Volume Calculator

Volume and surface area of a cube, cylinder, cone, sphere, tank and more, in litres, gallons or cubic units.

Shape

Length

Width

Height

Unit

Volume in

Decimal places

Volume

300 L

Cubic metre: 0.3 m³
Gallon (US): 79.25 US gal

Total surface area: 2.8 m²
Lateral surface: 1.6 m²
Base: 0.6 m²
Space diagonal: √161/10 ≈ 1.27 m

Show working

Choose a solid, type its dimensions, and get its volume in litres, cubic metres, cubic feet or US and imperial gallons, with its total, curved and base surface areas, the formulas worked in your numbers and a diagram drawn to scale. 15 solids are covered, from a box or a cylinder to a frustum, a spherical cap and a torus.

Tank fill answers the practical question about a tank: how much liquid it holds at a measured depth, as a volume and as a percentage of the full tank, for a horizontal or vertical cylinder or a box.

How to use it

Every dimension is in the one unit chosen under the fields; in feet a field also takes feet and inches (4' 6"). The volume shows in litres when the unit is metric and in cubic feet when it is imperial, and Volume in switches it to millilitres, cubic centimetres or metres, cubic inches, or either gallon. Surface areas are in the chosen unit squared. Answers show up to 2 decimal places, or ten significant figures with Decimal places set to Auto.

A US gallon (3.785411784 L) and an imperial gallon (4.54609 L) differ by a fifth, so the tool always names which one it means.

How it works

Exact measurements keep π exact: a cylinder of radius 5 and height 10 is 250π, about 785.4. A litre is exactly one cubic decimetre, so 1 m³ is exactly 1,000 L and the conversion adds no rounding. An ellipsoid's surface area has no formula in elementary terms; the tool evaluates Legendre's formula with elliptic integrals, accurate to the digits shown.

A horizontal cylindrical tank is filled to a depth d as a circle is filled to d: the liquid's end is a circular segment, and the volume is that segment's area times the tank's length. A vertical tank or a box fills in proportion to the depth.

Box: V = l × w × h, S = 2(lw + lh + wh)

Cylinder: V = πr²h, S = 2πrh + 2πr²

Cone: V = ⅓πr²h, S = πr(r + s), s = √(r² + h²)

Sphere: V = 4/3 πr³, S = 4πr²

Pyramid: V = ⅓ × base area × h

Frustum: V = ⅓πh(R² + Rr + r²)

Spherical cap: V = ⅓πh²(3R − h)

Torus: V = 2π²Rr², S = 4π²Rr

Horizontal tank at depth d: V = L × (r² acos((r − d) ÷ r) − (r − d)√(2rd − d²))

Examples

A tank 1 m × 0.6 m × 0.5 m in litres

The volume is 0.3 m³, which is 300 L: each cubic metre holds 1,000 litres.

A horizontal tank half and a quarter full

A tank 1.2 m across and 3 m long holds 3,392.92 L. At a depth of 0.6 m it is half full, 1,696.46 L. At 0.3 m, a quarter of the depth, it holds 663.32 L, only 19.55% of the tank: the narrow bottom of the circle holds little.

The surface of a 10 ft cylinder

A cylinder of radius 2 ft and height 10 ft has a total surface of 48π ≈ 150.7964474 ft², of which the curved side is 40π ≈ 125.6637061 ft², the area to paint or wrap.

Volume = πr²h V = π × 2² × 10 = 40π ≈ 125.6637061 ft³
Curved surface = 2πrh = 2π × 2 × 10 = 40π ≈ 125.6637061 ft²
Surface area = 2πrh + 2πr² S = 48π ≈ 150.7964474 ft²

Volume units

One of each unit in litres, US gallons and imperial gallons

Unit	Litres	US gallons	Imperial gallons
Litre (L)	1	0.2641720524	0.2199692483
Cubic metre (m³)	1,000	264.1720524	219.9692483
Cubic foot (ft³)	28.31684659	7.480519481	6.228835459
Cubic inch (in³)	0.016387064	0.004329004329	0.00360465015
Gallon (US) (US gal)	3.785411784	1	0.8326741846
Gallon (imperial) (imp gal)	4.54609	1.200949926	1

Frequently asked questions

Exactly 1,000. A litre is defined as one cubic decimetre, a cube 10 cm on each side, and a cubic metre holds 10 × 10 × 10 of them.