Equilateral Triangle Calculator
Every side equal, every angle 60°. Enter one side for the area, perimeter, height and the two circle radii.
An equilateral triangle is fixed by a single length.
How the equilateral triangle calculator works
An equilateral triangle is fixed by a single length. Its angles are always 60°, its height is a√3 ÷ 2, and its area is a²√3 ÷ 4. The center of the inscribed circle, the circumscribed circle, the centroid and the point where the heights meet are all the same point — a symmetry no other triangle has.
Formula: a² = b² + c² − 2bc·cos A; a / sin A = b / sin B = c / sin C; area = ½ab·sin C
Worked examples
| Inputs | Area | Note |
|---|---|---|
| Side 6 | 15.5885 | area 15.588, height 5.196 |
| Side 10 | 43.3013 | area 43.301 |
| Side 1 | 0.433 | the unit equilateral triangle, area 0.433 |
FAQFrequently asked questions
What is an equilateral triangle?
One with all three sides the same length, which forces all three angles to 60°.
What is the area formula?
a²√3 ÷ 4, where a is the side. For side 6 that is 36 × 1.732 ÷ 4 ≈ 15.59.
What is its height?
a√3 ÷ 2 — about 0.866 times the side.
Is an equilateral triangle also isosceles?
Yes. Isosceles means at least two equal sides, so every equilateral triangle qualifies.
Why are the center points all the same?
Because of its threefold symmetry: the centroid, incentre, circumcentre and orthocentre coincide, which happens only for equilateral triangles.
Where these figures come from
- NIST Digital Library of Mathematical Functions — reference definitions for elementary and special functions
- Wolfram MathWorld — definitions and formulas for every topic on this page
- NIST/SEMATECH e-Handbook of Statistical Methods — the statistical formulas (mean, variance, z, confidence intervals, sample size)
- Common Core State Standards — Mathematics — the terms and methods taught in US schools
Last checked: September 2026. Formulas are fixed by mathematics and do not change with tax years or regulations.