Case 1
- Side length
- 6
15.588457
Open with these valuesEquilateral Triangle Calculator
Change any value to update the result.
15.588457units²
Area: 15.588457 units²Examples
How the result moves
Side length → Area (units²)Your current valid inputs, with one value varied across the range.
How the result moves
| Side length | Area |
|---|---|
| 5.000 | 10.825318 |
| 6.000Your value | 15.588457 |
| 10.000 | 43.301270 |
One 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.Side length=6
- StepEnter it in any length unit.Side length=6
- ResultRead the area in the square of that unit.15.588457units²
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
MisconceptionArea = side × side ÷ 2, since base and height are both the side.
CorrectionThe height is s√3 ÷ 2, not s. That shortcut gives 18 for a side of 6 where the true area is 15.588457.
MisconceptionDoubling the side doubles the area.
CorrectionIt 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.
MisconceptionThe √3 ÷ 4 is a rounded constant somebody looked up.
CorrectionIt 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.