Equilateral Triangle Calculator

Enter any known value for an equilateral triangle to calculate the edge lengths, altitude, area, perimeter, inradius, and circumradius.

Solution:

sides:
a = 3
height:
h = 2.598
area:
T = 3.897
perimeter:
p = 9
inradius:
r = 0.866
circumradius:
R = 1.732


What is an Equilateral Triangle?

An equilateral triangle, also called a regular triangle, is a triangle with sides of equal length. An equilateral triangle is a special kind of isosceles triangle.

Since all sides are equal, all the angles in an equilateral triangle are also equal, each angle is 60°.

diagram showing the parts of an equilateral triangle

How to Calculate Edge Lengths of an Equilateral Triangle

It’s possible to solve the length of an equilateral triangle’s edge if you know the area or perimeter.

Solve Edge Length using Area

Given the area of an equilateral triangle, the edge lengths can be found using this formula:

a = (4T) ÷ √3

Thus, the edge length a is equal to the square root of 4 times the area T divided by the square root of 3.

Solve Edge Length using Perimeter

Given the perimeter of an equilateral triangle, the edge lengths can be found using this formula:

a = p3

Because each side is equal in length, the length of side a is equal to the perimeter p divided by three.

How to Calculate Height of an Equilateral Triangle

If you know the edge length of an equilateral triangle you can also solve the height. Use the formulas above to find the edge length, if needed.

h = a * √ 32

Thus, the height h is equal to the edge length a times the square root of 3, divided by 2.

How to Calculate Area and Perimeter

Given the edge length of an equilateral triangle the area and perimeter can also be solved.

Solve Area

The area can be found using this formula:

T = a² × √34

The area T of an equilateral triangle is equal to edge length a squared times the square root of 3, divided by 4.

Solve Perimeter

The perimeter can be found using this formula:

p = 3a

Because each side in an equilateral triangle is equal in length, the perimeter is equal to 3 times edge length a.

How to Calculate Inradius and Circumradius

There are also some easy formulas to solve the inradius and circumradius for an equilateral triangle.

Solve Inradius

The inradius is equal to 1/2 of the circumradius or 1/3 of the height/altitude of the triangle. If edge length is known then the following formula can also be used.

r = a × √36

The inradius r of the equilateral triangle is equal to edge a times the square root of 3, divided by 6.

Solve Circumradius

The circumradius is equal to 2/3 the height/altitude, or twice the value of the inradius.

R = 2r

The circumradius R is equal to 2 times the inradius r

You might also be interested in our right triangle calculator.