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 Calculator—P = 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.

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