About this calculator
Choose a shape, enter its measurements, and get its area (and perimeter where it has a simple one), with the formula worked through.
It covers rectangles, triangles (by base and height, or by three sides using Heron's formula), trapeziums, parallelograms, ellipses and regular polygons.
Worked examples
Real numbers, worked out by the same calculator. Press “Use these numbers” to try one above.
Rectangle 4 × 3
- Area
- 12
- Perimeter
- 14
The area of the rectangle is 12 square units and its perimeter is 14 units.
Show the working
- Area = length × width = 4 × 3 = 12.
- Perimeter = 2 × (length + width) = 2 × (4 + 3) = 14.
Triangle with sides 3, 4 and 5
- Area
- 6
- Perimeter
- 12
The area of the triangle is 6 square units and its perimeter is 12 units.
Show the working
- Half the perimeter: s = (3 + 4 + 5) ÷ 2 = 6.
- Heron's formula: area = √(s × (s − a) × (s − b) × (s − c)) = √(6 × 3 × 2 × 1) = 6.
- Perimeter = 3 + 4 + 5 = 12.
Regular hexagon, side 2
- Area
- 10.392305
- Perimeter
- 12
The area of the regular 6-sided polygon is 10.392305 square units and its perimeter is 12 units.
Show the working
- Area = n × s² ÷ (4 × tan(π ÷ n)) = 6 × 2² ÷ (4 × tan(π ÷ 6)) = 10.392305.
- Perimeter = n × s = 6 × 2 = 12.
Area formulas
- Rectangle: length × width
- Triangle: ½ × base × height
- Trapezium: ½ × (a + b) × height
- Parallelogram: base × perpendicular height
- Ellipse: π × a × b
- Regular polygon: n × side² ÷ (4 × tan(π ÷ n))
Heron's formula for three sides
If you know all three sides but not the height, work out the semi-perimeter s = (a + b + c) ÷ 2, then area = √(s(s − a)(s − b)(s − c)). The sides must satisfy the triangle rule: the two shorter sides together must be longer than the longest.
Units
Use the same unit for every measurement. The area is in that unit squared: centimetres give cm², metres give m². To change area units, use the area converter.
Frequently asked questions
How do I find the area of a triangle with three sides?
Use Heron's formula: with s half the perimeter, area = √(s(s − a)(s − b)(s − c)). Choose “Triangle (three sides)” above.
Why is there no perimeter for some shapes?
A triangle by base and height, a trapezium and a parallelogram don't give enough information to find the perimeter; you'd also need the slanted sides.
Is the ellipse perimeter exact?
No. There is no simple exact formula, so it uses Ramanujan's approximation, which is accurate to many decimal places.
What is the area of a regular hexagon with side 2?
About 10.3923 square units.
Formulas tested against hand-worked answers. Last reviewed 29 September 2026. These calculators do arithmetic only; they are not financial, tax or legal advice.