What this volume calculator does
This calculator gives the volume of a solid, the amount of space inside it, and the matching capacity in litres. Choose one of 11 solids (cube, rectangular box, sphere, hemisphere, cylinder, hollow tube, cone, truncated cone, square pyramid, triangular prism or ellipsoid), type its dimensions and the result appears as you type.
A drawing with the same letters as the input boxes shows what each number means, and the receipt also lists the total surface area for reference. It is handy for a water tank, a swimming pool, a planter to fill with soil, a concrete slab, a shipping box or a school exercise.
For the outside of the solid, such as the paint or wrapping it needs, use the surface area calculator. For flat shapes, use the area calculator.
How to use this calculator
- Pick the solid in the grid. The drawing shows which dimensions it needs.
- Choose the length unit (cm by default). Every box uses that same unit.
- Type each dimension. The volume and the capacity in litres update as you type.
- Read the volume in the big number, and the litres and total surface in the receipt.
- Tap the button under the result to see the surface area of the same solid with the same numbers.
An empty box simply keeps the receipt empty. A value that cannot work (zero, negative, an inner radius larger than the outer one) is explained next to the box to fix.
The formulas behind the results
Volume formulas follow one idea: base area times height, with a factor of one third for pointed solids.
Cylinder: V = π × r² × h · Cone: V = π × r² × h ÷ 3
Sphere: V = 4 ÷ 3 × π × r³ · Pyramid: V = a² × h ÷ 3
1 dm³ = 1 L · 1 m³ = 1,000 L
- A prism or cylinder is base area times height: πr² × h for a cylinder.
- A cone or pyramid is exactly one third of the prism with the same base and height.
- A sphere is 4/3 × π × r³, and a hemisphere is half of it.
- A hollow tube is the outer cylinder minus the inner one: π × (R² − r²) × h.
- A truncated cone is π × h × (R² + R × r + r²) ÷ 3.
Volumes are in cubic units: cm³, m³. The capacity in litres follows from 1 dm³ = 1 L, so 1,000 cm³ = 1 L and 1 m³ = 1,000 L. π is used at full precision and only the displayed result is rounded.
Worked examples
Example 1: how much water does a garden pool hold?
- Choose Rectangular box, unit m, and enter L = 8, l = 4 and h = 1.5.
- Volume: 8 × 4 × 1.5 = 48 m³.
- Capacity: 48 × 1,000 = 48,000 L.
48 m³, which is 48,000 litres. With a fill level 10 cm under the edge, use h = 1.4 for the real quantity: 44.8 m³.
Example 2: the capacity of a cylindrical tank
- Choose Cylinder, unit m, and enter r = 0.5 and h = 1.2.
- Volume: π × 0.5² × 1.2 ≈ 0.9425 m³.
- Capacity: 0.9425 × 1,000 ≈ 942.48 L.
About 0.94 m³, or roughly 942 litres. A 1,000-litre tank would need a height of about 1.27 m with the same radius.
Key concepts
Volume versus surface area
Volume measures the space inside a solid, in cubic units. Surface area measures its outside, in square units. Doubling every length multiplies the surface by 4 but the volume by 8, which is why a big tank holds so much more than its walls would suggest. For the outside, see the surface area calculator.
Volume and capacity: 1 dm³ = 1 L
A litre is the volume of a cube 10 cm on each side, that is 1 dm³ or 1,000 cm³. That is why a volume in cm³ divided by 1,000 gives litres, and a volume in m³ times 1,000 gives litres.
Inner and outer dimensions
A tank or a pipe has walls. For the quantity it can hold, measure the inside dimensions. For the material it takes, use the hollow tube, which subtracts the empty core.
Units that look alike
Do not mix cm and m in the same calculation. If needed, convert first with the unit converter.
Tips and common mistakes
Practical tips
- Measure inside the container for a capacity, not outside.
- A radius is the diameter divided by 2. A round tank 1 m across has r = 0.5.
- For a partly filled tank, use the water height as h, not the full height.
- Add 5 to 10% to concrete, soil or sand for waste and settling.
Common mistakes
- Typing the diameter in the radius box, which makes the volume four times too large.
- Mixing units, for example a radius in cm and a height in m.
- Reading a volume in m³ as litres: 1 m³ is 1,000 L, not 1 L.
- Using the vertical height where a cone's slant height is meant. This calculator only needs the vertical height.
Frequently asked questions
How do I find the volume of a cylinder?
Multiply the base area πr² by the height h. For r = 3 cm and h = 10 cm, that gives about 282.74 cm³, or 0.28 L.
How do I convert cubic metres to litres?
Multiply by 1,000. A volume of 2.5 m³ holds 2,500 litres. For other units, the unit converter can help.
Why is a cone one third of a cylinder?
A cone and a cylinder with the same base and height are linked by a factor of exactly 1/3. It can be proved with calculus or shown by filling a cone three times to fill a cylinder.
Does the calculator handle hollow objects?
Yes, with the hollow tube. Enter the outer radius, the inner radius and the length, and it subtracts the empty core.
Is the ellipsoid volume exact?
Yes. The volume of an ellipsoid is exactly 4/3 × π × a × b × c. Only its surface area is an approximation.
How do I get the surface of the same solid?
Use the button under the result. It opens the surface area calculator with the same solid and dimensions.