How this calculator works
The perimeter is the distance around the outside of a closed shape. For a polygon it is the sum of the side lengths, which is why squares, rhombi and kites reduce to simple multiples and a rectangle adds two lengths and two widths. A circle uses its circumference, 2πr. An ellipse has no elementary exact formula, so this calculator uses Ramanujan's second approximation. The four-side mode sums any four lengths that can close a quadrilateral; it requires the longest side to be shorter than the sum of the other three, otherwise the chain cannot meet. The semiperimeter is half this total and appears in Heron's formula and many triangle identities.
Formula
Square or rhombus: 4a. Rectangle or parallelogram: 2(l + w). Triangle: a + b + c. Circle: 2πr. Semicircle: πr + 2r. Sector: 2r + rθ. Annulus: 2π(R + r). Ellipse: π[3(a + b) - √((3a + b)(a + 3b))]. Kite: 2(a + b). Regular polygon: ns. Four-sided outline: a + b + c + d. Semiperimeter = perimeter/2.
Worked example
A rectangle 8 m by 5 m has perimeter 2 × 13 = 26 m and semiperimeter 13 m. A circle of radius 3 m has perimeter 6π ≈ 18.8496 m. A triangle with sides 3 m, 4 m and 5 m has perimeter 12 m.
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Frequently asked questions
Is perimeter the same as area?
No. Perimeter measures the length around the boundary in linear units, while area measures the surface enclosed in square units. A shape can have a large area and a small perimeter, or the reverse.
Why is the ellipse perimeter approximate?
The exact perimeter is an elliptic integral with no elementary closed form. Ramanujan's approximation is accurate enough for ordinary use but is still an approximation.
What is a semiperimeter?
Half the perimeter. It is a convenient quantity in Heron's formula and in the radii of inscribed and escribed circles of a triangle.
Which boundary counts for an annulus?
An annulus has two circular boundaries, so its total perimeter is the outer circumference plus the inner circumference, 2π(R + r). A sector perimeter includes its two straight radii and its arc.
How do I measure the perimeter of an irregular shape?
Break it into straight segments and circular arcs, measure each piece, and add them. This calculator handles common regular shapes rather than an arbitrary outline.