Equilateral triangle calculator

An equilateral triangle is a triangle in which all sides are equal (a = b = c), and all angles are equal to 60°. Due to symmetry, all heights, medians, and angle bisectors of an equilateral triangle coincide.

Area (S):

$$S=\frac{\sqrt{3}}{4}{a}^2$$

Height, median, and angle bisector (h = m = l):

In an equilateral triangle, the height drawn to any side also serves as the median and angle bisector.

$$h=\frac{\sqrt{3}}{2}a$$

Circumradius (R):

$$R=\frac{a}{\sqrt{3}}$$

Inradius (r):

$$r=\frac{a}{2\sqrt{3}}$$

Relationship Between Radii:

In any equilateral triangle, the circumradius is exactly twice the inradius:

$$R=2r$$

Perimeter (P):

$$P=3a$$

Available Calculation Options:

• By side (a) — finds the area, perimeter, height, and both radii.
• By height (h) — finds the side, area, perimeter, and radii.
• By inradius (r) — finds the side and all other parameters.
• By circumradius (R) — finds the side and all other parameters.
• By area (S) — finds the side, height, and perimeter.