Example 1
- a: 2
√3 ≈ 1.732
P = (4√3)/4 = √3. Height ≈ 1.732, perimeter 6.
Equilateral triangle area calculator
Type side length a. An equilateral triangle has equal sides and 60° angles. Formula P = (a² × √3) / 4. At a = 2 the area is √3, about 1.732. At a = 6 you get 9√3, about 15.588.
An equilateral triangle has equal sides and equal 60° angles. One side is enough for the rest.
Result
Enter the side length.
How it works
In an equilateral triangle every side has the same length. Area is P = (a² × √3) / 4. Height is h = (a × √3) / 2, and the perimeter is 3a. Draw the height and you split the triangle into two 30°-60°-90° right triangles. At a = 2: P = (4√3)/4 = √3 ≈ 1.732, height also ≈ 1.732, perimeter 6.
At a = 6: P = (36√3)/4 = 9√3 ≈ 15.588. This is not a generic triangle with base and height typed separately. That card wants two dimensions. Here one side is enough, because every side matches.
One field, Side length a, greater than zero. Type 2 or 6, click Calculate. A comma and a period both parse. The cm/inch switch changes the result label and does not convert a typed 2.
A 3-4-5 triangle is not equilateral: area 6 is (3×4)/2 on triangle area, and c = 5 on Pythagoras. A square of side 2 has area 4, with no √3.
Without a positive a, nothing computes. a = 2 still gives √3 if you mix cm and inches only in your head. Think both in one unit; the result is that unit squared.
At a = 4 the area is 4√3 ≈ 6.928. At a = 10 it is 25√3 ≈ 43.301. Height at a = 6 is 3√3 ≈ 5.196, not 15.588.
Formulas
Area: P = (a²√3)/4
Height: h = (a√3)/2
Perimeter: O = 3a
How to use
- Type side length a greater than zero, for example 2 or 6.
- Click Calculate. a = 2 gives √3 ≈ 1.732. a = 6 gives 9√3 ≈ 15.588.
- Read perimeter 3a and height (a√3)/2 from the calculator if it prints them, or work them beside it.
- The side must use one unit. The switch changes the cm² or in² label and does not turn a 2 into inches.
- A triangle with base and height lives on triangle area. 3-4-5 is not equilateral.
Area at a = 2 and √3
Equal sides and 60° angles. Formula (a² × √3) / 4. At a = 2 the area is √3, about 1.732. At a = 6 you get about 15.588.
- a
- Side. 2 gives √3 ≈ 1.732. 6 gives 9√3 ≈ 15.588. 10 gives 25√3 ≈ 43.301. Must be greater than zero.
- √3
- In the numerator. At a = 2 it is √3 alone. At a = 1 the result is √3/4 ≈ 0.433. Not ½ah from the plain triangle.
- P
- Area (a²√3)/4 in this calculator’s formula line. a = 2 is about 1.732. a = 6 is about 15.588.
Examples
Example 2
- a: 6
9√3 ≈ 15.588
A common textbook case.
Example 3
- a: 10
25√3 ≈ 43.301
Perimeter 30, height ≈ 8.660.
Example 4
- a: 1
√3/4 ≈ 0.433
The tidy unit case.
Related calculators
Frequently asked questions
What is the area at a = 2?
√3 ≈ 1.732. P = (4√3)/4. Height is also ≈ 1.732, perimeter 6.
What about a = 6?
9√3 ≈ 15.588. P = (36√3)/4. Height 3√3 ≈ 5.196, not the area itself.
What is the formula?
P = (a² × √3) / 4. One side is enough, because all three match and the angles are 60°.
How is this different from 3-4-5 area?
3-4-5 has area 6 from (3×4)/2 and is not equilateral. Here every side matches, and √3 sits in the formula.
What about a = 4 and a = 10?
4√3 ≈ 6.928 and 25√3 ≈ 43.301. Area is (√3/4) a² on both sides.
Can I type height instead of the side?
No. The input is side a. From height h recover a = 2h/√3, then come back.
What is the perimeter at a = 2?
6, because three equal sides. The area at a = 2 is √3, not the perimeter.
Does a square of side 2 have the same area?
A square 2×2 = 4. Here √3 ≈ 1.732. Different shape, no 90° at every vertex.
Can a be 0?
No. The side must be greater than zero. With no length there is no triangle.
Can I mix cm and inches?
Not in one run. One side, one unit, result in that unit squared.
Knowledge sources
The calculator computes the same formula as the definition below.
Page updated in 2026.