Volume Calculator
Find the volume of any common 3D solid in seconds. Choose from 12 shapes, enter the dimensions in metric or imperial units, and get the volume with full unit conversions (litres, gallons, cubic feet), the surface area, and a step-by-step worked solution.
Formula
Worked example
A cylinder with radius 5 cm and height 20 cm: V = pi x 25 x 20 = 1,570.80 cm³ = 1.571 L. The same cylinder hollowed with a 4 cm inner radius becomes a tube: V = pi x (25 - 16) x 20 = 565.49 cm³ = 0.565 L.
How the volume is calculated for each shape
Volume measures the three-dimensional space a solid occupies, always expressed in cubic units. A cube raises its side length to the power of three. A rectangular box multiplies its three dimensions. Curved solids bring in pi: a cylinder is the circle area times height, a cone is a third of that, and a sphere is four-thirds pi times the radius cubed. A hemisphere is half a sphere. A conical frustum (a truncated cone) uses a weighted average of the two circular faces. An ellipsoid is like a sphere but with three different radii. A capsule adds a sphere to the ends of a cylinder. A square pyramid is one-third of the bounding box. A triangular prism with an equilateral base uses the equilateral triangle area formula. A hollow cylinder (tube) subtracts the inner cylinder from the outer one.
Unit conversions and why they matter
Every dimension you enter must be in the same unit, chosen from the "Dimension units" dropdown. The primary result is in cubic units of that choice: enter centimetres, get cubic centimetres; enter inches, get cubic inches. The calculator then automatically converts to litres, US gallons, cubic feet, and more, so you can cross-check tank capacities or material orders without doing extra arithmetic. Litres are especially convenient because one litre equals exactly 1,000 cubic centimetres. A US gallon is about 3,785 cubic centimetres. Keep every dimension in one unit and rely on the conversion table at the bottom for the rest.
Surface area and why it is shown alongside volume
Surface area measures the total outer skin of the solid in square units. It is useful whenever you need to paint, coat, insulate, or cover an object. For example, the surface area of a cylinder tells you how much sheet metal to cut for a can, and the surface area of a sphere tells you how much leather to cut for a ball. The calculator returns both volume and surface area together so you can plan material quantities from one tool. The surface area formula for each shape matches the standard geometric definition: for a cone it includes the lateral surface and the base, for an ellipsoid it uses the Knud Thomsen approximation (accurate to within about one percent for most proportions).
Practical examples: tanks, shipping, and construction
A cylindrical water tank 1 metre in radius and 2 metres tall holds about 6,283 litres, enough for several days of household use. A rectangular shipping box 40 cm by 30 cm by 20 cm has a volume of 24,000 cm³, or 24 litres. A conical hopper with a top radius of 50 cm, bottom radius of 10 cm, and height of 80 cm holds about 223 litres of grain. An ellipsoidal storage tank with semi-axes of 2 m, 1.5 m, and 1 m holds roughly 12,566 litres. These examples show why the unit conversion table matters: the same number in cm³ is hard to visualise, but its litre or gallon equivalent makes sense at a glance.
Volume formulas for all 12 shapes
| Shape | Formula | Inputs needed |
|---|---|---|
| Cube | V = s³ | s |
| Box (rectangular prism) | V = l × w × h | l, w, h |
| Sphere | V = (4/3) π r³ | r |
| Hemisphere | V = (2/3) π r³ | r |
| Cylinder | V = π r² h | r, h |
| Hollow cylinder (tube) | V = π (R² - r²) h | R, r, h |
| Cone | V = (1/3) π r² h | r, h |
| Conical frustum | V = (1/3) π h (R² + Rr + r²) | R, r, h |
| Ellipsoid | V = (4/3) π a b c | a, b, c |
| Square pyramid | V = (1/3) s² h | s, h |
| Capsule | V = π r² (h + 4r/3) | r, h |
| Triangular prism (equilateral) | V = (sqrt(3)/4) b² h | b, h |
r = radius, h = height, s = edge, l/w = length/width, a/b/c = semi-axes, R = outer radius, b = base edge. Volume is in cubic units.
Frequently asked questions
What units does the volume come out in?
The primary result is in cubic units matching whatever length unit you chose in the "Dimension units" dropdown. For example, centimetres gives cubic centimetres (cm³), inches gives cubic inches (in³). The conversion table and secondary outputs then translate the same volume to litres, US gallons, cubic feet, and more automatically.
How do I convert the volume to litres or gallons?
If you measured in centimetres the result in cm³ equals millilitres, so divide by 1,000 to get litres. If you measured in inches, divide by 61.024 to get litres. The calculator does all of this for you in the output panel and in the unit-conversion table below the result. For US gallons, 1 gallon is about 3,785 cm³ or 231 cubic inches.
What is a conical frustum and when would I use that shape?
A conical frustum is a cone with its pointed top cut off by a flat horizontal plane, leaving two circular faces of different sizes. Common examples include buckets, flower pots, stadium cups, and grain hoppers. Enter the bottom radius (R), top radius (r), and height (h) to get the exact volume.
How is a capsule different from a cylinder?
A capsule has a cylindrical middle section capped on each end by a hemisphere. Its total volume equals the cylinder volume plus one full sphere of the same radius: V = pi × r² × h + (4/3) × pi × r³. The height input is the straight cylinder section only, not the overall length including the two caps. Capsule shapes appear in pharmaceutical tablets, some tanks, and submarines.
Why is the surface area of an ellipsoid approximate?
There is no simple closed-form formula for the surface area of a general ellipsoid. This calculator uses the Knud Thomsen approximation, which is accurate to within about one percent for most practical proportions. For a perfect sphere (all three semi-axes equal) the formula reduces to exactly 4 pi r², and for very elongated or flattened ellipsoids the error may be slightly higher.
Can I use this for a hollow pipe or tube?
Yes. Select "Hollow cylinder (tube)" and enter the outer radius (R), the inner radius (r, which must be smaller than R), and the length. The volume is the annular cross-section area (pi times R-squared minus r-squared) multiplied by the height. This gives the volume of material in the pipe wall, not the interior space.