Area & Volume Calculator
10 flat shapes and 8 solids
Choose a Shape
Circle area
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Perimeter-
Capacity-
2D Area Formulas
| Shape | Area | Perimeter |
|---|---|---|
| Rectangle | width × height | 2 × (width + height) |
| Square | side² | 4 × side |
| Triangle | base × height ÷ 2 | - |
| Circle | π × r² | 2 × π × r |
| Trapezoid | (a + b) × height ÷ 2 | - |
| Parallelogram | base × height | - |
| Rhombus | d1 × d2 ÷ 2 | 4 × √((d1/2)² + (d2/2)²) |
| Ellipse | π × a × b | Ramanujan approximation |
| Sector | π × r² × angle ÷ 360 | 2r + arc length |
| Regular polygon | n × side² ÷ (4 tan(180°/n)) | n × side |
3D Volume Formulas
| Shape | Volume | Surface area |
|---|---|---|
| Rectangular box | l × w × h | 2(lw + wh + hl) |
| Cube | side³ | 6 × side² |
| Cylinder | π × r² × h | 2πr(r + h) |
| Cone | π × r² × h ÷ 3 | πr(r + slant height) |
| Sphere | 4/3 × π × r³ | 4πr² |
| Hemisphere | 2/3 × π × r³ | 3πr² |
| Square pyramid | a² × h ÷ 3 | a² + 2a√((a/2)² + h²) |
| Triangular prism | base × height ÷ 2 × length | - |
1 liter = 1,000 cm³; 1 m³ = 1,000 liters; 1 ft³ = 28.32 liters = 7.48 US gallons. A cone's slant height is √(r² + h²).
Formulas & Sources
- π = 3.14159265… (full precision)
- Ellipse perimeter: Ramanujan's approximation π[3(a+b) − √((3a+b)(a+3b))]
- Capacity: 1 cm³ = 1 mL, 1 in³ = 16.387 mL, 1 ft³ = 28.317 L
Last reviewed: 2026-10-19
FAQ
How do I find the area of a circle?
Area = π × r². A circle with a 5-inch radius has an area of about 78.54 in² and a circumference of about 31.42 in.
What is the formula for the area of a trapezoid?
(top + bottom) × height ÷ 2. With sides 4 and 8 and a height of 5, the area is 30.
How do I convert volume to liters or gallons?
Calculate cubic units first: 1,000 cm³ = 1 liter, 1 in³ = 16.387 mL and 1 ft³ = 7.48 US gallons. The calculator shows both.
What are the volume and surface area of a sphere?
Volume = 4/3 × π × r³ and surface area = 4 × π × r². A 10 cm sphere holds about 4,189 cm³ (4.19 L).
Why is a cone one third of a cylinder?
A cone (or pyramid) always has one third of the volume of a cylinder (or prism) with the same base and height.