Equilateral Triangle Calculator

An equilateral triangle is a triangle in which all three sides are equal in length and all three interior angles are equal, each measuring 60°. It is also considered a special case of an isosceles triangle. Because of its symmetry, the altitudes, angle bisectors, perpendicular bisectors, and medians all coincide.

The area of an equilateral triangle with side length a is calculated using the formula K = (√3 / 4) × a². For example, if the side is 6 units, the area is (√3 / 4) × 36 ≈ 15.5885 square units.

The height (altitude) of an equilateral triangle with side a is h = (√3 / 2) × a. This comes from splitting the equilateral triangle into two right triangles and applying the Pythagorean theorem. For a side of 6, h ≈ 5.196 units.

Since all three sides of an equilateral triangle are equal, the perimeter is simply P = 3a, where a is the side length. For example, a triangle with side length 8 cm has a perimeter of 24 cm.

The inradius (r) is the radius of the largest circle that fits inside the triangle, calculated as r = a / (2√3) = a√3 / 6. The circumradius (R) is the radius of the circle passing through all three vertices, calculated as R = a / √3 = a√3 / 3. For an equilateral triangle, R = 2r.

Yes. Rearranging the area formula K = (√3 / 4) × a² gives a = √(4K / √3). Enter your area value in the calculator above, select 'Area (K)' as your known value, and all other properties will be computed automatically.

No. A right triangle has one angle of 90°, but an equilateral triangle requires all three angles to be exactly 60°. Since 60° + 60° + 60° = 180° and 90° ≠ 60°, no triangle can be both right-angled and equilateral.

The semiperimeter is simply half the perimeter: s = P / 2 = 3a / 2. It is used in Heron's formula and other geometric calculations. For an equilateral triangle with side 6, the semiperimeter is 9.