📐 Area & Perimeter

Calculate area and perimeter for any common shape.

Shape

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Area

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Perimeter

How to Use This Calculator

This calculator finds the area and perimeter of 8 common shapes: circle, square, rectangle, triangle, trapezoid, parallelogram, rhombus, and ellipse. Select the shape, enter the dimensions you know, and both area and perimeter appear instantly.

Select your shape from the dropdown. The input fields update to show exactly which measurements you need.

Enter dimensions in the same unit throughout (all centimetres, or all feet). The calculator does not convert units.

Read the area in square units and the perimeter in the same linear unit. For a circle, perimeter is the circumference.

For a triangle, enter base and height for area, or all three sides for a complete result using Heron's formula.

Key Area and Perimeter Formulas

Circle: A = pi x r², Circumference = 2 x pi x r Rectangle: A = length x width, P = 2(l + w) Square: A = side², P = 4 x side Triangle: A = 0.5 x base x height, P = a + b + c Trapezoid: A = 0.5 x (a + b) x height Parallelogram: A = base x height, P = 2(a + b)

Area is always in square units: if your measurements are in feet, area is in square feet (ft²). Perimeter is always the same linear unit as your inputs. For a circle, the perimeter is called circumference and equals 2 times pi times the radius, roughly 6.283 times the radius.

Worked Examples

Circle with radius 7 cmArea = 153.94 cm², Circumference = 43.98 cm

Rectangle 12 ft x 8 ft roomArea = 96 ft², Perimeter = 40 ft

Triangle: base 10 m, height 6 mArea = 30 m²

Square tile 30 cm x 30 cmArea = 900 cm² (0.09 m²)

Where Area and Perimeter Calculations Come Up

Knowing the area of a room tells you how much flooring, carpet, or paint you need. Knowing the perimeter tells you how much baseboard, trim, or fencing to buy. These two numbers show up in almost every home improvement project. A 12 x 15 ft bedroom has an area of 180 sq ft for flooring and a perimeter of 54 ft for baseboards, minus door openings.

In school and professional settings, area and perimeter appear in geometry, construction, engineering, and design. Architects use them to calculate floor space. Gardeners calculate them to figure out how much fertiliser or mulch a bed needs. Sports fields are measured this way too: a standard football field is 100 yards x 53.3 yards, giving an area of about 5,333 square yards. Any time you need to cover a surface or enclose a boundary, these two calculations are the starting point.

Frequently Asked Questions

What is the formula for the area of a circle?

A = π × r². For diameter d: A = π × (d/2)². Example: circle with radius 5 → A = π × 25 ≈ 78.54 square units.

How do I find the area of a triangle?

A = ½ × base × height. For sides a, b, c, use Heron's formula: s=(a+b+c)/2, A=√(s(s-a)(s-b)(s-c)).

What is the perimeter of a circle called?

The perimeter of a circle is called the circumference: C = 2πr or C = πd.

What is the area of a trapezoid?

A = ½ × (base₁ + base₂) × height. A trapezoid has one pair of parallel sides (the two bases).

How do I calculate the area of an irregular shape?

Divide it into regular shapes (rectangles, triangles), calculate each area, then add them up. Alternatively, use the shoelace formula for polygon vertices.