Area Calculator (rectangle, triangle, circle, trapezoid & more)

Understanding the area calculator — concept and principle

This calculator finds the area, and where possible the perimeter, of common flat shapes: rectangle, square, triangle, circle, ellipse, trapezoid, parallelogram, rhombus, circular sector, regular polygon and ring. Use it for homework, floor and garden plans, fabric and material estimates.

Area counts the unit squares that fit inside; perimeter measures the edge.

How it is calculated

Rectangle A = a × b; square A = a²; parallelogram A = base × height.
Triangle A = ½ × base × height; from three sides, Heron's formula A = √(s(s − a)(s − b)(s − c)) with s = (a + b + c) ÷ 2.
Circle A = πr²; ellipse A = πab (perimeter by Ramanujan's approximation).
Trapezoid A = (a + b) ÷ 2 × h; rhombus A = d₁ × d₂ ÷ 2.
Sector A = πr² × angle ÷ 360; regular n-gon A = n a² ÷ (4 tan(π/n)); ring A = π(R² − r²).

Any length unit works; the area is in that unit squared. The perimeter shows — when it needs a length you did not enter.

The principle

Area counts how many unit squares fit inside a shape. A rectangle a by b holds exactly a × b of them. Most other formulas come from cutting and rearranging: a parallelogram can be sliced and slid into a rectangle with the same base and height, a triangle is half a parallelogram, and a trapezoid is a rectangle with the average of the two parallel sides as its width. A circle can be cut into thin wedges that rearrange into a near-rectangle of width πr and height r, giving πr².

Worked example

Default inputs: rectangle, a = 8, b = 5 (c = 6 is not used).

Formula used: A = a × b, inputs used a, b.
Area = 8 × 5 = 40 square units.
Perimeter = 2 × (8 + 5) = 26 units.

Each point is the calculator re-run with only “a” changed; the gold point is the default example. Change the inputs above and this chart follows your numbers.

a	Area
2	10
4	20
6	30
8	40
10	50
12	60
16	80

How to read the result

Keep track of units: if you enter metres, the area is in m² and the perimeter in m. Doubling every length multiplies the area by four, not two. For real rooms or plots that are not perfect shapes, split them into simple pieces, find each area and add them up. If two shapes have the same perimeter, the one closer to a circle or square has the larger area.

Common mistakes

Using the slanted side instead of the perpendicular height for a triangle, parallelogram or trapezoid.
Entering a diameter where the radius is asked for.
Forgetting the ½ in the triangle and rhombus formulas.
Mixing units, such as metres and centimetres, in one calculation.

Keep in mind: Results are exact for ideal shapes. Real objects have rounded corners and uneven edges, so add an allowance when ordering material.

Frequently asked questions

How do I find the area of an L-shaped room?

Split it into two rectangles, calculate each and add them.

What is the area of a circle with radius 3?

π × 3² ≈ 28.27 square units.

Can I find a triangle's area without its height?

Yes, from its three sides with Heron's formula.

Sources: OpenStax, Prealgebra 2e (2020) and Algebra and Trigonometry 2e (2021), geometry formulas · S. Ramanujan (1914), "Modular equations and approximations to π" (ellipse perimeter)

Checked 9 Nov 2026. Standard plane-geometry formulas (e.g. OpenStax Prealgebra 2e and Algebra and Trigonometry 2e); Heron’s formula; Ramanujan’s second approximation for the ellipse perimeter (1914).

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