# Area Calculator — Triangle, Rectangle, Circle & More

> Find the area of a circle, rectangle, square, triangle, trapezoid, parallelogram, ellipse or regular polygon. Works in mm, cm, m, inches and feet. Free.

- **Category:** Math
- **Interactive calculator:** https://youcalc.com/en/math/area-calculator/
- **Price:** Free, no sign-up required

## Overview

Area is the amount of flat space a shape covers, measured in square units. This calculator handles the eight figures you meet most often — circle, rectangle, square, triangle, trapezoid, parallelogram, ellipse and regular polygon — and returns the area from the dimensions you type. Work in millimetres, centimetres, metres, inches or feet; the answer comes back in those units squared and is restated in every other unit so a length entered in inches can be read off in square metres without retyping. For the radius, diameter, circumference and sector area of a circle, use the dedicated Circle Calculator.

## How to read your result

The large figure is the area in the unit you chose, squared. Triangles offer two ways in: enter a base and the perpendicular height, or — when you only know the three side lengths — switch to “Three sides” and the calculator uses Heron’s formula. For a trapezoid, a and b are the two parallel sides and h is the perpendicular distance between them; for an ellipse, a and b are the semi-axes (half the full width and half the full height). The “same area in other units” panel converts the result through the square of the length factor, so 1 ft² = 0.0929 m².

## Method

Each shape has its own formula, all in the chosen unit squared. Circle: A = π × r². Rectangle: A = length × width. Square: A = side². Triangle: A = ½ × base × height, or by Heron’s formula A = √(s(s−a)(s−b)(s−c)) with s = (a+b+c) ÷ 2 when only the three sides are known. Trapezoid: A = ½ × (a + b) × h, where a and b are the parallel sides. Parallelogram: A = base × height. Ellipse: A = π × a × b, with a and b the semi-axes. Regular polygon with n equal sides of length s: A = ¼ × n × s² × cot(π ÷ n).

## Example

- **Setup:** A triangle with a base of 6 cm and a height of 4 cm.
- **Result:** The area is ½ × 6 × 4 = 12 cm². If instead you knew the three sides 3 cm, 4 cm and 5 cm, Heron’s formula gives s = (3 + 4 + 5) ÷ 2 = 6 and area = √(6 × 3 × 2 × 1) = 6 cm².

## Frequently asked questions

### How do I find the area of a triangle if I only know the three sides?

Use Heron’s formula. Add the three sides and halve the total to get the semi-perimeter s = (a + b + c) ÷ 2, then take the square root of s(s − a)(s − b)(s − c). For a 3-4-5 triangle, s = 6 and the area is √(6 × 3 × 2 × 1) = 6. Switch the triangle to “Three sides” mode and the calculator does this for you.

### What is the difference between a trapezoid and a parallelogram?

A trapezoid has one pair of parallel sides of different lengths (a and b), so its area is the average of those two sides times the height: ½ × (a + b) × h. A parallelogram has both pairs of sides parallel and equal, so the area is simply base × height. When a = b a trapezoid becomes a parallelogram and both formulas agree.

### How is the area of a regular polygon calculated?

A regular polygon has n equal sides of length s. Its area is ¼ × n × s² × cot(π ÷ n). For a regular hexagon (n = 6) with a side of 2, that is ¼ × 6 × 4 × cot(30°) = 6√3 ≈ 10.39 square units. As the number of sides grows, the area approaches that of the circle the polygon fits inside.

### Which units can I use, and how does the conversion work?

Millimetres, centimetres, metres, inches and feet. Lengths convert through the exact international definitions (1 inch = 2.54 cm, 1 foot = 0.3048 m), and areas convert by the square of that length factor — so 1 ft² = 0.3048² m² = 0.0929 m². The “other units” panel does this automatically for every result.

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## Sources

- https://mathworld.wolfram.com/Area.html
- https://en.wikipedia.org/wiki/Area
- https://mathworld.wolfram.com/HeronsFormula.html

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