What this calculator does
An equilateral triangle has all three sides equal and all three angles fixed at 60°, which means it is entirely determined by a single measurement: the side length. There is no need to enter a base and a separate height, or three separate sides, the way a general triangle calculator requires.
This equilateral triangle calculator takes that one side length and returns the area, perimeter, the perpendicular height, and the inradius and circumradius together, since knowing one side of an equilateral triangle is enough to know everything else about it.
The formula
The height splits the triangle into two identical right triangles, giving height = (√3/2) × s by Pythagoras. Area follows as (√3/4) × s², half the base times that height. The inradius, the distance from the centre to a side, is s / (2√3), and the circumradius, the distance from the centre to a corner, is s / √3, exactly twice the inradius.
| Term | Meaning |
|---|---|
| s | The side length, the single measurement that fixes an equilateral triangle completely. |
| Inradius | The radius of the circle inscribed inside the triangle, touching the midpoint of each side. |
| Circumradius | The radius of the circle passing through all three corners. |
The inputs explained
| Field | What to enter |
|---|---|
| Side length | The length of any one side. All three sides of an equilateral triangle are equal by definition. |
When to use it
A truss, gusset or bracket cut to an equilateral triangle
A structural gusset plate or decorative bracket cut as an equilateral triangle needs only the one side length measured on the drawing to get the area of material and the cutting height.
How to find the area of an equilateral triangle for a school problem
A geometry question giving a single side length is solved directly here, without first working out the height by hand using the 30-60-90 right triangle it hides.
Checking a triangle really is equilateral before using this shortcut
If two different side lengths are given, the triangle is isosceles or scalene rather than equilateral, and this calculator’s single-input approach no longer applies; the isosceles or scalene triangle calculators cover those cases instead.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
Equilateral triangle formula across a range of side lengths
The area, perimeter and height of an equilateral triangle across a range of side lengths.
Questions
What is an equilateral triangle?
An equilateral triangle has all three sides equal in length and all three interior angles equal to 60°. It is the most symmetric type of triangle, with three lines of symmetry.
What is the area formula for an equilateral triangle?
Area = (√3/4) × s², where s is the side length. It needs no separate height measurement, since the height is itself fixed once the side length is known.
Why are all the angles of an equilateral triangle 60°?
Every triangle’s angles sum to 180°. With all three sides equal, all three angles must also be equal by symmetry, and 180° divided three ways gives 60° each.
How is an equilateral triangle different from an isosceles triangle?
An equilateral triangle is a special case of an isosceles triangle where all three sides match rather than just two. Every equilateral triangle is isosceles, but most isosceles triangles are not equilateral.
For a triangle with only two equal sides, see the isosceles triangle calculator. For a triangle with three different known side lengths, see the triangle from three sides calculator.