Equilateral Triangle Calculator

Equilateral Triangle Calculator. Enter any known value — side length, height, area, perimeter, inradius, or circumradius — and the Equilateral Triangle Calculator will compute all remaining properties. Results include the side (a), altitude (h), area (K), perimeter (P), semiperimeter (s), inradius (r), and circumradius (R) of your equilateral triangle. Also try the use the Cuboid Calculator (Rectangular Prism).

Results

Side Length (a)

Height / Altitude (h)

Area (K)

Perimeter (P)

Semiperimeter (s)

Inradius (r)

Circumradius (R)

What is an equilateral triangle?

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. See also our calculate Hexagon Area (A).

How do I find the area of an equilateral triangle?

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.

How do I find the height of an equilateral triangle?

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.

How do I find the perimeter of an equilateral triangle?

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.

What are the inradius and circumradius of an equilateral triangle?

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.

Can I calculate the side length if I only know the area?

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.

Can a right triangle be equilateral?

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.

What is the semiperimeter of an equilateral triangle?

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. You might also find our Circumference Calculator useful.