Volume Calculator: Box Volume by Length, Width, Height

Volume Calculator: Find the Volume of a Box

A volume calculator finds the amount of three-dimensional space inside a rectangular box or container. It works by multiplying length, width, and height. This tool takes those three measurements and returns the volume, rounded to two decimal places, along with a 3D preview of the shape. It has no unit selector: the answer is in "cubic units" of whatever unit you measured in.

Volume Formula for a Box

The volume of a rectangular box, which mathematicians call a rectangular cuboid, is:

$V = L \times W \times H$

Where:

• $V$ = volume, in cubic units
• $L$ = length
• $W$ = width
• $H$ = height

All three measurements must use the same unit. Mixing inches and feet, or centimeters and meters, produces a wrong answer.

The formula works because volume counts how many unit cubes fit inside the box. A box that is 3 units long, 2 units wide, and 2 units tall holds 3 × 2 × 2 = 12 unit cubes, so its volume is 12 cubic units.

How to Calculate Volume Step by Step

1. Measure the length of the box.
2. Measure the width, using the same unit as the length.
3. Measure the height, using the same unit as the other two.
4. Multiply the three numbers together.
5. Label the answer with the matching cubic unit, such as cubic inches or cubic feet.

The calculator on this page performs these steps automatically. Enter length, width, and height, and it displays the volume and a scaled 3D box. All three numbers must be greater than zero.

Worked Examples

Small package box. Length 12 inches, width 9 inches, height 6 inches. 12 × 9 × 6 = 648 cubic inches.

Moving box. Length, width, and height all 1.5 feet. 1.5 × 1.5 × 1.5 = 3.375 cubic feet. The calculator rounds this to 3.38.

Both examples use one consistent unit throughout, which is why the results are correct.

Converting Between Volume Units

Converting a volume from one unit to another means cubing the linear conversion factor, not just multiplying by it. The metric figures below follow from the NIST conversion factors, which give 1 cubic foot as 0.028 316 85 cubic meters and 1 liter as 0.001 cubic meters.

• 1 cubic foot = 1,728 cubic inches (since 12³ = 1,728)
• 1 cubic yard = 27 cubic feet (since 3³ = 27)
• 1 cubic meter ≈ 35.31 cubic feet
• 1 cubic meter = 1,000,000 cubic centimeters (since 100³ = 1,000,000)
• 1 liter = 1,000 cubic centimeters

A common error is forgetting to cube the factor. Since 1 foot equals 12 inches, 1 cubic foot equals 12³ = 1,728 cubic inches, not 12.

Volume and Shipping: Dimensional Weight

Shipping carriers often charge by dimensional weight rather than actual weight for large, light packages. Dimensional weight is calculated by dividing the box's volume in cubic inches by a fixed number called a DIM divisor. The divisor depends on the carrier and the service. For USPS commercial Priority Mail, the Domestic Mail Manual says that a rectangular parcel over 1,728 cubic inches is measured to whole inches, its volume is divided by 139, and the result is rounded up to whole pounds. The postage is based on the actual weight or the dimensional weight, whichever is greater.

For example, a box measuring 20 × 20 × 20 inches has a volume of 8,000 cubic inches. Divided by 139, that is 57.55, which rounds up to a dimensional weight of 58 pounds. The package is billed at this weight even if the actual contents, such as pillows, weigh only 3 pounds. This is why bulky but light items often cost more to ship than their scale weight would suggest.

Volume Formulas for Other Shapes

This calculator handles rectangular boxes only. Other common shapes use different formulas:

• Cylinder: $V = \pi r^2 h$, where $r$ is the radius and $h$ is the height.
• Sphere: $V = \frac{4}{3} \pi r^3$, where $r$ is the radius.
• Cone: $V = \frac{1}{3} \pi r^2 h$, where $r$ is the radius and $h$ is the height.

For an irregular shape, one option is to submerge it in water and measure how much water it displaces. Another option is to measure the smallest rectangular box that would contain the object, since packaging and shipping costs are usually based on that box, not the object itself.

Frequently Asked Questions

What is volume?

Volume is the amount of three-dimensional space inside an object or container. It is measured in cubic units, such as cubic inches, cubic feet, or cubic meters.

How do you calculate the volume of a box?

Multiply length by width by height: V = L × W × H. For example, a box 2 meters long, 3 meters wide, and 4 meters tall has a volume of 2 × 3 × 4 = 24 cubic meters.

How do I calculate cubic feet?

Measure all three dimensions in feet, then multiply them. For dimensions given in inches, divide each one by 12 first. A box measuring 36 × 24 × 24 inches equals 3 × 2 × 2 feet, which is 12 cubic feet.

How accurate is this volume calculator?

The calculator's arithmetic is exact; any error comes from the input measurements. A small measuring mistake has a large effect because it applies to all three dimensions at once. For a box meant to measure 10.5 × 10.5 × 10.5 inches, if the actual side length is 10.75 inches, the true volume is about 1,242 cubic inches instead of the assumed 1,158 cubic inches, a difference of about 7%. Measuring to the nearest quarter-inch or half-centimeter is accurate enough for most shipping, storage, and construction uses.

Can this calculator handle irregular or non-rectangular shapes?

No. It is built for rectangular boxes and containers only. Cylinders, spheres, and cones need their own formulas, listed above. For an irregular object that will ship in a box, measure the smallest rectangular box that contains it.

How does box volume affect shipping cost?

Carriers convert a package's volume into a dimensional weight and charge for whichever is greater, actual weight or dimensional weight. A 20 × 16 × 12 inch box has a volume of 3,840 cubic inches. With the USPS Priority Mail divisor of 139, that is 27.6, rounded up to 28 pounds of dimensional weight, regardless of how light the actual contents are. Other carriers and services use their own divisors.

References

1. Weisstein, Eric W. Cuboid. MathWorld, Wolfram Research. mathworld.wolfram.com — volume of a rectangular cuboid is the product of its three side lengths.
2. National Institute of Standards and Technology. NIST Guide to the SI, Appendix B.8: Factors for Units Listed Alphabetically. nist.gov — 1 ft³ = 2.831 685 × 10⁻² m³; 1 L = 1.0 × 10⁻³ m³.
3. United States Postal Service. Domestic Mail Manual 223, Commercial Priority Mail: Prices and Eligibility. pe.usps.com — dimensional weight for rectangular parcels over 1,728 in³: divide L × W × H by 139 and round up; postage on actual or dimensional weight, whichever is greater.