Perimeter Calculator

How to Find the Perimeter of a Shape

Perimeter is the total length of the outer boundary of a two-dimensional shape. The word comes from Greek: peri ("around") + metron ("measure"). Unlike area (which measures surface), perimeter measures distance around.

For shapes with straight edges, the perimeter is simply the sum of all side lengths. For curved shapes like circles and ellipses, you need a formula.

Perimeter Formulas

Square

P = 4a — Four times the side length. Example: a = 5 → P = 20.

Rectangle

P = 2l + 2w — Twice the length plus twice the width. Example: 10 + 10 + 6 + 6 = 32.

Triangle

P = a + b + c — Sum of all three sides. Example: 3 + 4 + 5 = 12.

Circle (Circumference)

C = 2πr — Two times π times the radius. Alternatively: C = πd (π times the diameter). Example: r = 7 → C = 43.982.

Ellipse

There is no exact closed-form formula for the perimeter of an ellipse. The best approximation is Ramanujan's formula:

P ≈ π[3(a+b) − √((3a+b)(a+3b))]

Where a is the semi-major axis and b is the semi-minor axis. Example: a = 10, b = 6 → P ≈ 51.054.

Trapezoid

P = a + b + c + d — Sum of all four sides (two bases + two legs). Example: 8 + 6 + 5 + 5 = 24.

Parallelogram

P = 2a + 2b — Since opposite sides are equal. Example: a = 10, b = 6 → P = 32.

Rhombus

P = 4a — All four sides are equal. Example: a = 7 → P = 28.

Sector

P = 2r + arc length, where arc = rθ (θ in radians). This is the two straight edges (radii) plus the curved arc. Example: r = 7, angle = 90° → P = 14 + 10.996 = 24.996.

Regular Polygon (n-gon)

P = n × a — Number of sides times the side length. Works for pentagon (n=5), hexagon (n=6), octagon (n=8), or any regular polygon.

Perimeter vs. Area vs. Circumference

• Perimeter: Distance around a shape (linear units: ft, m, cm)
• Circumference: Perimeter of a circle — same concept, different name
• Area: Space inside a shape (square units: ft², m²). See our Area Calculator

Frequently Asked Questions

Is perimeter the same as circumference?

Both measure the boundary length, but perimeter is used for shapes with straight sides, while circumference specifically refers to the boundary of a circle. Mathematically, the circumference is the perimeter of a circle.

How do I find the perimeter of an irregular shape?

Measure each edge individually and add them all together. If some edges are curved, you'll need the appropriate formula for each curved section. For a completely irregular shape, measuring with a flexible tape or string is often the easiest approach.

Why is perimeter measured in linear units, not squared?

Perimeter is a one-dimensional measurement (distance), so it uses linear units like feet, meters, or centimeters. Area is two-dimensional (length × width), which is why it uses squared units.

Why do you calculate perimeter?

Common real-world uses include: calculating fencing needed for a yard, baseboard trim for a room, string lights for windows, framing for pictures, and edging for garden beds.