Enter the two equal legs and base — or the base and height — to calculate an isosceles triangle's area, perimeter, and angles.

How to Use the Isosceles Triangle Calculator

Switch between Legs & Base and Base & Height mode depending on which pair of measurements is on hand. Either way, the calculator returns the triangle's height, area, perimeter, and both base angles plus the apex angle.

An isosceles triangle has exactly two equal sides (the legs) meeting at the apex, with a third side (the base) connecting their ends. Splitting it straight down the middle, from the apex to the base's midpoint, produces two mirror-image right triangles — the trick behind every formula here:

height = √(leg² − (base ÷ 2)²)
area = ½ × base × height
base angle = cos⁻¹((base ÷ 2) ÷ leg)
apex angle = 180° − 2 × base angle

That right-triangle split only works if the legs are long enough to reach past half the base — a leg shorter than half the base can't close the shape at all, which is what the validation on this page is checking for.

In Base & Height mode the direction reverses: the leg comes from that same right triangle, leg = √((base ÷ 2)² + height²), and everything else follows the same way.