Mathematics · Geometry
Area Calculator — Any Shape
Find the area — and perimeter or circumference — of 12 shapes: square, rectangle, triangle (from base and height or from three sides), circle, semicircle, sector, ellipse, trapezoid, parallelogram, rhombus and any regular polygon, with the formula and your numbers substituted.
Your inputs
Quick start — try a typical case
Your result Live
Area of the rectangle
40 cm²
For length 8, width 5
- Perimeter
- 26 cm
- Area in m²
- 0.004 m²
Working
A: Step 1 · Area
A = l × w = 8 × 5
Expression becomes 40 cm²
P: Step 2 · Perimeter
P = 2(l + w)
Expression becomes 26 cm
How this is calculated
Rectangle lw · Triangle ½bh · Heron √(s(s−a)(s−b)(s−c)) · Circle πr² · Trapezoid ½(a + b)h · Regular polygon ns² ÷ (4 tan(π/n))
- s
- Semi-perimeter (a + b + c) ÷ 2 in Heron's formula; side length for regular polygons
- π
- 3.14159…
Area measures the flat surface inside a shape, in square units. Each shape has its own formula; the working shows it with your numbers. If you know a triangle's three sides but not its height, Heron's formula finds the area anyway.
Assumptions & sources
- Regular polygons have equal sides and angles; the ellipse perimeter uses Ramanujan's approximation (error far below 0.01 %).
Calculator ID MATH-AREA-001 · version 1.0.0
Common questions
How do I find the area of a triangle without the height?
Use Heron's formula: with sides a, b, c and s = (a + b + c) ÷ 2, the area is √(s(s−a)(s−b)(s−c)). A 5-6-7 triangle has an area of about 14.7.
What's the area of a circle of radius 7 cm?
πr² = π × 49 ≈ 153.94 cm².