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Volume Calculator

The volume and surface area of a cube, box, cylinder, cone, sphere or pyramid — with the steps, the answer in terms of π, and the capacity in gallons or liters.

Choose a shape and enter its measurements to see its volume.

You know the

Choose inches, feet or yards to see the capacity in US gallons, or centimeters or meters for liters.

Exact calculation. Given your inputs, this is the answer — no estimation involved.

How this calculator works

Volume is the space a solid takes up, in cubic units. For a box it is length times width times height. A cylinder is the same idea with a circle for its base: the area of the circle, π r², times the height.

Pointed shapes hold a third as much as the straight-sided shape with the same base and height. A cone is one third of the matching cylinder, and a pyramid is one third of the matching box. A sphere is four thirds of π times the radius cubed.

Surface area is the total area of the outside, in square units: what it would take to wrap or paint the shape. It is given alongside the volume because the two are often needed together, and often confused.

Choose a unit to see the capacity as well. In inches, feet or yards it is given in US gallons, at 231 cubic inches to the gallon; in centimeters or meters it is given in liters, at 1,000 cubic centimeters to the liter.

The formula

Exactly what happens to your numbers, step by step.

  1. Cube and box

    V = s³          V = l × w × h

  2. Cylinder

    V = π r² h      SA = 2π r (r + h)

  3. Cone

    V = ⅓ π r² h    SA = π r (r + √(r² + h²))

  4. Sphere

    V = ⁴⁄₃ π r³     SA = 4π r²

  5. Rectangular pyramid

    V = ⅓ × l × w × h

    A right pyramid, with its tip above the center of its base.

  6. Capacity

    gallons = in³ ÷ 231        liters = cm³ ÷ 1,000

A worked example

A round bucket 12 inches across and 24 inches tall.

What you enter

Shape
Cylinder
Diameter
12 in
Height
24 in

Step by step

Radius
r = 12 ÷ 2 = 6 in
Volume
V = π × 6² × 24 = 864π
As a decimal
864π ≈ 2,714.3361 in³
In gallons
2,714.3361 ÷ 231 = 11.7504 gal

About 11.75 US gallons

That is the volume to the brim. A bucket is usually filled a few inches short of the top, so its working capacity is less.

Volume questions, worked out

Common homework and household questions, each solved with the same formula the calculator uses.

  1. 1.What is the volume of a cylinder with a radius of 3 and a height of 10?

    1. V = π r² h = π × 3² × 10 = 90π ≈ 282.7433

    90π, or about 282.7433 cubic units.

  2. 2.How many gallons does a cylinder 12 inches across and 24 inches tall hold?

    1. r = d ÷ 2 = 12 ÷ 2 = 6 in
    2. V = π r² h = π × 6² × 24 = 864π ≈ 2,714.3361 in³
    3. A US gallon is 231 cubic inches: 2,714.3361 ÷ 231 = 11.7504 gallons.

    About 11.7504 US gallons.

  3. 3.What is the volume of a sphere with a radius of 6 cm?

    1. V = ⁴⁄₃ π r³ = ⁴⁄₃ × π × 6³ = 288π ≈ 904.7787 cm³
    2. A liter is 1,000 cm³: 904.7787 ÷ 1,000 = 0.9048 liters.

    288π, or about 904.7787 cm³ — 0.9048 liters.

  4. 4.What is the volume of a cone with a radius of 3 and a height of 4?

    1. V = ⅓ π r² h = ⅓ × π × 3² × 4 = 12π ≈ 37.6991

    12π, or about 37.6991 cubic units.

  5. 5.How many gallons does a 2 by 3 by 4 foot tank hold?

    1. V = l × w × h = 2 × 3 × 4 = 24 ft³
    2. A cubic foot is 1,728 cubic inches, and a gallon is 231: 24 × 1,728 ÷ 231 = 179.5325 gallons.

    About 179.5325 US gallons.

Assumptions

Every result here rests on these. Change your inputs and the result changes with them.

  • Shapes are solid and regular: a cylinder’s ends are flat and parallel, and a pyramid’s tip sits over the center of its base.
  • Measurements are of the inside if you want capacity; for a container with thick walls, the outside measurements give more than it holds.
  • Gallons are US liquid gallons of 231 cubic inches, not imperial gallons.

What this cannot tell you

  • Tapered containers such as most buckets and planters are not true cylinders. Measure across the middle for an estimate, or treat it as a cone with its tip cut off.
  • Capacity is to the brim. It says nothing about how full a container can safely be filled.
  • For concrete, gravel or mulch, the dedicated calculators add waste allowances and convert to bags or cubic yards.

Questions people ask

How do you find the volume of a cylinder?

Multiply the area of the circular end by the height: π × r² × h. For a radius of 3 and a height of 10, that is π × 9 × 10 = 90π, about 282.7433 cubic units. If you have the diameter, halve it first.

How many gallons are in a cubic foot?

About 7.4805. A cubic foot is 12 × 12 × 12 = 1,728 cubic inches, and a US gallon is 231 cubic inches, so 1,728 ÷ 231 = 7.4805 gallons. A liter is 1,000 cubic centimeters, so a cubic meter holds 1,000 liters.

Why is a cone one third of a cylinder?

A cone with the same base and height as a cylinder holds exactly a third as much, which you can show by filling one from the other three times. The same is true of a pyramid and the box with the same base and height.

What is the difference between volume and surface area?

Volume is how much a shape holds, in cubic units. Surface area is how much material covers its outside, in square units. A can’s volume is how much soup is in it; its surface area is how much metal it took to make.

Related calculators

Sources and review

Sources

Methodology version 1.0.0 · Last reviewed

Cite this calculator

For coursework, a resource list or your own site. How every calculator is built and checked is set out on the methodology page.

Citation

Chalk Calculator. (2026, October 5). Volume Calculator (Methodology version 1.0.0). https://chalkcalculator.com/volume-calculator/

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