What is Perimeter?
The perimeter of a two-dimensional shape is the total length of its boundary — the distance you would travel if you walked all the way around its outer edge. It is measured in the same linear units as the sides (millimetres, centimetres, metres, kilometres, inches, feet, yards, or miles).
Perimeter is used in countless practical situations: fencing a garden, framing a picture, measuring the edge of a running track, or calculating how much trim is needed for a room. This calculator supports 12 geometric shapes and both metric (mm, cm, m, km) and imperial (in, ft, yd, mi) units.
Perimeter Formulas for All 12 Shapes
| Shape | Required Inputs | Formula |
|---|---|---|
| Square | Side a | P = 4a |
| Rectangle | Sides a, b | P = 2(a + b) |
| Triangle | Sides a, b, c | P = a + b + c |
| Circle (Circumference) | Radius r | P = 2πr |
| Circle Sector | Radius r, central angle α (radians) | P = r(α + 2) |
| Ellipse | Semi-major axis a, semi-minor axis b | P ≈ π[3(a+b) − √((3a+b)(a+3b))] |
| Trapezoid | All four sides a, b, c, d | P = a + b + c + d |
| Parallelogram | Sides a, b | P = 2(a + b) |
| Rhombus | Side a | P = 4a |
| Kite | Two distinct side lengths a, b | P = 2(a + b) |
| Annulus | Outer radius R, inner radius r | P = 2π(R + r) |
| Regular Polygon | Number of sides n (≥ 3), side length s | P = n × s |
Shape Descriptions and Formula Notes
Square
A square has four equal sides. Its perimeter is simply 4 times the length of one side: P = 4a. A square is a special case of both a rectangle and a rhombus.
Rectangle
A rectangle has two pairs of parallel equal sides. The perimeter adds both lengths and widths: P = 2(a + b). When a = b, it becomes a square.
Triangle
Any triangle (scalene, isosceles, or equilateral) has a perimeter equal to the sum of all three sides: P = a + b + c. For an equilateral triangle all sides are equal, so P = 3a.
Circle (Circumference)
The perimeter of a circle is called the circumference. It is calculated as P = 2πr, where r is the radius and π ≈ 3.14159.
Circle Sector
A circle sector is a "pie slice" of a circle. Its boundary consists of two radii and one arc. The formula is P = r(α + 2), where α is the central angle in radians (e.g., π/2 ≈ 1.5708 rad for a quarter circle).
Ellipse
There is no exact elementary formula for the perimeter of an ellipse. This calculator uses Ramanujan's approximation: P ≈ π[3(a+b) − √((3a+b)(a+3b))]. It is accurate to within 0.5% for typical ellipses. Here a is the semi-major axis (longer half) and b is the semi-minor axis (shorter half).
Trapezoid
A trapezoid (or trapezium) has four sides, only one pair of which may be parallel. The perimeter is just the sum of all four sides: P = a + b + c + d.
Parallelogram
A parallelogram has two pairs of equal parallel sides. Its perimeter is P = 2(a + b) — the same formula as a rectangle, but the angles need not be 90°.
Rhombus
A rhombus is a parallelogram with all four sides equal. Therefore: P = 4a. A square is a special rhombus with right angles.
Kite
A kite has two pairs of consecutive equal sides. If one pair has length a and the other has length b, then: P = 2(a + b).
Annulus
An annulus is the region between two concentric circles (like a ring or washer). Its total perimeter includes both the outer circumference and the inner circumference: P = 2π(R + r).
Regular Polygon
A regular polygon has n equal sides of length s. The perimeter is simply: P = n × s. For example, a regular hexagon with side 5 cm has P = 6 × 5 = 30 cm.
Metric vs Imperial Units
This calculator supports the following units of measurement:
Metric
- mm — millimetres
- cm — centimetres (default)
- m — metres
- km — kilometres
Imperial / US Customary
- in — inches
- ft — feet
- yd — yards
- mi — miles
All dimension inputs must use the same unit. The perimeter result is returned in the same unit you selected.
Frequently Asked Questions
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What is the difference between perimeter and area?
Perimeter is the total length around the outside of a shape (a one-dimensional measurement in linear units such as cm or m). Area is the amount of surface enclosed inside the shape (a two-dimensional measurement in square units such as cm² or m²).
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Why is the ellipse formula an approximation?
Unlike a circle, an ellipse perimeter cannot be expressed with a simple closed-form formula using basic functions. The exact value requires an elliptic integral. Ramanujan's approximation
P ≈ π[3(a+b) − √((3a+b)(a+3b))]is accurate to better than 0.5% for all practical ellipses and is widely used in engineering and science. -
Why must the circle sector angle be in radians?
The formula
P = r(α + 2)works directly only when α is in radians, because arc length = r × α (in radians). If you have an angle in degrees, convert it first: α (rad) = α (deg) × π / 180. For example, 90° = π/2 ≈ 1.5708 rad. -
What is the minimum number of sides for a polygon?
A polygon must have at least 3 sides (a triangle). This calculator accepts any integer value of n ≥ 3. Common examples include: triangle (3), square (4), pentagon (5), hexagon (6), octagon (8), decagon (10).
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Can I use this calculator for irregular quadrilaterals?
Yes — select Trapezoid / Quadrilateral and enter all four side lengths. The formula P = a + b + c + d works for any quadrilateral regardless of angles, as long as you know all four side lengths.
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How do I convert between metric and imperial units?
Common conversion factors:
- 1 inch = 2.54 cm
- 1 foot = 30.48 cm = 12 inches
- 1 yard = 91.44 cm = 3 feet
- 1 mile = 1.60934 km
Enter all your measurements in a single consistent unit and select that unit from the dropdown.
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What is an annulus and when is its perimeter useful?
An annulus is the area between two concentric circles — like a ring, a washer, or the cross-section of a pipe. Its perimeter includes both the outer circle (circumference = 2πR) and the inner circle (circumference = 2πr), giving
P = 2π(R + r). This is useful when calculating the total edge length of ring-shaped objects.