Perimeter Calculator

Common Examples

Input	Result
Rectangle: 10 × 5	30 units
Triangle: sides 3, 4, 5	12 units
Circle: radius 7	43.98 units
Regular hexagon: side 5	30 units
Trapezoid: sides 10, 6, 5, 5	26 units

How It Works

Rectangle: P = 2 x (length + width)

Add the length and width, then multiply by 2. A rectangle has two pairs of equal sides, so the perimeter is twice the sum of one length and one width. For a rectangle with length 10 and width 5, the perimeter is 2 x (10 + 5) = 30 units. A square is a special case where length equals width, so its perimeter is simply 4 times the side length.

Triangle: P = a + b + c

Add all three side lengths together. This works for any triangle: equilateral, isosceles, scalene, or right. For a right triangle with sides 3, 4, and 5, the perimeter is 3 + 4 + 5 = 12 units. Note that this formula requires the actual side lengths, not the base and height used for area calculations.

Circle (Circumference): C = 2 x π x r

Multiply 2 by π (approximately 3.14159) by the radius. The circumference can also be written as π x d, where d is the diameter. For a circle with radius 7, the circumference is 2 x π x 7 = 14π ≈ 43.98 units.

Trapezoid: P = a + b + c + d

Add all four side lengths. In a trapezoid, sides a and b are typically the two parallel bases, while c and d are the non-parallel legs. For a trapezoid with bases 10 and 6, and legs 5 and 5, the perimeter is 10 + 6 + 5 + 5 = 26 units.

Regular Polygon: P = n x s

Multiply the number of sides (n) by the length of each side (s). A regular polygon has all sides of equal length. For a regular hexagon with side length 5, the perimeter is 6 x 5 = 30 units. This formula applies to equilateral triangles (n=3), squares (n=4), pentagons (n=5), hexagons (n=6), and any other regular polygon.

Worked Example

For a rectangle with length 12 and width 8: Perimeter = 2 x (12 + 8) = 2 x 20 = 40 units. For a triangle with sides 5, 12, and 13 (a right triangle): Perimeter = 5 + 12 + 13 = 30 units. For a circle with radius 10: Circumference = 2 x pi x 10 = 20 x pi ≈ 62.83 units. For a regular pentagon with side length 7: Perimeter = 5 x 7 = 35 units.

Related Calculators

Area Calculator

Calculate the area of common shapes: rectangle, triangle, circle, trapezoid, and ellipse.

Circle Calculator

Calculate the area, circumference, and diameter of a circle from any known value.

Volume Calculator

Calculate the volume of common 3D shapes: cube, rectangular prism, sphere, cylinder, and cone.

Frequently Asked Questions

What is the difference between perimeter and area?

Perimeter measures the total distance around the outside of a shape, expressed in linear units (such as meters or feet). Area measures the surface enclosed within the shape, expressed in square units (such as square meters or square feet). For example, a 4x3 rectangle has a perimeter of 14 units and an area of 12 square units.

What units does the perimeter calculator use?

The calculator works with any consistent unit. If you enter dimensions in centimeters, the result is in centimeters. If you enter dimensions in feet, the result is in feet. The output shows 'units' as a generic placeholder.

Why is the perimeter of a circle called circumference?

The word circumference comes from the Latin 'circumferre,' meaning to carry around. It specifically refers to the perimeter of a circle or any curved closed shape. While 'perimeter' is the general term for the boundary distance of any shape, 'circumference' is the standard term used for circles.

How do I find the perimeter if I only know the area?

For most shapes, you cannot determine the perimeter from the area alone because different shapes can have the same area but different perimeters. The exception is a circle, where area = pi x r squared, so you can solve for the radius and then calculate circumference. For a square, area = side squared, so side = square root of area, and perimeter = 4 x side.

What is a regular polygon?

A regular polygon is a shape where all sides have equal length and all interior angles are equal. Common examples include equilateral triangles (3 sides), squares (4 sides), regular pentagons (5 sides), and regular hexagons (6 sides). The perimeter of any regular polygon is simply the number of sides multiplied by the side length.