Isosceles Triangle Calculator

Calculate the area, perimeter, height, base angles, and leg length of an isosceles triangle from any two known measurements.

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How to use

Choose an input type, then enter the equal side length and either the base or the apex angle. The calculator finds all properties of the isosceles triangle.

Enter values Provide the equal side length and base to calculate all properties.

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Geometry

Isosceles triangle sides, angles, area, and height

The isosceles triangle calculator solves for missing sides, angles, area, perimeter, and height from any two known measurements of a triangle with two equal sides.

Isosceles triangle formulas

An isosceles triangle has two equal sides (legs) and a distinct base. The two base angles are always equal. The height from the apex bisects the base at right angles, splitting the triangle into two congruent right triangles.

Area = (base * height) / 2. The height from the apex is h = sqrt(leg^2 - (base/2)^2). Perimeter = 2 * leg + base.

h = sqrt(a^2 - (b/2)^2)

Height from the apex, where a is the leg length and b is the base.

A = b * h / 2

Area from base b and height h.

Input modes

You can solve from leg and base, leg and apex angle, leg and base angle, base and height, or base and base angle. Each pair determines the full triangle because the two-equal-sides constraint removes one degree of freedom.

Limitations

The calculator assumes a valid triangle. The base must be less than twice the leg length, and angles must be between 0 and 180 degrees exclusive.

Frequently asked questions

What makes a triangle isosceles?

Exactly two sides are equal in length. The angles opposite those sides are also equal.

 How do I find the height of an isosceles triangle?

Drop a perpendicular from the apex to the base. The height equals sqrt(leg^2 - (base/2)^2).

 Is an equilateral triangle also isosceles?

Yes. An equilateral triangle has three equal sides, so any pair of sides satisfies the isosceles condition. Every equilateral triangle is isosceles, but not every isosceles triangle is equilateral.

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