Isosceles Triangle Calculator

About this calculator

An isosceles triangle has two equal sides (the “legs”) and a base of a different length, which gives it two useful shortcuts once you know the base b and equal side a. Its height, drawn from the apex to the midpoint of the base, follows directly from the Pythagorean theorem: h = √(a² − (b/2)²). The area then works out to A = (b/4)√(4a² − b²), and the perimeter is simply P = 2a + b.

The defining symmetry of an isosceles triangle — the altitude to the base also bisects the base and the apex angle — is what makes it a favorite in geometry proofs, but it’s just as common in the physical world: roof trusses and gable ends are frequently built as isosceles triangles for structural symmetry, and architects and engineers rely on the same height and area formulas to size roof pitches, A-frame structures, and triangular support brackets.

Enter the base and equal side length, and this calculator returns the isosceles triangle’s area, height and perimeter in one step.