Mathematics · Geometry
Surface Area Calculator — Cube, Cylinder, Cone, Sphere & More
Find the total surface area of 11 solids — cube, cuboid, cylinder, cone, sphere, hemisphere, pyramid, frustum, capsule, tube and ellipsoid — with the formula and your numbers shown step by step, plus the volume and capacity.
A ready-made version of the Volume Calculator — Any Solid.
Your inputs
Quick start — try a typical case
Your result Live
Surface area of the cylinder
245.04423 cm²
For radius 3, height 10
- Volume
- 282.74334 cm³
- 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/surface-area · version 1.1.0
Common questions
What is the surface area of a cylinder?
2πr² for the two ends plus 2πrh for the curved side: 2πr(r + h). For r = 3 cm and h = 10 cm that's 2π × 3 × 13 ≈ 245.04 cm².
What's the surface area of a sphere?
4πr² — exactly four times the area of a circle with the same radius.
Is surface area the same as volume?
No: surface area is the total area of the outside (square units); volume is the space inside (cubic units).