How this calculator works
Each shape uses its own standard area formula. Every length field is converted to metres first, so mixed metric and imperial measurements are safe to combine, and the result is shown in the area unit you choose. Quadrilaterals multiply perpendicular dimensions, a triangle uses Heron's formula from three sides or a sine formula from two sides and the included angle, and a regular polygon uses the number of sides together with one side length. All measurements must be greater than zero, a triangle must satisfy the triangle inequality, and an annulus needs an inner radius smaller than its outer radius.
Formula
Square: s². Rectangle: l × w. Triangle: ½bh, Heron's formula, ½bc sin A, or c² sin A sin B / (2 sin(A + B)). Circle: πr². Semicircle: ½πr². Sector: ½r²θ. Ellipse: πab. Trapezoid: ½(a + b)h. Parallelogram: bh. Rhombus and kite: ½d₁d₂. Annulus: π(R² - r²). Quadrilateral: ½ef sin θ. Regular polygon: n s² / (4 tan(π/n)).
Worked example
A circle of radius 3 has area π × 9 ≈ 28.2743 m². A trapezoid with parallel sides 6 m and 4 m and height 3 m has area ½ × 10 × 3 = 15 m². A triangle with sides 3 m, 4 m and 5 m has semiperimeter 6 m and area √(6 × 3 × 2 × 1) = 6 m².
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Frequently asked questions
Which height should I measure?
Use the perpendicular distance, not a slanted side. For a triangle it runs from a base to the opposite vertex; for a trapezoid or parallelogram it is the distance between the parallel sides.
Why does the three-side triangle reject my values?
Any two sides must add up to more than the third side. If they do not, the three lengths cannot meet to form a closed triangle.
What angle belongs in the quadrilateral mode?
Enter the angle where diagonals e and f cross. The area of any quadrilateral is half the product of its diagonals and the sine of the angle between them.
Can I mix feet and metres?
Yes. Each length is converted to metres before the formula runs. Choose the output unit beside the area to read the result in square feet or square inches.