Mathematics · Geometry
Volume Calculator — Any Solid
Find the volume and surface area of 11 solids — cube, cuboid or tank, cylinder, cone, sphere, hemisphere, pyramid, frustum (bucket), capsule, tube or pipe, and ellipsoid — with the formula worked through, and the capacity in litres and gallons.
Your inputs
Quick start — try a typical case
Your result Live
Volume of the cylinder
282.74334 cm³
For radius 3, height 10
- Surface Area
- 245.04423 cm²
- Capacity
- 0.28274334 litres · 0.074692888 US gal · 0.00028274334 m³
Working
V: Step 1 · Volume
V = πr²h = π × 3² × 10
Expression becomes 282.74334 cm³
SA: Step 2 · Surface area
SA = 2πr(r + h)
Expression becomes 245.04423 cm²
How this is calculated
Cylinder πr²h · Cone ⅓πr²h · Sphere ⁴⁄₃πr³ · Pyramid ⅓ × base × h · Frustum ⅓πh(r₁² + r₁r₂ + r₂²)
- 1 litre
- 1,000 cm³ = 0.001 m³ · 1 US gallon = 3.785 litres
Volume is the space a solid takes up, in cubic units; surface area is the total area of its faces. Pick the solid, enter its dimensions, and the working shows the formula with your numbers. For tanks and containers, the capacity is given in litres and gallons too.
Assumptions & sources
- Ellipsoid surface area uses Knud Thomsen's approximation (within about 1 %).
Calculator ID MATH-VOLUME-001 · version 1.1.0
Common questions
How many litres does a cylindrical tank hold?
Volume = πr²h. A tank 1 m across (r = 0.5 m) and 1.5 m tall holds π × 0.25 × 1.5 ≈ 1.178 m³ = 1,178 litres.
Why is a cone one third of a cylinder?
A cone with the same base and height as a cylinder has exactly one third of its volume — the same relationship as between a pyramid and a prism.