Perimeter Calculator
The distance around a rectangle, square, triangle, circle, ellipse, trapezoid, parallelogram or regular polygon.
Result
Perimeter: 44 ft
A measurement, not a material estimate. Nothing is added for waste or offcuts.
- Area
- 120 ft² (17,280 in², 11.1484 m²)
- Shown only where the sides fix the shape
https://calcgallery.com/geometry/perimeter-calculator/
Results follow the mathematical operation and values shown. Check that you selected the intended operation, convention and dataset type before relying on the result. Read the full disclaimer
How to use the Perimeter Calculator
- Choose the shape.
- Enter each side, or the radius or semi-axes for a round shape, in whatever unit you measured in.
- Read the perimeter. Where the sides you entered fix the shape, its area is shown as well.
The formulas
| Shape | Perimeter |
|---|---|
| Rectangle | 2 × (l + w) |
| Square | 4 × s |
| Triangle | a + b + c |
| Circle | 2 × π × r, the circumference |
| Trapezoid | a + b + c + d |
| Parallelogram | 2 × (a + b), a and b being two adjacent sides |
| Regular polygon | n × s |
| Ellipse | ≈ π(a + b)(1 + 3h ÷ (10 + √(4 − 3h))), with h = (a − b)² ÷ (a + b)² |
Every shape except the ellipse is exact. For the triangle, the three sides must be able to close: each must be shorter than the other two added together, and the page refuses sides that cannot.
Why the ellipse is different
Every other shape here has a perimeter you can write with ordinary arithmetic. An ellipse does not. Its exact perimeter is a complete elliptic integral of the second kind. That can be calculated to any precision, but not with a short formula.
The page uses Ramanujan’s second approximation, published in 1914. It is extremely accurate for ordinary ellipses: for semi-axes of 5 and 3 it differs from the exact value in about the eleventh significant figure. It becomes less accurate as the ellipse flattens. At 10 to 1 it is about 0.001% short, and even for an ellipse squashed almost to a line it is only about 0.04% short. The result row says approximate whenever the ellipse is selected.
Some pages give the ellipse perimeter as 2π√((a² + b²) ÷ 2). That formula is simpler but much worse. It overstates the perimeter: by about 1.5% for a 5 by 3 ellipse, nearly 10% at 10 to 1, and about 11% for a very flat one.
Circumference
A circle’s perimeter is its circumference, 2πr, or π times the diameter. If you know a circle’s area or circumference rather than its radius, the circle calculator works back from any one of the four.
Units
Each side can be entered in a different unit and the page converts before adding. The total is shown in feet or metres depending on the unit system, with other units alongside.
With your numbers
- Perimeter = 2 × (12 ft + 10 ft)
- Perimeter = 44 ft
Quick reference
A measurement, not a material estimate. Nothing is added for waste or offcuts.
| Example | Perimeter |
|---|---|
| Rectangle, 12 × 10 ft | 44 ft |
| Circle, radius 2.5 m | 15.708 m |
| Triangle, 3, 4 and 5 m | 12 m |
| Hexagon, 2 m sides | 12 m |
| Ellipse, 5 × 3 m semi-axes | 25.527 m |
| Square, 25 ft sides | 100 ft |
| Trapezoid, 8, 5, 4 and 4 m | 21 m |
| Parallelogram, 7 and 4 ft | 22 ft |
Common questions about the Perimeter Calculator
- What is the difference between perimeter and circumference?
- None in meaning: both are the distance all the way round. Circumference is the name used for a circle, and sometimes an ellipse; perimeter is used for everything else.
- How do I measure an irregular perimeter?
- Measure each straight run separately and add them, which is exactly what the trapezoid and triangle options do for four and three sides. For a curved edge, lay a string or a flexible tape along it and measure the string. For a garden or a plot, a measuring wheel is quicker than a tape.
- Why is the ellipse perimeter approximate?
- Because there is no exact formula for it using ordinary arithmetic and square roots. The exact value needs an elliptic integral, a function most calculators do not have. The page uses Ramanujan’s 1914 approximation, which is within about 0.04% for any ellipse, including a very flat one, and much closer for ordinary shapes. For a 5 by 3 ellipse it is out by about two parts in a hundred billion.
- Why is there no area for my trapezoid or parallelogram?
- Four sides do not fix a trapezoid’s height, and two sides do not fix a parallelogram’s angle. The same lengths can be pushed into a taller or flatter shape, changing the area without changing the perimeter. Use the area calculator with the base and the perpendicular height instead.
- Does the perimeter include waste for fencing or trim?
- No. This is the exact distance round the shape. When buying fencing, skirting or edging, add an allowance for cuts and joins; the fence calculator does that for a fence.