Equilateral Triangle Calculator
Calculate every property of an equilateral triangle from its side length. Find the area, perimeter, height, inradius (inscribed circle), and circumradius (circumscribed circle) instantly.
An equilateral triangle has three equal sides and three equal angles of 60 degrees each. It is the most symmetric triangle and has several elegant mathematical properties.
Equilateral Triangle Formulas (side length = s):
- Area: A = (sqrt(3) / 4) x s^2
- Perimeter: P = 3s
- Height: h = (sqrt(3) / 2) x s
- Inradius: r = s / (2 x sqrt(3)) = s x sqrt(3) / 6
- Circumradius: R = s / sqrt(3) = s x sqrt(3) / 3
The inradius is exactly half the circumradius (r = R/2) for equilateral triangles, and the centroid, circumcenter, incenter, and orthocenter all coincide at the same point. The height creates two 30-60-90 special right triangles.
Equilateral triangles are used in structural engineering (trusses, geodesic domes), road signs (yield signs), tessellations, and the construction of other geometric shapes. Six equilateral triangles form a regular hexagon.