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Volume Calculator

Find the volume of a box, cube, cylinder, sphere, cone or rectangular pyramid, with liters, US gallons, cubic meters and cubic feet.

Level: Grades 6–8

  • Common Core standard 6.G.A.2Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = l w h and V = b h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems.
  • Common Core standard 8.G.C.9Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.
Printable worksheet

Volume Calculator

Know the answer you need? Pick an input to work backward.

Inputs

Result

Volume

24 ft³

The volume is 24 ft³ (679.6 liters).

In liters
679.6043 L
In US gallons
179.5325 US gal
In cubic meters
0.6796 m³

See the step-by-step solution ↓

Step-by-step solution

  1. Multiply the length, width and height of the box

    4×3×2=24 ft³

  2. Convert to liters: 1 ft³ = 28.31684659 L

    24 ft³×28.31684659=679.604318 L

  3. Convert to US gallons: 1 US gallon = 3.785411784 L

    679.604318 L3.785411784=179.532468 US gal

Test yourself

20 quick questions built from this calculator's formula: work out results, predict what happens when an input changes, and work backward from an answer. Every answer comes with the working.

What this calculator does

Find out how much a box, tank, ball or other solid shape holds. That's its volume: the amount of space it takes up, measured in cubic units. It tells you how much a container holds. It also tells you how much soil or concrete fills a garden bed or a slab, or how much water a tank needs.

Choose a shape, pick the unit you measured in and enter its measurements. You'll get the result in that unit cubed. It's also converted to liters, US gallons, cubic meters and cubic feet.

Where it's used

Why this math matters outside the classroom:

  • Moving boxes. A box 18 in by 18 in by 16 in holds 5,184 cubic inches, which is exactly 3 cubic feet.
  • Fish tanks. A tank 60 cm by 30 cm by 40 cm holds 72,000 cm³, or 72 liters, of water.
  • Post holes. A round post hole 0.3 m wide and 1 m deep takes π × 0.15² × 1, about 0.071 m³, of concrete.
  • Ice cream cones. A cone 5 cm across and 12 cm deep holds (1/3)π × 2.5² × 12, about 78.5 cm³.
  • Garden soil. A raised bed 8 ft by 4 ft by 1 ft needs 32 cubic feet of soil, about 1.2 cubic yards.

Grade level and standards: Grades 6–8; Common Core State Standards for Mathematics 6.G.A.2, 8.G.C.9. © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.

How to use it

  1. Pick the shape: a box, cube, cylinder, sphere (ball), cone or rectangular pyramid.
  2. Pick the unit you measured in: mm, cm, meters, inches, feet or yards.
  3. Enter the measurements shown for that shape. Each must be greater than zero.
  4. Read the volume and its conversions to liquid and cubic units.

What the inputs mean

Shape
The shape to measure. For a cylinder lying on its side, the “height” is its length.
Measurement unit
The unit of every measurement you enter. The volume comes out in the same unit, cubed.
Edge length
The length of one edge of the cube.
Radius
Half the diameter (the distance across), measured from the center. For a cylinder or cone, it's the radius of the round base.
Height
For a cone or pyramid, the straight-up height from the base to the tip, not the length of a slanted side.

Formula and method

Box: V = length × width × height
Cube: V = side³
Cylinder: V = π × r² × height
Sphere: V = 4/3 × π × r³
Cone: V = π × r² × height ÷ 3
Rectangular pyramid: V = length × width × height ÷ 3
1 L = 0.001 m³;  1 US gallon = 231 in³ = 3.785411784 L

In the formulas, V is the volume and r is the radius. π (pi) is about 3.14159, and a small ³ or ² means multiply a number by itself three or two times.

A cone holds exactly one third of a cylinder with the same base and height. A pyramid holds one third of a box with the same base and height. That's why both formulas divide by 3.

To convert cubic units, cube the length conversion. 1 ft = 0.3048 m exactly, so 1 ft³ = 0.028316846592 m³ = 28.316846592 L. Officially, the US gallon is exactly 231 cubic inches. That works out to exactly 3.785411784 liters.

Worked example

A raised garden bed is 4 ft long, 3 ft wide and 2 ft deep. How much soil fills it?

  1. Volume: 4 × 3 × 2 = 24 ft³.
  2. In liters: 24 × 28.316846592 ≈ 679.60 L.
  3. In US gallons: 679.60 ÷ 3.785411784 ≈ 179.53 gal.
  4. In cubic meters: 679.60 ÷ 1,000 ≈ 0.6796 m³.

Result: The bed holds 24 cubic feet. That's about 680 liters, 179.5 US gallons or 0.68 cubic meters.

Understanding the result

Bulk materials such as soil and gravel are often sold by the cubic yard. One cubic yard is 27 cubic feet, so 24 ft³ is just under 0.9 yd³. Choose yards as the unit to get that figure directly.

Volume grows much faster than size. Double every measurement of a shape, and its volume becomes eight times bigger.

Assumptions and limitations

  • All measurements are in the same unit and describe a perfect shape.
  • If you want to know how much a container holds, use inside measurements.
  • Gallons are US liquid gallons. US units use the international definitions.
  • Imperial (UK) gallons, which are larger than US gallons, aren't shown.
  • It doesn't handle partly filled tanks, hollow shells or shapes other than the six listed.
  • Wall thickness isn't subtracted. Measure the inside for how much a container holds.

Frequently asked questions

How do I find the volume of a cylindrical tank in gallons?

Choose Cylinder. Measure the inside radius (half the diameter) and the height or length. Then read the US gallons line. A tank with a 1 ft radius and 1 ft height holds about 23.5 gallons.

Why do the cone and pyramid formulas divide by three?

A cone or pyramid narrows to a point. It fills exactly one third of the cylinder or box that shares its base and height. That ratio holds for any solid that narrows to a point from a flat base.

How many liters are in a cubic foot?

Exactly 28.316846592 liters. That's because a foot is exactly 0.3048 meters, and a liter is exactly 0.001 cubic meters.

Is a US gallon the same as a UK gallon?

No. The US gallon is 3.785411784 liters. The imperial gallon used in the UK is larger, at about 4.55 liters. This calculator shows US gallons.

How this calculator is checked

Method: Standard Euclidean volume formulas; international foot definition; US gallon defined as 231 cubic inches. The calculation is covered by automated tests with known reference values and edge cases. Last updated 2026-10-18. Found a problem? Tell us.

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