Area Calculator

Calculate the area of a square, rectangle, triangle, parallelogram, trapezoid, rhombus, circle, sector, or ellipse — just pick a shape and the formula does the rest.

Area formulas by shape

Shape Formula
Square Area = side × side
Rectangle Area = width × height
Triangle Area = base × height ÷ 2
Parallelogram Area = base × height
Trapezoid Area = (top base + bottom base) × height ÷ 2
Rhombus Area = diagonal 1 × diagonal 2 ÷ 2
Circle Area = π × radius2
Circular sector Area = π × radius2 × (central angle ÷ 360)
Ellipse Area = π × semi-major axis × semi-minor axis

The area's unit is the square of whatever length unit you entered (e.g. enter values in cm and the result is in cm²).

Tips

  • For a more detailed triangle calculation (e.g. finding angles from three sides), use the sister tool "Triangle Calculator". This tool is meant for the simple case where you already know the base and height.
  • When a sector's central angle is 360°, its area equals the area of the full circle — you can verify this with the formula this tool uses.
  • A rhombus's area can be found from its two diagonals alone — no side lengths or angles needed.
  • An ellipse's area equals a circle's area (π × radius²) when its semi-major and semi-minor axes are equal.

FAQ

If you place two identical trapezoids together, rotated 180° from each other, they form a parallelogram whose base is the sum of the top and bottom bases and whose height matches the trapezoid's height. That parallelogram's area (base × height) is exactly twice the area of one trapezoid, which is where the ÷ 2 comes from.

This tool takes degrees (0–360). If your angle is given in radians, convert it first with degrees = radians × 180 ÷ π.

It uses JavaScript's built-in floating-point value (Math.PI, roughly 3.14159265358979). Results may differ very slightly from hand calculations that use 3.14.

This tool doesn't assume a specific length unit, so the area's unit is simply the square of whatever unit you entered. For example, if you enter lengths in centimeters, read the result as cm² (square centimeters).
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Side Note — Why a circle's area is "π times radius squared"

The formula for a circle's area, πr², is famously tied to Archimedes, who argued that slicing a circle into countless thin, near-triangular sectors and rearranging them produces a shape approaching a parallelogram — with a base equal to the circle's circumference (2πr) and a height equal to its radius (r). Since a parallelogram's area is base × height, that gives (2πr) × r ÷ 2 = πr², an intuitive derivation of the formula.

A sector's area formula (πr² × angle/360) simply applies the fraction of the full circle's angle (360°) that the sector covers to the full circle's area. The length of the corresponding arc follows the same logic (2πr × angle/360) — both area and arc length scale proportionally with the central angle, a core property of circles.

The formula for a trapezoid's area is recorded as far back as the Rhind Mathematical Papyrus of ancient Egypt (roughly 1650 BCE), a reminder that humans have needed to calculate the area of shapes — for land surveying and other practical purposes — since very early in recorded history.

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