Perimeter Calculator
Calculate the perimeter or circumference of squares, rectangles, triangles, circles, and regular polygons.
Perimeter Formulas Reference
| Shape | Formula | Variables |
|---|---|---|
| Square | P = 4s | s = side length |
| Rectangle | P = 2(l + w) | l = length, w = width |
| Triangle | P = a + b + c | a, b, c = side lengths |
| Circle | C = 2πr | r = radius |
| Regular Polygon | P = n × s | n = sides, s = side length |
Frequently Asked Questions
What is the difference between perimeter and circumference?
Perimeter is the total length around any polygon (a shape with straight sides). Circumference is the same concept applied specifically to circles. Mathematically they are the same idea: the distance around the outside of a shape. This calculator uses 'circumference' for circles and 'perimeter' for all other shapes.
How do I calculate the perimeter of a triangle?
Add all three side lengths: P = a + b + c. For a right triangle, if you only know two sides you can find the third using the Pythagorean theorem (a² + b² = c²) before calculating the perimeter. Note that three side lengths can only form a valid triangle if the sum of any two sides is greater than the third.
What is a regular polygon?
A regular polygon is a shape where all sides are equal length and all interior angles are equal. Common examples: equilateral triangle (3 sides), square (4 sides), regular pentagon (5), hexagon (6), and octagon (8). The perimeter of any regular polygon is simply the number of sides multiplied by the side length: P = n × s.
How do I find the circumference of a circle from its diameter?
The circumference formula using radius is C = 2 × π × r. If you have the diameter instead, use C = π × d, since diameter = 2 × radius. For a circle with diameter 10 cm, C = π × 10 ≈ 31.42 cm.
What is the triangle inequality theorem?
The triangle inequality theorem states that the sum of any two sides of a triangle must be greater than the third side. If this condition is not met, the sides cannot form a closed triangle. For example, sides 1, 2, and 10 cannot form a triangle because 1 + 2 = 3, which is less than 10.