Perimeter Formulas

The perimeter is the total length of a figure's boundary. Here are the formulas for rectangles, squares, triangles, parallelograms, rhombuses, trapezoids, regular polygons and the circumference of a circle.

15 formulas · Grades 5–9

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All 15 formulas on this page
  1. Perimeter of a rectangle
  2. Perimeter of a square
  3. Perimeter of an arbitrary triangle
  4. Perimeter of an equilateral triangle
  5. Perimeter of an arbitrary polygon
  6. Circumference (via diameter)
  7. Circumference (via radius)
  8. Perimeter of an isosceles triangle
  9. Perimeter of a trapezoid
  10. Perimeter of a parallelogram
  11. Perimeter of a rhombus
  12. Perimeter of a regular polygon
  13. Perimeter of a square (via diagonal)
  14. Perimeter of an isosceles trapezoid
  15. Perimeter of a triangle (via inradius and area)

Perimeter of a rectangle

Grade 5
P=2⋅(a+b)P = 2 \cdot (a + b)

Sum of the lengths of all sides of a rectangle.

ab
The perimeter is the sum of the lengths of all four sides.
Legend:
  • a — Side a
  • b — Side b

Perimeter of a square

Grade 5
P=4⋅aP = 4 \cdot a

Sum of the four equal sides of a square.

aaaa
All four sides of a square are equal.
Legend:
  • a — Side a

Perimeter of an arbitrary triangle

Grade 5
P=a+b+cP = a+b+c

Sum of the lengths of all three sides of a triangle.

abc
The perimeter is the sum of the three side lengths.
Legend:
  • a — Side a
  • b — Side b
  • c — Side c

Perimeter of an equilateral triangle

Grade 5
P=3aP = 3a

Sum of the three equal sides of an equilateral triangle.

aaa
Three equal sides — the perimeter is three times a side.
Legend:
  • a — Side a

Perimeter of an arbitrary polygon

Grade 5
P=a1+a2+a3+a4+a5P = a_1 + a_2 + a_3 + a_4 + a_5

The perimeter of any polygon equals the sum of the lengths of all its sides. Shown for a pentagon — for any other number of sides the sides are added the same way.

a₁a₂a₃a₄a₅
The perimeter is the sum of the lengths of all the sides, however many there are.
Legend:
  • a1 — Side a₁
  • a2 — Side a₂
  • a3 — Side a₃
  • a4 — Side a₄
  • a5 — Side a₅

Circumference (via diameter)

Grade 6
C=π⋅dC = \pi \cdot d

Calculating the circle's boundary length from its diameter.

d
d is the diameter — it passes through the centre from edge to edge.
Legend:
  • d — Diameter (d)

Circumference (via radius)

Grade 6
C=2πrC = 2 \pi r

Calculating the circle's boundary length from its radius.

r
r is the radius — from the centre to any point on the circle.
Legend:
  • r — Radius (r)

Perimeter of an isosceles triangle

Grade 7
P=2a+bP = 2a + b

Perimeter of a triangle with legs a and base b.

aab
The two legs are equal, b is the base.
Legend:
  • a — Leg a
  • b — Base b

Perimeter of a trapezoid

Grade 8
P=a+b+c+dP = a + b + c + d

Sum of the lengths of all four sides of a trapezoid.

cdab
The perimeter is the sum of the two bases and the two legs.
Legend:
  • a — Base a
  • b — Base b
  • c — Leg c
  • d — Leg d

Perimeter of a parallelogram

Grade 8
P=2(a+b)P = 2(a+b)

Sum of the lengths of all sides of a parallelogram.

ab
Opposite sides of a parallelogram are equal.
Legend:
  • a — Side a
  • b — Side b

Perimeter of a rhombus

Grade 8
P=4aP = 4a

Sum of the four equal sides of a rhombus.

aaaa
All four sides of a rhombus are equal.
Legend:
  • a — Side a

Perimeter of a regular polygon

Grade 8
P=n⋅aP = n \cdot a

Perimeter of a regular polygon as the number of sides times the side length.

a
n equal sides of length a.
Legend:
  • n — Number of sides (n)
  • a — Side (a)

Perimeter of a square (via diagonal)

Grade 8
P=22 dP = 2\sqrt{2}\, d

Perimeter of a square expressed through its diagonal.

dP = 4a
d is the diagonal of the square — the perimeter can be expressed through it too.
Legend:
  • d — Diagonal (d)

Perimeter of an isosceles trapezoid

Grade 8
P=a+b+2cP = a + b + 2c

Perimeter of an isosceles trapezoid, whose two legs are equal.

abcc
Both legs c are equal — the trapezoid is isosceles.
Legend:
  • a — Base a
  • b — Base b
  • c — Leg c

Perimeter of a triangle (via inradius and area)

Grade 9
P=2SrP = \frac{2S}{r}

Perimeter of a triangle from its area and the inradius.

rS
S is the area of the triangle, r is the inradius.
Legend:
  • S — Area (S)
  • r — Inradius (r)

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