Equilateral Triangle Calculator
An equilateral triangle is a triangle with all three sides of equal length and all three interior angles equal to 60 degrees. This type of triangle appears frequently in mathematics, geometry, and nature. This calculator computes all the key properties of an equilateral triangle when you provide the length of one side. The calculator determines the area using the formula based on the side length and the height, the perimeter as three times the side length, the height from any vertex to the opposite side, the circumradius (the radius of a circle that passes through all three vertices), and the inradius (the radius of a circle that fits inside the triangle and touches all three sides). All outputs are calculated using standard geometric formulas and update instantly as you change the input value.
Equilateral triangle formulas
Area = (sqrt(3)/4) * a^2
Perimeter = 3 * a
Height = (sqrt(3)/2) * a
Circumradius (R) = a / sqrt(3)
Inradius (r) = a / (2 * sqrt(3))
Example calculation
For an equilateral triangle with side length 10:
- Area = (sqrt(3)/4) * 10^2 = (1.732/4) * 100 = 43.30 square units
- Perimeter = 3 * 10 = 30 units
- Height = (sqrt(3)/2) * 10 = 0.866 * 10 = 8.66 units
- Circumradius = 10 / 1.732 = 5.77 units
- Inradius = 10 / 3.464 = 2.89 units
Equilateral triangle calculator: frequently asked questions
What is an equilateral triangle?
An equilateral triangle is a triangle with all three sides of equal length. All interior angles are also equal, each measuring 60 degrees. It is the only regular polygon with three sides.
What is the formula for the area of an equilateral triangle?
The area of an equilateral triangle with side length a is (sqrt(3)/4) * a^2, or approximately 0.433 * a^2. This formula comes from the base-times-height formula, where the height equals (sqrt(3)/2) * a.
What is the circumradius of an equilateral triangle?
The circumradius (the radius of the circumscribed circle) of an equilateral triangle with side length a is a/sqrt(3), or approximately 0.577 * a. The center of this circle is at the centroid of the triangle.
What is the inradius of an equilateral triangle?
The inradius (the radius of the inscribed circle) of an equilateral triangle with side length a is a/(2*sqrt(3)), or approximately 0.289 * a. This is half the circumradius.
Why are all angles in an equilateral triangle 60 degrees?
The sum of angles in any triangle is 180 degrees. In an equilateral triangle, all three angles are equal, so each angle is 180/3 = 60 degrees. This is a fundamental property of regular polygons.
Official sources
- Wolfram MathWorld: Equilateral Triangle.
- ISO 80000-2: Mathematical signs and symbols.
Reviewed by the CalculatorHub team, edited by James Graham, 14 June 2026. See our methodology.