Charts & references · 3 min read
Geometry Formulas Cheat Sheet: Area, Perimeter, Volume
Plane shapes
| Shape | Area | Perimeter |
|---|---|---|
| Rectangle | l × w | 2(l + w) |
| Square | s² | 4s |
| Triangle | ½ × b × h | a + b + c |
| Parallelogram | b × h | 2(a + b) |
| Trapezoid | ½(a + b) × h | sum of sides |
| Circle | πr² | 2πr |
Solids
| Solid | Volume | Surface area |
|---|---|---|
| Cube | s³ | 6s² |
| Cuboid | lwh | 2(lw + wh + lh) |
| Cylinder | πr²h | 2πr(r + h) |
| Sphere | 4/3 πr³ | 4πr² |
| Cone | 1/3 πr²h | πr(r + l) |
Sphere with radius 3
Step-by-step working 3 steps
- 1Volume
V = 4/3 πr³ = 4/3 × π × 3³ = 113.097336
- 2Surface area
A = 4πr² = 4π × 3² = 113.097336
- 3Units
If lengths are in cm, volume is in cm³ and surface area in cm². Keep every length in the same unit.
Triangles
- Pythagorean theorem (right triangles): a² + b² = c²
- Heron’s formula: A = √(s(s−a)(s−b)(s−c)), s = (a+b+c)/2
- Angles in a triangle add to 180°
Try the triangle calculator or Pythagorean theorem calculator.
Units
Area is in square units and volume in cubic units. Convert all lengths to one unit first — see the area and perimeter guide.
Frequently asked questions
What is the difference between area and perimeter?
Area measures the surface inside a shape; perimeter measures the distance around it.
How do I find the volume of a cylinder?
Multiply the area of the circular base (πr²) by the height.
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