Perimeter Formulas for Common Shapes
The perimeter is the total length of a shape's outer boundary. For straight-sided shapes, it is the sum of all side lengths. For curves, it uses π.
Core Formulas
Square: P = 4s
Rectangle: P = 2(l + w)
Triangle: P = a + b + c
Circle: C = 2πr (circumference)
Regular n-gon: P = n × sWorked Examples
Rectangle 12 m × 7 m:
P = 2(12 + 7) = 2 × 19 = 38 m
Equilateral triangle, side 9 cm:
P = 3 × 9 = 27 cm
Circle, radius 5 m:
C = 2π × 5 = 10π ≈ 31.42 mIrregular Shapes
L-shaped room (6×8 m with 2×3 notch):
Break into segments:
6 + 8 + 2 + 3 + 4 + 5 = 28 m perimeter
(Label each edge, add all sides)Real-World Applications
- Fencing a garden (how much material to buy)
- Framing a picture or mirror
- Running track distances (400 m standard = circumference)
- Tiling border around a room
- Sealing edges in construction
Calculate any perimeter: Free Perimeter Calculator
Perimeter Formulas by Shape
- Square: P = 4a
- Rectangle: P = 2(l + w)
- Triangle: P = a + b + c
- Equilateral triangle: P = 3a
- Circle (circumference): C = 2πr = πd
- Regular n-gon: P = n × side length
- Parallelogram: P = 2(a + b)
Real-World Applications
Perimeter calculations appear throughout everyday life and professional practice. Fencing a garden requires the perimeter of the plot in metres. Fitting skirting boards or cornice around a room uses room perimeter. Framing a picture or window requires the perimeter of the opening. In textiles, hemming fabric needs the perimeter of the piece. Landscapers calculate the perimeter of flowerbeds to estimate edging materials. Civil engineers calculate road perimeters for kerbing and boundary walls. In sports, the perimeter of a football pitch is roughly 400 m; standard athletics tracks are exactly 400 m.
Frequently Asked Questions
What is the difference between perimeter and circumference?
Circumference is the specific term for the perimeter of a circle. All other closed shapes use "perimeter." Circumference = 2πr where r is the radius, or πd where d is the diameter. π ≈ 3.14159. A circle with diameter 10 m has circumference ≈ 31.416 m.
How do I find the perimeter of an irregular shape?
Add up the lengths of all sides. For irregular quadrilaterals or polygons, you need all individual side lengths — there is no shortcut formula. On a map or plan, you can use a piece of string laid along the boundary and then measured, or use digital tools that sum segment lengths.
Does the shape with the largest area always have the largest perimeter?
No. The isoperimetric inequality says that for a fixed perimeter, the circle encloses the maximum area. Conversely, for a fixed area, the circle has the minimum perimeter. A square with perimeter 40 m encloses 100 m², while a long thin rectangle 1 m × 19 m with the same perimeter encloses only 19 m². Perimeter and area are related but independent.