What is an equilateral triangle?
An equilateral triangle has three equal sides and three equal interior angles of 60°. Knowing just one measurement—such as a side, height, perimeter or area—is enough to calculate all its other dimensions.
Its height runs from a vertex to the midpoint of the opposite side. This line is also a median, perpendicular bisector and angle bisector. The centroid, incenter, circumcenter and orthocenter all coincide.
How to use the equilateral triangle calculator
- Select the measurement you know: side length, height, area or perimeter.
- Enter a positive value and select its unit. For area, enter square units—for example, cm².
- Read the calculated dimensions and calculation steps. Results update automatically, or you can select Calculate.
The unit selector labels the measurement you enter. For example, changing 6 cm to meters treats the input as 6 m; it does not convert 6 cm into 0.06 m.
Equilateral triangle formulas
Let a be the side length, h the height, A the area, P the perimeter, r the inradius and R the circumradius.
| Measurement | Formula |
|---|---|
| Perimeter | P = 3a |
| Height | h = (√3 / 2)a |
| Area | A = (√3 / 4)a² |
| Inradius | r = a / (2√3) = h / 3 |
| Circumradius | R = a / √3 = 2h / 3 |
| Each interior angle | 60° |
Find the side length from another measurement
Why is the height a√3 / 2?
The altitude splits the triangle into two right triangles. Each has hypotenuse a and base a/2. Applying the Pythagorean theorem:
h = a√3 / 2
Substituting this height into A = ½ × base × height gives A = (√3/4)a².
Worked example: side length of 6 cm
- Perimeter: P = 3 × 6 = 18 cm.
- Height: h = (√3/2) × 6 = 3√3 ≈ 5.19615 cm.
- Area: A = (√3/4) × 6² = 9√3 ≈ 15.5885 cm².
- Inradius: r = 6/(2√3) = √3 ≈ 1.73205 cm.
- Circumradius: R = 6/√3 = 2√3 ≈ 3.4641 cm.
Example: find the side from an area of 25 cm²
Use a = √(4A/√3). Substituting A = 25 gives a = √(100/√3) ≈ 7.59836 cm. The perimeter is approximately 22.7951 cm and the height is approximately 6.58037 cm.
Quick reference table
Lengths below use the same unit; area uses that unit squared. Values are rounded to four decimal places.
| Side | Height | Area | Perimeter |
|---|---|---|---|
| 1 | 0.8660 | 0.4330 | 3 |
| 2 | 1.7321 | 1.7321 | 6 |
| 5 | 4.3301 | 10.8253 | 15 |
| 6 | 5.1962 | 15.5885 | 18 |
| 10 | 8.6603 | 43.3013 | 30 |
Frequently asked questions
Are all angles of an equilateral triangle 60°?
Yes. Its three angles are equal and sum to 180°, so each angle is 60°.
Is an equilateral triangle also isosceles?
Yes, under the inclusive definition of isosceles as having at least two equal sides. An equilateral triangle has all three sides equal.
What is the difference between the inradius and circumradius?
The inradius is the radius of the circle inside the triangle that touches all three sides. The circumradius is the radius of the circle through all three vertices. In an equilateral triangle, the circumradius is twice the inradius.
Can I calculate the area from the height?
Yes. The area is A = h²/√3. You can also choose Height in the calculator to find the area and other dimensions.
What happens when the side length doubles?
The height, perimeter, inradius and circumradius double. The area becomes four times as large because it depends on the square of the side length.
Can an equilateral triangle have a right angle?
No. All its angles are 60°, so every equilateral triangle is acute.