Perimeter Calculator

Perimeter Formulas for Common Shapes

Perimeter is the total distance around the outside edge of a two-dimensional shape, found by adding up the length of every side. It is measured in linear units, such as inches or meters, the same units used for a single side length, unlike area which uses squared units. Knowing a shape’s perimeter is useful anytime you need to measure a boundary directly, such as fencing a yard, framing a picture, or trimming material along an edge.

Regular shapes have shortcut formulas that avoid adding several separate numbers by hand. A square, with four equal sides of length s, has perimeter 4s. A rectangle, with two pairs of equal opposite sides, has perimeter 2(l + w), where l and w are its length and width. A general triangle and a general trapezoid do not simplify the same way, since their sides can all differ, so their perimeters are simply the sum of all three or four side lengths. For a triangle specifically, not just any three lengths work: the sum of any two sides must be greater than the third, or no triangle can actually be formed.

A regular polygon, a shape with n equal sides and equal angles such as a pentagon or hexagon, follows the same shortcut logic as a square: multiply the side length by the number of sides, P = n × s. As n grows larger while the side length stays fixed, the polygon approaches the shape of a circle, which is part of why a circle’s circumference formula, covered separately in the Circle Calculator, can be seen as the limiting case of this same pattern applied to infinitely many, infinitely short sides.