Equilateral Triangle Calculator

An equilateral triangle has three equal sides and three 60° angles. In other words, it is both equilateral and equiangular.

Equilateral Triangle Calculation Method

For a right triangle, if any two of the hypotenuse, height, base, non-right angle, and area are given, all remaining values can be derived.

When the base and height are known

Formula for the hypotenuse of a right triangle

The triangle height (h) is 0 .

The side length of the triangle is 0 .

The perimeter of the triangle is 0 .

The area (S) of the triangle is 0 .

About This Calculator

An equilateral triangle has three equal sides and three equal 60° angles, making it the most symmetrical triangle. One measurement — side, height, perimeter or area — determines all the others.

Enter any one known value to have the side length, height, perimeter and area calculated together.

An equilateral triangle with side a has height (√3/2)a and area (√3/4)a², so a side of 6 gives 5.196 and 15.588. All three angles are 60°, and the centroid, circumcentre and incentre coincide — a property that no other triangle possesses.

Key Formula:Area = (√3 / 4)a² · Height = (√3 / 2)a

Frequently Asked Questions

What is the height of an equilateral triangle?

It is √3/2 ≈ 0.866 times the side length. A triangle with 10 cm sides therefore has a height of about 8.66 cm, independent of how it is oriented.

How do I find the area of an equilateral triangle from its perimeter?

Divide the perimeter by 3 to get the side, then apply √3/4 × a². A perimeter of 12 cm gives sides of 4 cm and an area of about 6.93 cm².

How do I find the height of an equilateral triangle?

Drop a perpendicular from a vertex; it bisects the base and creates a right triangle with hypotenuse a and one leg a/2. Pythagoras gives h = √(a² − a²/4) = (√3/2)a.

What is the inradius of an equilateral triangle?

It is one third of the height, r = a√3/6, and the circumradius is twice that, R = a√3/3. For a side of 6 the inradius is 1.732 and the circumradius 3.464.

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Sources & last update

2026-10-19