Equilateral Triangle Calculator
From a single side length, get the area, the height, and the perimeter — the three numbers that describe any equilateral triangle.
One side, three answers
Enter the side length and the calculator returns the area ((√3/4)s²), the height ((√3/2)s), and the perimeter (3s) at once.
Keep units consistent
The side is unit-agnostic — your answers come back in the same unit (squared for the area), so don't mix centimetres with inches.
What is an equilateral triangle calculator?
One side in, full triangle out
An equilateral triangle has three equal sides and three 60° angles, so a single measurement — the side length — fixes its whole shape. This calculator turns that one number into the three quantities that describe the triangle: its area, its height, and its perimeter. Because every equilateral triangle is similar (the same shape at a different scale), each output follows directly from the side and the constant √3. That makes the side the only input you need for trusses, signage, tiling patterns, warning signs, and any geometry homework where a regular triangle shows up.
Enter the side length in any length unit to get the area, height, and perimeter instantly.
Three short formulas, all built from the side length s and the constant √3 (about 1.732051).
area = (√3/4) × s²The perimeter is simply three times the side (3 × s), and the height — the perpendicular distance from a side to the opposite vertex — is (√3/2) × s. The area, the space enclosed, is (√3/4) × s²: square the side first, then multiply by √3/4. Because the side is squared, the area grows much faster than the height or perimeter as the triangle gets bigger.
Suppose you have an equilateral triangle with a side of 6.
Perimeter
3 × 6 = 18 — the distance around all three equal sides.
Height
(√3/2) × 6 ≈ 5.196152 — the perpendicular distance to the opposite vertex.
Area
(√3/4) × 6² = (√3/4) × 36 ≈ 15.588457 square units — the space inside.
The three outputs answer three different everyday questions. The perimeter (18 for a side of 6) is the total length of edging you would need to frame the triangle. The height (about 5.196152) is how tall the triangle stands when one side rests flat — useful for fitting it under a beam or laying out a sign. The area (about 15.588457 square units) is the surface you cover — the material in a triangular panel, the paint on a sign, the tiles in a pattern. The key insight is that area scales with the side squared: double the side from 6 to 12 and the area jumps fourfold, from 15.588457 to 62.353829, while the height and perimeter only double. Because every equilateral triangle is similar, all of these quantities scale directly from the single side length, and the height doubles as the perpendicular bisector and the line from a vertex to the centroid. That is why this shape is so common in trusses, signage, and tiling: one measurement pins down everything else.
The formulas are exact, but a couple of practical points are worth keeping in mind.
Truly equal sides and consistent units
These formulas describe a perfect equilateral triangle — three exactly equal sides and three 60° angles. A triangle that is only roughly equilateral, or cut with rounded corners, will differ a little from the computed value. The side is also unit-agnostic, so the answers are only meaningful if you keep one unit throughout: a side in centimetres gives a height and perimeter in centimetres and an area in square centimetres, never a mix.