Perimeter Calculator

Calculate the perimeter of common shapes: rectangle, triangle, square, regular polygon, and trapezoid. Find the total distance around any polygon from side lengths.

📐 Geometry📐 P = sum of all sides🔢 Math
Shape
Side 1 / length
Side 2 / width
Side 3 (triangle)
Side 4 (trapezoid)
Number of sides n (regular polygon)
Please enter valid values.

Formula & Reference

VariableSymbolFormulaUnits
Perimeter CalculatorP = sum of all sideslinear units

Step-by-Step Examples

Example 1
Rectangle

l=8, w=5.

  • P=2(8+5)=2×13=26
✓ P = 26 units
Example 2
Triangle

a=3, b=4, c=5 (right triangle).

  • P=3+4+5=12
  • Verify right triangle: 3²+4²=5² ✓
✓ P = 12 units
Example 3
Regular Hexagon

n=6, side=4.

  • P=6×4=24
  • Interior angles each 120°
✓ P = 24 units

Real-World Applications

Common Mistakes to Avoid

⚠️
Perimeter vs area

Perimeter is the boundary length (1D). Area is the enclosed space (2D). A large perimeter does not mean large area.

⚠️
Circle perimeter is called circumference

C = 2πr or πd. It is not called perimeter for circles — use circumference.

⚠️
All side lengths, not just two

For non-regular shapes, you must sum ALL sides. There is no shortcut unless the shape has symmetry.

Frequently Asked Questions

What is the perimeter?
The total length of the boundary of a 2D shape. Sum of all side lengths. Measured in linear units (cm, m, ft).
Why is perimeter in linear units?
Perimeter measures a one-dimensional length, not area. If sides are in meters, perimeter is in meters, not square meters.
How to find perimeter from coordinates?
Find the distance between each pair of consecutive vertices using the distance formula, then sum all the segment lengths.
What shape has the most area for a given perimeter?
The circle maximizes enclosed area for a given perimeter. Among polygons, regular polygons have more area than irregular ones with the same perimeter.
What is the isoperimetric inequality?
For any closed curve of perimeter P enclosing area A: 4πA ≤ P². Equality holds only for circles.

Related Math Calculators

Formula Explorer connections

Interpretation: This relationship connects dimensions, coordinates, angles or trigonometric ratios to a geometric measurement. Assumption: Use a consistent angle mode and length unit, identify the intended shape or coordinate system, and verify that the supplied dimensions form valid geometry.

Pythagorean Theorem Calculator →Regular Polygon Calculator →Sector Area Calculator →Math Formula Explorer →