Math calculators
Area and volume calculator
Area and perimeter of circles, triangles, polygons and more, and volume and surface area of spheres, cylinders, cones, cubes and pyramids.
Inputs
Results
Methodology
Conventions
- All lengths are in the same unit; areas are in that unit squared and volumes cubed.
- A triangle takes three sides (Heron's formula) or a base and height. The pyramid has a square base.
- An ellipse's perimeter has no closed form; Ramanujan's second approximation is used, which is very accurate unless the ellipse is extremely flat.
References
- Ramanujan, Modular equations and approximations to π (1914)
Formulas
- Heron
- A = \sqrt{s(s - a)(s - b)(s - c)},\quad s = \tfrac{a + b + c}{2}
- Ellipse perimeter
- P \approx \pi(a + b)\left(1 + \frac{3h}{10 + \sqrt{4 - 3h}}\right),\ h = \frac{(a - b)^2}{(a + b)^2}
- Sphere
- V = \tfrac43 \pi r^3,\quad S = 4\pi r^2
- Cone
- V = \tfrac13 \pi r^2 h,\quad S = \pi r(r + \sqrt{r^2 + h^2})