Perimeter Calculator
A square with 5-unit sides has a perimeter of 20, and a circle with a 7-unit radius has a circumference of 43.9823. This perimeter calculator finds the distance around five common shapes: a square, a rectangle, a triangle, a circle, and a regular polygon. Pick the shape that matches your problem, enter its side lengths or radius, and the calculator applies the correct formula automatically, including a validity check for triangles. Perimeter is one of the first geometry concepts most people meet in school, and it stays useful well past the classroom. Fencing a yard, framing a picture, trimming a garden bed, hemming fabric, and laying edge molding around a room all depend on knowing the exact distance around a shape. Because each shape uses a different formula, this tool switches the required inputs the moment you change the shape, so you never have to remember five separate equations.
Quick answer
A square's perimeter is 4 times the side length, since all four sides are equal.
What this tells you
- •A square's perimeter is 4 times the side length, since all four sides are equal.
- •A rectangle's perimeter is 2 times the sum of the length and width, because opposite sides match in pairs.
- •A triangle's perimeter is the sum of its three sides, but only if the three lengths can actually form a triangle.
- •A circle does not have straight sides, so its perimeter is called the circumference, equal to 2 times pi times the radius.
- •A regular polygon's perimeter is the number of sides times the length of one side, since every side is identical.
- •Every input must be a positive number. Negative, zero, or non-numeric values return no result.
How to Use
- 1Select the shape you are measuring: square, rectangle, triangle, circle, or regular polygon.
- 2Enter the side length for a square, or the length and width for a rectangle.
- 3For a triangle, enter all three side lengths. The calculator confirms the three lengths form a valid triangle before computing the perimeter.
- 4For a circle, enter the radius. The calculator also reports the equivalent diameter for reference.
- 5For a regular polygon, enter the whole number of sides (at least 3) and the length of one side.
- 6Read the perimeter result along with the formula breakdown showing exactly how the number was calculated.
How It Works
Formula
Square: P = 4s. Rectangle: P = 2(l + w). Triangle: P = a + b + c. Circle: C = 2*pi*r. Regular polygon: P = n*s.Each shape has its own perimeter rule based on how many sides it has and whether those sides are equal. A square has four equal sides, so multiplying one side by 4 gives the full distance around it. A rectangle has two pairs of equal sides, so doubling the sum of the length and width covers all four edges. A triangle has three sides that can differ from each other, so the perimeter is a simple sum, but the three lengths must satisfy the triangle inequality: each side must be shorter than the sum of the other two, or the shape cannot physically close. A circle has no straight sides at all, so its boundary length is called the circumference and is found by multiplying the radius by 2 and by pi, since the ratio of a circle's circumference to its diameter is always pi. A regular polygon, such as a pentagon or hexagon, has n equal sides, so multiplying the number of sides by one side's length gives the total perimeter directly.
Calculation note: values are processed in the order shown above, using the current input units.
Worked Examples
Square with a 5-unit side
4 x 5 = 20, since all four sides of a square are equal.
Rectangle 8 by 3
2 x (8 + 3) = 2 x 11 = 22.
3-4-5 right triangle
3 + 4 + 5 = 12. Each side is shorter than the sum of the other two, so the triangle is valid.
Circle with a 7-unit radius
2 x pi x 7 = 43.9823, using pi to four decimal places of precision in the final rounding.
Regular hexagon with a 6-unit side
6 sides x 6 units each = 36, since every side of a regular hexagon is the same length.
Perimeter Formulas by Shape
Quick reference for the formula and required inputs for each shape this calculator supports.
| Shape | Formula | Required inputs |
|---|---|---|
| Square | P = 4 x side | 1 side length |
| Rectangle | P = 2 x (length + width) | 2 side lengths |
| Triangle | P = a + b + c | 3 side lengths |
| Circle | C = 2 x pi x radius | 1 radius |
| Regular polygon | P = sides x side length | side count and 1 side length |
Why the triangle inequality matters
Not every set of three numbers can form a real triangle. If one side is too long compared to the other two, the shorter sides cannot reach each other and the triangle collapses flat instead of closing. The triangle inequality rule states that each side must be strictly less than the sum of the other two sides. For example, 3, 4, and 5 pass the test because 3 is less than 4 plus 5, 4 is less than 3 plus 5, and 5 is less than 3 plus 4. But 1, 1, and 5 fail, since 5 is not less than 1 plus 1, and no triangle with those three side lengths can exist.
This calculator checks the triangle inequality automatically before returning a perimeter, so an invalid combination of sides never produces a misleading result. If your three measurements do not pass, double-check them, since a small measurement or entry error is the most common cause.
Common mistakes
- Confusing perimeter with area. Perimeter is the distance around a shape, measured in linear units like feet or meters, while area is the space inside the shape, measured in square units.
- Entering three triangle sides that cannot form a real triangle, such as 2, 3, and 10. The calculator flags these as invalid rather than returning a misleading total.
- Mixing units within the same shape, such as entering a rectangle's length in feet and its width in inches. All measurements must share the same unit before you calculate.
- Using the diameter instead of the radius for a circle without dividing by 2 first, which doubles the circumference by mistake.
- Assuming a regular polygon formula works for an irregular polygon. The sides-times-length shortcut only applies when every side is the same length, as in a regular pentagon, hexagon, or octagon.
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