Triangle Height Calculator

Calculate the height of a triangle by entering the base and area dimensions below.

Solution:

How to Calculate the Height of a Triangle

Triangle height, also referred to as its altitude, can be solved using a simple formula using the length of the base and the area.

h = 2 T b

Thus, the height or altitude of a triangle h is equal to 2 times the area T divided by the length of base b.

Diagram of a triangle showing base and height

How to Solve Triangle Height Without the Area

Given the length of the triangle's three sides it is possible to calculate the height by first solving for the area. The area of a triangle can be found using Heron's formula.

The first step is to find the perimeter of the triangle p, which can be found by adding all three sides.

p = a + b + c

Then, using the perimeter solve for the semiperimeter s which is equal to half the perimeter.

s = p 2

Finally, use the semiperimeter s and the length of three sides a, b, and c with Heron's formula to solve the area of a triangle.

T = s(s – a)(s – b)(s – c)

Thus, the area T of a triangle is equal to the square root of s times s minus a times s minus b times s minus c .

Then, to solve for height, use the area and the base with the formula above.

How to Solve the Height of a Right Triangle

For a right triangle there is a simple formula to solve the height, which is derived from the Pythagorean theorem.

h = ab c

The altitude h of a right triangle is equal to a times b, divided by c.

diagram of a right triangle showing legs a and b, hypotenuse c, angles alpha and beta, and height h

How to Solve the Height of an Isosceles Triangle

An isosceles triangle has two heights, the height of base a and the height of base b. Use the following formulas to solve the heights of each.

ha = √(a² – (0.5 × b)²) × b a

The altitude ha of base a is equal to the square root of a squared minus 0.5 times b, squared, times b, divided by a.

hb = a² – (0.5 × b)²

The altitude hb of base b is equal to the square root of a squared minus 0.5 times b, squared.

Diagram of an isosceles triangle showing the altitude of base b and side a

How to Solve the Height of an Equilateral Triangle

Since an equilateral triangle has three equal sides and three equal angles, it also has three equal heights. The formula to find the height of an equilateral triangle is:

h = a × √3 2

The altitude h is equal to a times the square root of 3, divided by 2.

diagram showing the parts of an equilateral triangle