Isosceles Triangle Calculator

Enter any two known values for an isosceles triangle to calculate the edge lengths, altitude, angles, area, perimeter, inradius, and circumradius.

diagram of a isosceles triangle showing leg a, base c, angles alpha and beta, and height h

Solution:

side a:
3
base b:
5
 
angle α:
33.557° | 0.5857 rad
angle β:
112.89° | 1.97 rad
 
height h:
1.658
 
area:
4.146
perimeter:
11
 
inradius:
0.7538
circumradius:
2.714

Type of Triangle:

obtuse isosceles triangle
Learn how we calculated this below


On this page:


What is an Isosceles Triangle?

An isosceles triangle is a triangle that has two edges, or legs, of the same length. The third edge is called the base.

The two angles adjacent to the base are called the base angles, while the angle opposite the base is called the vertex angle.

Because the legs are of equal length, the base angles are also identical.

diagram of a isosceles triangle showing leg a, base c, angles alpha and beta, and height h

Types of Isosceles Triangles

There are four types of isosceles triangles: acute, obtuse, equilateral, and right.

An acute isosceles triangle is a triangle with a vertex angle less than 90°, but not equal to 60°.

An obtuse isosceles triangle is a triangle with a vertex angle greater than 90°.

An equilateral isosceles triangle is a triangle with a vertex angle equal to 60°. An equilateral triangle is a special case where all the angles are equal to 60° and all three sides are equal in length. Try our equilateral triangle calculator.

diagram of an equilateral triangle showing the sides, angles, and height

A right isosceles triangle is a triangle with a vertex angle equal to 90°, and base angles equal to 45°. This is also referred to as a 45 45 90 special right triangle.

diagram of a special right 45 45 90 triangle showing legs a and b, hypotenuse c, 45 degree angles, and height h

We have a special right triangle calculator to calculate this type of triangle.

How to Calculate Edge Lengths of an Isosceles Triangle

Given the height, or altitude, of an isosceles triangle and the length of one of the legs or the base, it’s possible to calculate the length of the other sides.

Find the Base Length

Use the following formula to solve the length of the base edge:

b = 2a² – h²

The base length b is equal to 2 times the square root of leg a squared minus the height h squared.

Find the Leg Length

Use the following formula to solve the length of the legs:

a = h² + (b ÷ 2)²

The leg length a is equal to the square root the height h squared plus the base b divided by 2, squared.

How to Calculate the Angles of an Isosceles Triangle

Given any angle in an isosceles triangle, it is possible to solve the other angles.

Find the Base Angle

Use the following formula to solve the base angle:

α = 180° – β / 2

The base angle α is equal to 180° minus vertex angle β, divided by 2.

Find the Vertex Angle

Use the following formula to solve the vertex angle:

β = 180° – 2α

The vertex angle β is equal to 180° minus 2 times the base angle α.

How to Calculate Area and Perimeter

Given the sides of an isosceles triangle, it is possible to solve the perimeter and area using a few simple formulas.

Find the Perimeter

You can find the perimeter of an isosceles triangle using the following formula:

p = 2a + b

Thus, the perimeter p is equal to 2 times leg a plus base b.

Find the Semiperimeter

Given the perimeter, you can find the semiperimeter. The semiperimeter s is equal to half the perimeter.

s = p / 2

Find the Area

You can find the area of an isosceles using the formula:

area = s(s – a)(s – a)(s – b)

The area is equal to the square root of the semiperimeter s times semiperimeter s minus leg a times semiperimeter s minus a times semiperimeter s minus base b.

This is known as Heron’s formula.