An equilateral triangle’s area, perimeter, and height, all computed directly from its single side length.
How it works
The area formula (√3 ÷ 4 times side squared) comes from splitting the triangle into two 30-60-90 right triangles; the perimeter is simply three times the side; the height uses a similar √3-based relationship.
What this does not include
This does not include general (non-equilateral) triangles — for those, use this site’s triangle area calculator with a separately known base and height instead.
How to use this calculator
- Enter the side length.
A worked example
An equilateral triangle with side 6: area = 15.588457, perimeter = 3 × 6 = 18, height = 5.196152.
Side 10: perimeter = 30.
What the variables mean
| Variable | Meaning |
|---|---|
| Side length | Length of each of the three equal sides |
Edge cases worth knowing
A single side length fully determines an equilateral triangle — all three angles are fixed at 60° by definition, so no additional measurements are needed.
Height scales linearly with side length, but area scales with its square — doubling the side length doubles the height but quadruples the area, an easy detail to overlook when scaling a design up.
Frequently asked questions
Why does the formula involve the square root of 3?
It comes from the height of the triangle, found using the Pythagorean theorem on half the base and the full side — a relationship that consistently produces a √3 term for equilateral triangles.
Are all three angles always 60 degrees?
Yes — since all three sides are equal, all three angles must also be equal, and they sum to 180 degrees, making each exactly 60.
Does doubling the side length double the area?
No — area scales with the side length squared, so doubling the side quadruples the area.
