Area Calculator

How to Calculate Area

Area is the measure of a two-dimensional surface — the number of unit squares that fit inside a shape. Select the shape that matches your problem, enter the required measurements, and the calculator shows area and perimeter instantly.

Area Formulas for Common Shapes

Shape	Area Formula	Perimeter Formula
Rectangle	A = width × height	P = 2(w + h)
Square	A = side²	P = 4 × side
Circle	A = πr²	C = 2πr
Triangle	A = ½ × base × height	P = a + b + c
Trapezoid	A = ½(a + b) × height	P = a + b + c + d
Ellipse	A = π × a × b	P ≈ 2π√((a²+b²)/2)

Frequently Asked Questions

For irregular shapes, divide the shape into familiar geometric pieces (rectangles, triangles, circles), calculate each area separately, and add them together. For very complex shapes, digitization tools or the Shoelace formula (for polygons defined by coordinates) can help.

Area measures the two-dimensional space inside a shape (in square units). Perimeter measures the total length around the boundary of a shape (in linear units). A 10×10 square has area 100 sq ft and perimeter 40 ft.

Pi (π ≈ 3.14159) is the ratio of a circle's circumference to its diameter — a universal constant. The area formula A = πr² comes from calculus: integrating thin concentric rings from radius 0 to r produces this exact result. π appears everywhere in circular and wave mathematics because of the fundamental geometry of circles.

Common conversions: 1 square foot = 144 square inches; 1 square meter = 10,000 square centimeters; 1 acre = 43,560 square feet; 1 hectare = 10,000 square meters = 2.471 acres. To convert square units, square the linear conversion factor: since 1 m = 100 cm, 1 m² = 100² = 10,000 cm².