Perimeter Calculator – Find Perimeter & Circumference with Steps

Perimeter is the total distance around the outside boundary of a two-dimensional shape. The universal rule is to add every exterior edge once. Shortcut formulas such as rectangle P = 2L+2W or square P = 4s are simply compressed forms of that addition.

Keep all side lengths in compatible units. Perimeter is a length, so the answer uses ordinary units such as m, cm or ft—not square units. For curved shapes, the boundary includes arc length; for a circle the perimeter has the special name circumference.

A rectangle has two equal lengths and two equal widths, so P = L + W + L + W = 2(L+W). A 12 m × 8 m rectangle has P = 2(12+8) = 40 m.

The perimeter measures only the outside boundary. Do not multiply length by width—that gives area. In practical work, rectangle perimeter may represent fencing, skirting, edging or trim required around the boundary.

All four sides of a square are equal, so add the side four times: P = 4s. If s = 7 cm, P = 4 × 7 = 28 cm.

Because perimeter is one-dimensional, the unit remains cm rather than cm². If you are given the square’s area instead of its side, first find s = √A and then multiply the side by 4.

Add the three side lengths: P = a+b+c. If all three sides are known, the calculation is direct. If a side is missing, it must first be found from other valid information such as right-triangle Pythagoras, the Law of Cosines or the Law of Sines.

Do not use the triangle’s height as one of the perimeter sides unless that height actually lies on the outer boundary. An altitude drawn inside a triangle is normally not part of the perimeter.

The perimeter of a circle is called its circumference. If the radius is known, use C = 2πr. If the diameter is known, use C = πd because d = 2r.

For a 10 cm diameter circle, C = π × 10 ≈ 31.416 cm. A common mistake is to use πr², which calculates area rather than circumference.

Multiply the diameter by π: C = πd. For example, if d = 8 in, C = 8π ≈ 25.133 in.

The relationship comes from the definition of π: for every circle, circumference divided by diameter equals π. That is why the same constant works for circles of every size.

Perimeter measures distance around a boundary and uses linear units. Area measures the surface enclosed by that boundary and uses square units. For a 6 m × 4 m rectangle, P = 20 m while A = 24 m².

The distinction matters in applications: fencing or edging depends on perimeter, while flooring, paint coverage or turf depends on area. One cannot generally be substituted for the other.

Trace the outside boundary and add each exterior segment exactly once. Interior construction lines, diagonals or shared edges between sub-shapes are not part of the external perimeter unless the problem explicitly asks for them.

If a boundary contains curves, calculate each arc length separately and add it to the straight segments. The calculator includes an irregular-polygon option where known side lengths can be entered as a list and summed.

Yes, when the total perimeter and all the other boundary lengths are known. Rearrange the addition: missing side = total perimeter − sum of known sides.

For example, a quadrilateral has perimeter 30 m and three known sides 8 m, 7 m and 6 m. The missing side is 30 − (8+7+6) = 9 m. Shape-specific equality rules can provide additional information—for example, opposite rectangle sides are equal.

A semicircle’s boundary contains half of the circle’s circumference plus the diameter. With radius r, the curved part is πr and the straight diameter is 2r, so P = πr + 2r.

A frequent mistake is to calculate only half the circumference and forget the straight edge. Whether that diameter is included depends on whether the problem asks for the full boundary of the semicircular region.

Perimeter is a one-dimensional distance. You are adding lengths, so metres remain metres and feet remain feet. There is no multiplication of one length dimension by another.

Square units appear in area because two perpendicular dimensions are multiplied. Keeping this dimensional distinction is a useful way to catch mistakes: a perimeter result in m² or ft² is a warning that the wrong type of formula may have been used.

Unlike a circle, an ellipse does not have a simple elementary circumference formula. This calculator uses a high-quality approximation based on the semi-major and semi-minor axes, such as Ramanujan’s approximation.

The result is therefore an approximation rather than a simple exact expression like 2πr. For ordinary planning and educational use it is very accurate, but specialized high-precision work may use numerical elliptic-integral methods.