Equilateral Triangle Calculator
Enter the side length of an equilateral triangle and instantly get its area, perimeter, height, inradius and circumradius.
(√3/4) × a²
- 1
Side squared
6² = 36 - 2
Area
(√3 ÷ 4) × 36 = 15.5885
How does this calculator work?
An equilateral triangle with side a: Area=(√3/4)a², Perimeter=3a, Height=(√3/2)a, Inradius=a√3/6, Circumradius=a√3/3. Enter the side length; all measurements are derived from this single value using the triangle's 60° angle symmetry.
Formula
How this is calculated
An equilateral triangle has all three sides equal and all three interior angles equal to 60°. Because of its perfect symmetry every formula reduces to a single variable — the side length a.
The area follows from the standard triangle formula: base times height divided by 2. The height of an equilateral triangle, found by dropping a perpendicular from one vertex to the opposite side and applying the Pythagorean theorem, is h = (√3/2)a. Substituting gives Area = (1/2)·a·(√3/2)·a = (√3/4)a². The perimeter is simply 3a.
The inradius (radius of the inscribed circle that touches all three sides) is r = a√3/6, and the circumradius (radius of the circumscribed circle passing through all three vertices) is R = a√3/3. Note that R = 2r for an equilateral triangle, reflecting that the centroid divides each median in a 2:1 ratio.
Frequently asked questions
All three interior angles of an equilateral triangle are exactly 60°. Because the triangle is equiangular (all angles equal), it is also equilateral (all sides equal), and vice versa.
Drop a perpendicular from any vertex to the midpoint of the opposite side. This creates two congruent 30-60-90 right triangles. The hypotenuse is the side a; the base of each right triangle is a/2; applying the Pythagorean theorem gives h = √(a²−(a/2)²) = √(3a²/4) = (√3/2)a.
For an equilateral triangle, R = 2r — the circumradius is exactly twice the inradius. Both are measured from the centroid, which is also the incenter and circumcenter. The centroid divides each median in a 2:1 ratio from vertex to midpoint.
Also known as
TG we-Calculate Editorial Team. (2026). Equilateral Triangle Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/equilateral-triangle-calculator
TG we-Calculate Editorial Team. "Equilateral Triangle Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/equilateral-triangle-calculator.
TG we-Calculate Editorial Team, "Equilateral Triangle Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/equilateral-triangle-calculator
@misc{wecalculate_equilateral_triangle_calculator, title = {Equilateral Triangle Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/equilateral-triangle-calculator}}, year = {2026}, note = {TG we-Calculate} }
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