What Is the Equilateral Triangle Height Calculator?
An equilateral triangle has three equal sides and three equal 60° angles. This calculator finds the height (also called the altitude) of an equilateral triangle when you know the length of one side. Because all sides are equal, a single measurement is all that's needed. The tool also returns the area and perimeter for convenience.
How to Use It
Enter the side length (a) in any unit you like — centimeters, inches, meters. Click calculate and you'll get the height in the same units, along with the area (square units) and perimeter (units). The math is unit-agnostic, so the answer scales directly with whatever unit you provide.
The Formula Explained
The altitude of an equilateral triangle splits it into two 30-60-90 right triangles. Applying the Pythagorean theorem to half the base gives the height:
$$h = \frac{\sqrt{3}}{2}\cdot a$$
Since \(\sqrt{3} \approx 1.7320508\), the height is always about 0.8660254 times the side length. The area follows from \(A = \frac{1}{2}\cdot \text{base} \cdot \text{height} = \frac{\sqrt{3}}{4}\cdot a^{2}\), and the perimeter is simply \(3a\).
Worked Example
Suppose the side length is \(a = 10\). Then $$h = \frac{\sqrt{3}}{2}\cdot 10 = 0.8660254 \times 10 \approx 8.6603.$$ The area is \(\frac{\sqrt{3}}{4}\cdot 100 \approx 43.3013\) square units, and the perimeter is \(3 \times 10 = 30\) units.
FAQ
Is the height the same as the side length? No. The height is always shorter than the side — about 86.6% of it.
What units does the result use? Whatever unit you enter the side in. The calculator does not assume any particular measurement system.
Does this work for other triangles? No — this formula is specific to equilateral (all-equal-sided) triangles. Scalene or isosceles triangles need different formulas.
