Case 1
- Side length
- 6
15.588457
Open with these valuesEquilateral Triangle Calculator
15.588457units²
Result: 15.588457 units²One side determines everything: the area is s²√3 ÷ 4, the height s√3 ÷ 2 and the perimeter 3s. Enter the side in any length unit and the area comes back squared in that unit. Every angle is 60°, whatever the size.
Worked examples
Case 2
- Side length
- 1
0.433013
Open with these valuesCase 3
- Side length
- 10
43.301270
Open with these valuesHow it's calculated
A = s² × √3 ÷ 4
- StepMeasure one side — in an equilateral triangle all three are equal.
- StepEnter it in any length unit.
- ResultRead the area in the square of that unit.
What this number means
One number settles the whole shape
Area, height, perimeter and all three angles follow from the single side length. A side of 6 gives a perimeter of 18, a height of about 5.196 and an area of 9√3 ≈ 15.588457.
The height is not the side
It is s√3 ÷ 2, roughly 0.866 of the side, because the perpendicular cuts the triangle into two 30-60-90 halves. For a side of 6 that comes to about 5.196, not 6.
Always 60°, at any size
Every angle is 60° whether the side is 1 or 10. Scaling changes lengths and area but never the angles, which is why one number is enough.
Side 2 is a coincidence, not a rule
At a side of 2 the area and the height are both √3 ≈ 1.732051, which makes the pair easy to remember. It happens at that one side length only.
Commonly misread
Area = side × side ÷ 2, since base and height are both the side.
The height is s√3 ÷ 2, not s. That shortcut gives 18 for a side of 6 where the true area is 15.588457.
Doubling the side doubles the area.
It quadruples it, because the side is squared. A side of 1 gives 0.433013 and a side of 2 gives 1.732051, four times as much.
The √3 ÷ 4 is a rounded constant somebody looked up.
It is exact. The √3 comes from the 30-60-90 halves the height creates, so s² × √3 ÷ 4 is a closed form and only the displayed decimals are rounded.
Reference table
| Side | Exact | Area |
|---|---|---|
| 1 | √3 ÷ 4 | 0.433013 |
| 2 | √3 | 1.732051 |
| 4.5 | 5.0625√3 | 8.768507 |
| 6 | 9√3 | 15.588457 |
| 10 | 25√3 | 43.301270 |
Questions
How do you find the area of an equilateral triangle?
Square the side, multiply by √3 and divide by 4. A side of 6 gives 9√3, about 15.59 square units.
How tall is an equilateral triangle?
The height is s√3 ÷ 2, roughly 0.866 of the side. For a side of 6 that is about 5.196.
Where does the √3 come from?
The height splits the triangle into two 30-60-90 halves, and √3 is the ratio in that right triangle. Half base times height then gives s²√3 ÷ 4.
What is the perimeter?
Three times the side, since all three sides are equal. A side of 6 gives 18.
Sources and last check
Information, not professional advice.