Area Formulas: Every Common Shape
Area measures the two-dimensional space enclosed by a shape, expressed in square units (cm², m², ft², etc.). The formula depends on the shape — here are the most commonly needed.
Core Area Formulas
- Rectangle/Square: A = length × width
- Triangle: A = ½ × base × height
- Circle: A = π × r² ≈ 3.14159 × r²
- Trapezoid: A = ½ × (a + b) × h (a, b = parallel sides)
- Parallelogram: A = base × height
- Ellipse: A = π × a × b (semi-axes a and b)
- Regular hexagon: A = (3√3 ÷ 2) × s² (s = side length)
Triangle: Three Methods
Base × height: A = ½bh
Heron's formula: A = √[s(s−a)(s−b)(s−c)], s = (a+b+c)÷2
Two sides + included angle: A = ½ab × sin(C)Circle from Diameter
A = π × (d÷2)² = π × d² ÷ 4
Diameter 10cm → A = π × 25 = 78.54 cm²Unit Conversions
- 1 m² = 10,000 cm²
- 1 ft² = 144 in²
- 1 acre = 4,047 m² = 43,560 ft²
- 1 hectare = 10,000 m² = 2.471 acres
Calculate area for any shape: Free Area Calculator