How to calculate area and perimeter
- 1.
Choose the type
2D shapes (area, perimeter, diagonals) or 3D solids (volume, surface area).
- 2.
Choose the shape
E.g. a triangle from base and height or from three sides, a circle by radius or diameter, a trapezoid or a cylinder.
- 3.
Enter dimensions
Use one unit for all lengths and select it from the list (mm, cm, dm, m, km or no unit).
- 4.
Read the results
See the results, the formulas with your numbers substituted and a labelled diagram; copy the calculation if you need it.
Area and perimeter formulas for 2D shapes
| Shape | Area | Perimeter |
|---|---|---|
| Square | A = a² | P = 4a |
| Rectangle | A = ab | P = 2a + 2b |
| Triangle | A = ah/2 | P = a + b + c |
| Equilateral triangle | A = a²√3/4 | P = 3a |
| Circle | A = πr² | C = 2πr = πd |
| Trapezoid | A = (a + b)h/2 | P = a + b + c + d |
| Parallelogram | A = ah | P = 2a + 2b |
| Rhombus | A = ef/2 | P = 4a |
| Regular hexagon | A = 3a²√3/2 | P = 6a |
| Ellipse | A = πab | ≈ π[3(a + b) − √((3a + b)(a + 3b))] |
Example: a circle with r = 5 cm has an area of about 78.5398 cm² and a circumference of about 31.4159 cm. A rectangle of 4 × 2.5 m has an area of 10 m² and a perimeter of 13 m. For the trapezoid and parallelogram the perimeter appears once you enter the optional legs or side.
Heron’s formula: a triangle from three sides
When you know all three sides but not the height: A = √(s(s − a)(s − b)(s − c)), where s = (a + b + c)/2 is the semi-perimeter. Sides 13, 14, 15 give s = 21 and A = √(21 · 8 · 7 · 6) = √7056 = 84.
The sides must satisfy the triangle inequality - each side shorter than the sum of the other two. Lengths 2, 3 and 6 cannot form a triangle, and the calculator reports this instead of returning a wrong area.
Volume and surface area of solids
| Solid | Volume | Total surface area |
|---|---|---|
| Cube | V = a³ | S = 6a² |
| Cuboid (box) | V = abc | S = 2(ab + bc + ac) |
| Cylinder | V = πr²h | S = 2πr² + 2πrh |
| Cone | V = πr²h/3 | S = πr² + πrl, l = √(r² + h²) |
| Sphere | V = 4/3·πr³ | S = 4πr² |
| Square pyramid | V = a²H/3 | S = a² + 2a·hₛ |
Example: a 2 × 3 × 4 cuboid has V = 24 and S = 52; its space diagonal is √29 ≈ 5.39. For the cylinder, cone and pyramid the results also include the lateral surface area, and for the cone and pyramid the slant height.
Units and common mistakes
Area is in square units and volume in cubic units, so conversions grow fast: 1 m² = 10,000 cm² and 1 m³ = 1,000,000 cm³ = 1,000 litres. The unit list is metric; for inches or feet choose “no unit”, enter the values and read the area in in² or ft² yourself (1 ft² = 144 in²). To convert lengths first, use the length converter.
- Radius vs diameter - r is half of d. Switch the circle input to diameter if that is what you measured.
- Slanted side instead of height - a parallelogram’s area uses the perpendicular height, not side b.
- Mixed units - 2 m and 50 cm must become 2 m and 0.5 m before multiplying.
Measuring a room or a wall? The square meter calculator and the paint calculator handle real-life layouts.
Frequently asked questions
How do I find the area of a circle?
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How do I find the area of a triangle from its sides?
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How do I find the volume of a cylinder?
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What is the difference between area and perimeter?
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How many cm² are in 1 m²?
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Can I use inches or feet?
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Is the ellipse perimeter exact?
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