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Perimeter Formula
Perimeter is a fundamental geometry metric representing the total length of a shape's border. Whether fencing a yard or solving geometry homework, standard perimeter formulas simplify calculations. Try our perimeter calculator or check flat space measurements with the area calculator.
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What is the perimeter formula?
The simplest way to calculate the perimeter of any polygon is to add the lengths of all its sides. However, regular shapes with equal side lengths or parallel sides have streamlined formulas.
All perimeter outputs are expressed in **linear units** (ft, cm, m, in) because you are measuring a 1-dimensional length.
Standard 2D Perimeter Formulas
| Shape | Perimeter Formula | Variables Explained |
|---|---|---|
| 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 (Circumference) | C = 2πr | r = radius, π ≈ 3.14159 |
Worked Examples
Example 1: Perimeter of a Square
Find the perimeter of a square sandbox with side lengths of 4 meters.
- Formula: P = 4s
- Given: s = 4 m
- Calculation: P = 4 × 4
- Result: P = 16 meters (m)
Example 2: Perimeter of a Rectangle
Find the perimeter of a rectangular frame that is 10 feet long and 5 feet wide.
- Formula: P = 2(l + w)
- Given: l = 10 ft, w = 5 ft
- Calculation: P = 2 × (10 + 5) = 2 × 15
- Result: P = 30 feet (ft)
Common Mistakes with Perimeter
- Including Interior Lines: If you divide a shape internally (like partitioning a field), do not count those internal lines toward the perimeter. Only count the outermost boundary.
- Confusing Perimeter and Area Equations: Be careful not to use area equations (like A = l × w for a rectangle) when you mean to find perimeter (P = 2l + 2w).
- Forgetting unit matching: If side dimensions are given in different increments (feet and inches), convert all variables to the same units before summing.
Run the numbers
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Frequently asked questions
Perimeter is the total boundary distance around the edge of a two-dimensional shape. It is measured in linear units (such as feet, meters, or inches).
The boundary distance around a circle is called its circumference, which is calculated using the formula C = 2πr (or C = πd).
Perimeter measures the 1-dimensional boundary length around a shape. Area measures the 2-dimensional flat space inside the shape.
For polygons with irregular shapes, you find the perimeter by adding together the lengths of all outer boundary sides.