Volume Calculator

How this is calculated

Each 3D shape has its own volume formula based on its dimensions. Select a shape above, enter its measurements, and the calculator applies the matching formula automatically.

Volume formulas by shape

Volume measures the three-dimensional space enclosed by a shape, expressed in cubic units. The formula depends entirely on the shape's geometry.

Formulas

Example: a cylinder with a 4-unit radius and 10-unit height has a volume of π × 4² × 10 ≈ 502.65 cubic units.

Quick reference table

Shape	Dimensions	Volume
Cylinder	r = 4, h = 10	502.65
Sphere	r = 5	523.60
Cube	side = 6	216.00
Cone	r = 3, h = 9	84.82

Common pitfalls

• Mixing units — all dimensions must be in the same unit (all inches, or all centimeters) before calculating.
• Confusing radius and diameter — these formulas use radius; if you only know the diameter, divide it by 2 first.
• Forgetting to cube the result unit — a volume in inches is in cubic inches, not square inches or plain inches.

Tips

• A cone's volume is always exactly one-third that of a cylinder sharing the same radius and height — useful as a quick sanity check.
• For irregular or composite shapes, break them into simple shapes like these, calculate each volume separately, and add them together.

Frequently asked questions

How do you find the volume of a cylinder? Multiply pi by the radius squared, then multiply by the height: Volume = π × r² × h.

What is the formula for the volume of a sphere? Volume = (4/3) × π × r³, where r is the sphere's radius.

How do I calculate the volume of a cube? Multiply the side length by itself three times: Volume = side³. A cube with 6-inch sides has a volume of 6³ = 216 cubic inches.

What is the volume of a cone? Volume = (1/3) × π × r² × h — exactly one-third the volume of a cylinder with the same base radius and height.

How is the volume of a rectangular box calculated? Multiply length × width × height. A box measuring 8 × 5 × 4 inches has a volume of 160 cubic inches.

What units does volume use? Volume is expressed in cubic units matching whatever length unit you enter — cubic inches, cubic feet, cubic centimeters, or cubic meters, for example. Keep all dimensions in the same unit before calculating.

What's the difference between volume and surface area? Volume measures the three-dimensional space a shape occupies (cubic units), while surface area measures the total area of its outer faces (square units) — this calculator shows both.

Worked examples

Example 1 — Cylindrical water tank: radius 4 ft, height 10 ft → volume ≈ 502.65 cubic feet, surface area ≈ 351.86 square feet.

Example 2 — Spherical ball: radius 5 in → volume ≈ 523.60 cubic inches, surface area ≈ 314.16 square inches.

Example 3 — Shipping box: 8 in × 5 in × 4 in → volume = 160 cubic inches, surface area = 184 square inches.

Turning volume into practical quantities

Example: a cylinder

A cylindrical tank has a radius of 3 m and a height of 10 m. Its volume is π × 3² × 10 ≈ 282.7 cubic metres. Because 1 cubic metre equals 1,000 litres, the tank holds about 282,700 litres.

Handy volume conversions

From	To
1 cubic metre	1,000 litres
1 litre	1,000 cubic centimetres
1 cubic foot	about 7.48 US gallons
1 cubic yard	27 cubic feet

Typical uses

• Estimating how much water a pool, tank or aquarium holds.
• Ordering soil, gravel or concrete, which are sold by the cubic yard or cubic metre.
• Choosing packaging and storage containers.
• Checking homework in geometry and physics.

More questions

Why is a cone one third of a cylinder? A cone with the same base and height as a cylinder fits into it exactly three times, so its volume is one third.

How accurate are tank estimates? They are idealised. Real tanks have thick walls, curved ends and fittings, so measure the interior dimensions for the best result.