Geometry
Perimeter Calculator
Find the distance around any shape — rectangle, square, triangle, circle, parallelogram, rhombus, trapezoid, regular polygon, or ellipse. Pick a shape, type the measurements, and the perimeter updates instantly with every step shown.
Rectangle perimeter
P = 2(l + w)Double the sum of the length and width.
Perimeter
16
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The basics
What is perimeter?
Perimeter is the total distance around the outside of a flat shape — walk the boundary once and measure how far you went. For any shape with straight sides you simply add the sides up; for a circle the same idea is called the circumference. Because it is a length, perimeter is always in linear units, never square units.
P = sum of all sides
Add the edges
For any polygon, perimeter is just the sum of its side lengths. A formula like P = 2(l + w) is only a shortcut for adding the sides when some of them are equal.
A 3-4-5 triangle: 3 + 4 + 5 = 12
Length, not area
Measured in linear units
Perimeter shares its units with the sides — centimetres, metres, inches, feet. Area lives inside the shape and uses square units; perimeter wraps the outside and uses plain ones.
Sides in metres → perimeter in metres
Method
How to find a perimeter by hand
Three moves cover every shape on this page, from a square to a 12-sided polygon.
- 1
Identify the shape and its sides
Decide what you have — a rectangle, a circle, a regular polygon — and label the measurements you know, such as length l, width w, or radius r.
rectangle → l, w - 2
Pick the matching formula
Equal sides let you multiply instead of adding one by one. A rectangle doubles the sum of two sides; a regular polygon multiplies one side by the side count.
P = 2(l + w) · P = n × s - 3
Substitute and evaluate
Plug the numbers in, do the arithmetic, and keep the unit. The result is the distance once around the shape.
P = 2(5 + 3) = 16 units
Worked examples
See it across shapes
The same routine — formula, substitute, evaluate — applied to five common shapes. Switch tabs to compare.
Given l = 8, w = 5
Formula: P = 2(l + w)
Substitute: P = 2 × (8 + 5) = 2 × 13
P = 26
Reference
Every perimeter formula
The complete set this calculator supports. Each one is just a faster way to add the sides.
| Shape | Formula | In words |
|---|---|---|
| Rectangle | P = 2(l + w) | Double the sum of the length and width. |
| Square | P = 4a | Four equal sides, so four times one side. |
| Triangle | P = a + b + c | Add the three side lengths. |
| Circle | C = 2πr | A circle's perimeter is its circumference. |
| Parallelogram | P = 2(a + b) | Opposite sides are equal, so double their sum. |
| Rhombus | P = 4a | All four sides are equal, just like a square. |
| Trapezoid | P = a + b + c + d | Add all four sides — none need be equal. |
| Regular polygon | P = n × s | Equal sides, so the side count times one side. |
| Ellipse | P ≈ π(a + b)·… | No exact formula — Ramanujan's gives a tight estimate. |
Quick chart
What is the perimeter of an l × w?
A live lookup for the searches people actually type — “perimeter of a 10 by 12 rectangle”, “perimeter of a square with side 8”. Edit the rows to match your numbers.
| l \ w | 3 | 4 | 5 | 6 |
|---|---|---|---|---|
| 4 | 14 | 16 | 18 | 20 |
| 5 | 16 | 18 | 20 | 22 |
| 6 | 18 | 20 | 22 | 24 |
| 8 | 22 | 24 | 26 | 28 |
| 10 | 26 | 28 | 30 | 32 |
| 12 | 30 | 32 | 34 | 36 |
Each cell is the perimeter of an l × w rectangle: P = 2(l + w).
Worth knowing
Rules and edge cases
A handful of facts that clear up most perimeter confusion.
Perimeter ≠ area
Same perimeter, different area
Shapes with equal perimeters can enclose wildly different areas. Among all rectangles with a fixed perimeter, the square encloses the most space.
C = 2πr = πd
Two ways to write a circle
You can use the radius or the diameter — the diameter is twice the radius, so πd and 2πr give the same circumference.
More sides → circle
Polygons approach a circle
As a regular polygon gains sides, its perimeter creeps toward the circumference of the circle that surrounds it. A 100-sided polygon is nearly a circle.
Scale by k → perimeter ×k
Perimeter scales linearly
Enlarge a shape by a factor of k and its perimeter grows by k — while its area grows by k².
Composite shapes
Trace only the outline
For an L-shape or any composite figure, add only the outer edges. Interior cuts and shared borders are not part of the boundary.
Ellipse has no exact P
The ellipse is special
Unlike the circle, an ellipse has no elementary perimeter formula. Approximations like Ramanujan's are used everywhere in practice.
Where it shows up
Why perimeter matters
Perimeter is the quiet measurement behind anything you have to go around or wrap.
Fencing & edging
Yards and gardens
How much fence, edging, or trim you buy is set by the perimeter of the area you are enclosing — measured in metres or feet of material.
Framing & trim
Picture frames
The length of moulding for a frame, or skirting board for a room, equals the perimeter of the rectangle being bordered.
Tracks & laps
Running & racing
The distance of one lap is the perimeter of the track. Lane lengths differ because the outer lanes have a larger perimeter.
Common mistakes
Where perimeter trips people up
Most errors are not arithmetic — they are mixing up what perimeter is.
Squaring the unit
Using square units
Perimeter is a length. Writing the answer in cm² or m² turns a perimeter into an area by accident — keep the units plain.
Forgetting to double
Adding only two sides
A rectangle has four sides. l + w is only half the trip; perimeter doubles it to 2(l + w).
Mixing units
Sides in different units
If one side is in cm and another in m, convert first. Add lengths only once they share a unit, then report the perimeter in that unit.
Radius vs diameter
Using diameter as radius
In 2πr the r is the radius. Plug a diameter in by mistake and the circumference comes out twice too big.
FAQ
Common questions
Perimeter is the total distance around the outside edge of a two-dimensional shape. You find it by adding the lengths of all the sides, or by using the shape's formula. Because it is a length, perimeter is always measured in linear units such as cm, m, in, or ft — never square units.
Add the length and the width, then double the result: P = 2(l + w). A rectangle that is 5 by 3 has a perimeter of 2 × (5 + 3) = 16 units.
Yes. A circle has no straight sides, so the distance once around it is called the circumference. It equals 2 × π × radius (or π × diameter), and it plays exactly the same role that perimeter plays for a polygon.
Just add the three sides: P = a + b + c. This works for every triangle — scalene, isosceles, or equilateral — because perimeter never depends on the angles, only the side lengths.
A regular polygon has equal sides, so multiply the side length by the number of sides: P = n × s. A regular hexagon with 4 cm sides has a perimeter of 6 × 4 = 24 cm.
Perimeter is a length, so it uses the same linear units as the sides — millimetres, centimetres, metres, kilometres, inches, feet, yards, or miles. If your sides are in metres, the perimeter is in metres. Area, by contrast, uses square units.
Perimeter measures the distance around a shape's boundary (a length, in linear units). Area measures the surface enclosed inside it (in square units). Two shapes can share a perimeter yet have very different areas — a long thin rectangle and a square can both be 20 units around.
No — an ellipse has no simple closed-form perimeter, unlike a circle. The calculator uses Ramanujan's second approximation, which is accurate to better than one part in a billion for typical shapes, so for practical purposes it is exact.
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Ugo CharlesBuilt and fact-checked against our editorial standards · Last updated June 2026
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