What this calculator does
An equilateral triangle is a triangle whose three sides are all equal and whose three interior angles are each 60 degrees. This calculator takes a single number — the side length a — and instantly returns the triangle's area, perimeter, and height. It is purely geometric and works in any unit system: if you enter the side in meters, the area comes out in square meters, while the perimeter and height stay in meters.
How to use it
Type the side length a into the input box and submit. The value must be greater than zero — a side of zero or a negative number does not describe a real triangle, so all outputs return zero in that case. The tool is unit-agnostic: pick whatever length unit you like (cm, inches, feet, meters) and read the results in that same unit, with area in the squared version of it.
The formulas explained
For an equilateral triangle with side length a:
Area: $$S = a^{2}\cdot \frac{\sqrt{3}}{4}.$$ The factor \(\frac{\sqrt{3}}{4} \approx 0.4330\) comes from splitting the triangle into two 30-60-90 right triangles.
Perimeter: \(L = 3a\), simply three equal sides.
Height: $$h = a\cdot \frac{\sqrt{3}}{2}.$$ This is the perpendicular distance from a vertex to the opposite side, also found via the Pythagorean theorem.
Worked example
Suppose a = 2. Then $$S = 2^{2}\cdot \frac{\sqrt{3}}{4} = \frac{4 \cdot 1.7320508}{4} = 1.7320508.$$ The perimeter is \(L = 3 \cdot 2 = 6\), and the height is \(h = 2 \cdot \frac{\sqrt{3}}{2} = \sqrt{3} = 1.7320508\). So a triangle with sides of length 2 has an area of about 1.732 square units.
FAQ
What is √3 used in the formula? \(\sqrt{3} \approx 1.7320508\). It appears because the height of an equilateral triangle equals half the side times \(\sqrt{3}\).
Does the unit matter? No. Enter the side in any unit; area is reported in that unit squared, and perimeter and height in that same unit.
What if I enter zero or a negative number? A non-positive side length does not form a triangle, so the calculator returns zero for all outputs rather than an error.
