Isosceles Triangle Height Calculator

This isosceles triangle height calculator will calculate for you the two heights of an isosceles triangle. It will also tell you whether you have a valid isosceles triangle. Read on to learn about:

• What is an isosceles triangle?
• How to calculate the height of an isosceles triangle.
• The isosceles triangle height formula.

An isosceles triangle is a triangle where two sides are of equal length. You can also argue that a triangle where all three sides are equal (an equilateral triangle) is a special case of an isosceles triangle.

Isosceles triangles date back to ancient Egypt, where it was used for decoration and in their architecture — even the face of a pyramid is an isosceles triangle.

We can derive the formula for the height of an isosceles triangle (as measured from the base to the vertex between the two equal legs) from Pythagoras's Theorem if we look for a right-angle triangle inside the isosceles triangle.

You can form one if you only consider half of an isosceles triangle, cutting at the midpoint of the base (side $b$ in the figure above the calculator). Then we can derive the height $h$ starting from Pythagoras's equation:

Using this isosceles triangle height calculator is really straightforward. Here are the steps to follow:

1. Enter a value for the length of each leg of the triangle (the two equal sides).
2. Input the length of the base of your isosceles triangle.
3. You'll instantly receive a value for the height of the triangle, as measured from the base to the vertex (h_b).
4. As a bonus, you'll also get the height as measured from the leg side to the opposite vertex at the end of the base (h_a).

Note that if you want to calculate the lengths in different units, you can change the unit before entering a value. Changing the unit after entering a value, the calculator is also a length unit converter.

Here are some other isosceles triangle calculators that you might be interested in:

• The isosceles triangle angles calculator;
• The isosceles triangle find A calculator;
• The iIsosceles triangle area calculator;
• The isosceles triangle side calculator;
• The isosceles right triangle calculator; and
• The triangle vertices calculator.