How do you calculate the area of a circle?

The area of a circle is pi times the radius squared, written as A = pi r squared. If you know the diameter instead of the radius, divide by two first. The circumference (perimeter) is 2 times pi times r.

What is the area formula for a trapezoid?

A trapezoid has two parallel sides called bases (a and b) and a height (h) measured perpendicularly between them. The area is half the sum of the parallel sides multiplied by the height: A = (a + b) / 2 times h.

How is the perimeter of an ellipse calculated?

There is no simple exact formula for the perimeter (circumference) of an ellipse. This calculator uses Ramanujan's second approximation: P is approximately pi(a+b)[1 + 3h/(10 + sqrt(4 - 3h))], where h = (a - b)^2 / (a + b)^2 and a and b are the semi-major and semi-minor axes. It is accurate to better than about 0.01% for virtually all ellipses.

Area Calculator

This area calculator finds the area and perimeter of six common two-dimensional shapes: circle, square, rectangle, triangle, trapezoid, and ellipse. Each shape has its own set of inputs and its own formula, but the idea is the same throughout. You choose the shape from the dropdown, enter the required measurements in your preferred unit (centimetres, metres, inches, or anything else), and the calculator instantly returns both the area in square units and the perimeter or circumference in linear units. For a circle you enter the radius and get pi times r squared for the area and two times pi times r for the circumference. For a square you enter the side length and get the side squared for the area. For a rectangle you enter width and height, giving width times height for area and twice the sum for perimeter. For a triangle you enter a base and perpendicular height, giving half base times height. For a trapezoid you enter the two parallel bases and the perpendicular height, giving the average of the bases times the height. For an ellipse you enter the two semi-axes, giving pi times a times b for the area and Ramanujan's approximation for the perimeter. The default example is a rectangle 8 units wide and 5 units tall, giving an area of 40 square units and a perimeter of 26 units. This tool suits students working through geometry exercises, tradespeople estimating materials, designers calculating surface coverage, and anyone needing a quick area figure without a full geometry package. Results are for reference only.

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Shape

Width

Height

Radius

Side length

Base

Perpendicular height

Parallel side a

Parallel side b

Height

Semi-major axis (a)

Semi-minor axis (b)

40.00

area (square units)

Perimeter / Circumference26.00

ShapeRectangle

How it works

Select your shape and the relevant input fields appear. The formulas used are: Rectangle area = width × height, perimeter = 2(w+h). Circle area = πr², circumference = 2πr. Square area = s², perimeter = 4s. Triangle area = ½ × base × height (perpendicular). Trapezoid area = ½(a+b) × h. Ellipse area = πab, perimeter uses Ramanujan's second approximation: π(a+b)[1 + 3h/(10 + √(4−3h))], where h = (a−b)²/(a+b)².

Worked example

With the default rectangle (width=8, height=5): area = 8 × 5 = 40.00 square units. Perimeter = 2 × (8+5) = 26.00 units. If you switch to a circle with radius=7, the area = π × 49 = 153.94 square units and circumference = 2π × 7 = 43.98 units.

Related calculators

Volume Calculator: extend to 3D shapes including cylinders, spheres and cones.
Triangle Calculator: solve any triangle from sides and angles, not just base and height.
Heron's Formula Calculator: find triangle area from three side lengths alone.
Percentage Calculator: express one area as a percentage of another.

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