it in Python

length = 10   # length (inches in this example)
width = 20    # width (same unit as length)
height = 12   # height (same unit as length)

volume = length * width * height   # volume (input unit cubed, in3 in this example)
volume_gal = volume / 231          # in US gallons (for inputs in inches)
volume_ft3 = volume / 1728         # in cubic feet (for inputs in inches)

print(f"Volume: {volume} in3")
print(f"In US gallons: {volume_gal} gal")
print(f"In cubic feet: {volume_ft3} ft3")

Runs with the standard library only. "*" is multiplication and "/" is division. Change the length, width and height at the top and run it. This example uses inches; if you use feet, the volume is in cubic feet, and multiplying it by 1728 and dividing by 231 gives US gallons.

How to write it in LaTeX and other math languages (copy and paste)

Volume of a rectangular prism

V = l × w × h

V = l \times w \times h

<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
  <mrow>
    <mi>V</mi>
    <mo>=</mo>
    <mi>l</mi>
    <mo>&#xD7;</mo>
    <mi>w</mi>
    <mo>&#xD7;</mo>
    <mi>h</mi>
  </mrow>
</math>

V = l xx w xx h

l*w*h

V := l*w*h;

V = l*w*h;

V = l × w × h

Base area × height (volume of a prism)

V = S × h

V = S \times h

<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
  <mrow>
    <mi>V</mi>
    <mo>=</mo>
    <mi>S</mi>
    <mo>&#xD7;</mo>
    <mi>h</mi>
  </mrow>
</math>

V = S xx h

s*h

V := S*h;

V = S*h;

V = S × h

Converting volume units (in³ to 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 mathvariant="normal">ft</mi><mn>3</mn></msup></mrow></msub>
    <mo>=</mo>
    <msub><mi>V</mi><mrow><msup><mi mathvariant="normal">in</mi><mn>3</mn></msup></mrow></msub>
    <mo>&#xF7;</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).

An aquarium shaped like a rectangular prism is 20 inches long, 10 inches wide and 12 inches tall.
Find each of the following:
1. The volume of the aquarium in cubic inches (in³)
2. That volume in US gallons (1 gallon = 231 in³)

Show the formulas you used and the numbers from the execution result.

How to Use

1

Enter your numbers

Type the numbers you want to calculate with into the input fields
2

Calculate

Press the "Calculate" button
3

Check the result

The result appears on the spot. The same page also explains the idea behind the calculation and the formula