Perimeter Calculator
Calculate the perimeter (total boundary length) of common 2D shapes.
Rectangle
Circle
Triangle
Polygon
Quick Examples
Perimeter Formulas
| Shape | Formula | Notes |
|---|---|---|
| Rectangle | P = 2(l + w) | Sum of all four sides |
| Circle (Circumference) | C = 2 pi r | Also C = pi d |
| Triangle | P = a + b + c | Sum of three sides |
| Square | P = 4s | Four equal sides |
| Regular Polygon | P = n x s | n = number of sides |
What is Perimeter?
Perimeter is the total distance around the outside of a 2D shape. For a circle, it's called circumference. It's measured in linear units like meters, feet, or centimeters.
How to Use This Perimeter Calculator
- Choose the shape: click Rectangle, Circle, Triangle, or Polygon at the top of the tool.
- Enter the measurements: type the side lengths (or the radius for a circle, or the number of sides plus side length for a regular polygon).
- Click "Calculate Perimeter": the result appears instantly, together with the formula the tool used.
- Read the units: the answer comes back in the same unit as your inputs — meters in, meters out.
Perimeter Formulas Explained
Every perimeter formula adds up the boundary of the shape; the shortcuts below just do that addition more efficiently:
- Rectangle: P = 2 × (length + width). Opposite sides are equal, so add one length and one width, then double. A 12 m by 8 m rectangle has P = 2 × (12 + 8) = 40 m.
- Square: P = 4 × side. A square with side 2.75 m has P = 4 × 2.75 = 11 m.
- Triangle: P = a + b + c — simply the sum of all three sides. Sides of 5, 7, and 9 give P = 21.
- Circle (circumference): C = 2πr = πd. A circle with radius 10 cm has C = 2 × π × 10 ≈ 62.83 cm.
- Regular polygon: P = n × side, where n is the number of sides. A regular octagon with side 7 has P = 8 × 7 = 56.
Perimeter vs Circumference vs Area
These three terms are often confused. Here is how they differ:
| Term | What it measures | Applies to | Units |
|---|---|---|---|
| Perimeter | Total length of all sides | Polygons (straight-sided shapes) | cm, m, ft |
| Circumference | Distance around a circle | Circles only (C = 2πr) | cm, m, ft |
| Area | Surface enclosed inside | Any 2D shape | cm², m², ft² |
Worked Examples
Garden fence
A rectangular garden measures 15 m by 8 m. P = 2 × (15 + 8) = 46 m of fencing. Add 5–10% extra for posts, gates, and cutting waste: 46 × 1.10 = 50.6, so order about 51 m.
Running track
A circular track has radius 50 m. One lap is C = 2 × π × 50 ≈ 314.16 m.
Picture frame
A square frame 30 cm on each side needs P = 4 × 30 = 120 cm of molding.
Triangular plot
A plot with sides 20 m, 25 m, and 30 m has perimeter P = 20 + 25 + 30 = 75 m.
Finding Perimeter from Area
Area alone only fixes the perimeter for shapes determined by a single number:
- Square: side = √area. A square of area 64 m² has side 8 m, so P = 4 × 8 = 32 m.
- Circle: r = √(area/π). A circle of area 100 m² has r = √(100/π) ≈ 5.6419 m, so C = 2 × π × 5.6419 ≈ 35.45 m.
- Rectangle: impossible from area alone. An area of 120 m² could be 6 × 20 (P = 52 m), 10 × 12 (P = 44 m), or 8 × 15 (P = 46 m) — each with a different perimeter.
Common Mistakes
- Adding only two sides of a rectangle: the formula doubles the sum because a rectangle has four sides, not two.
- Using base and height for a triangle's perimeter: that pair gives area, not perimeter. You need all three side lengths.
- Three lengths that cannot form a triangle: sides like 1, 2, and 3 violate the triangle inequality (any two sides must sum to more than the third), so no perimeter exists.
- Entering the diameter as the radius: halve the diameter before using C = 2πr.
- Reporting perimeter in square units: perimeter is a length, so it never uses cm² or m² — those units belong to area.
Tip: for fencing, edging, or trim, always round your material order up and add 5–10% waste allowance. You can reuse offcuts, but you cannot stretch a short board.
Circle: Diameter or Radius?
Both forms give the same circumference — pick whichever matches your measurement:
Example: a manhole cover with diameter 14 cm has C = π × 14 ≈ 43.98 cm. Measuring straight across (diameter) is often easier than locating the center for the radius.
Perimeter of Irregular Shapes
When no formula applies, the definition does the work: add every side. An irregular pentagon with sides 3, 5, 4, 6, and 2 has P = 3 + 5 + 4 + 6 + 2 = 20 units. Walk the boundary, write down each length, and sum them.
Semi-Perimeter: Half the Boundary
Some formulas use s, the semi-perimeter — half the perimeter. Heron's formula for triangle area needs it: a 6-8-10 triangle has P = 24, so s = 12, and A = √[12 × (12−6) × (12−8) × (12−10)] = √[12 × 6 × 4 × 2] = √576 = 24, matching ½ × 6 × 8.
Perimeter in Everyday Projects
Baseboards
A 4 m × 5 m room has perimeter 2 × (4 + 5) = 18 m. Subtract a 1 m doorway and add 10% waste: (18 − 1) × 1.10 = 18.7, so order about 19 m of baseboard.
Edging a garden bed
A trapezoidal bed with sides 8, 12, 6, and 7 m needs P = 8 + 12 + 6 + 7 = 33 m of edging.
Units Checklist
- All side lengths must share one unit before you add them.
- The answer is in that same unit, not squared.
- For circles, decide radius or diameter first, then pick the matching formula.