Introduction
An isosceles triangle has two equal sides and two equal angles. This Isosceles Triangle Calculator lets you find every measurement of an isosceles triangle when you know just two values. Enter any combination of sides, angles, heights, area, or perimeter, and the tool instantly solves for the rest. You get the full set of results: all three sides, all three angles, both heights, area, perimeter, inradius, circumradius, and medians. It also draws the triangle and shows a chart of the angle distribution. This calculator gives you fast, accurate answers without any manual math.
How to Use Our Isosceles Triangle Calculator
Enter at least two known values about your isosceles triangle below. The calculator will find all missing sides, angles, heights, area, and perimeter for you.
Length Unit: Pick the unit for all side and height values, such as centimeters, inches, or meters. Leave it blank if you do not need a unit.
Angle Unit: Choose degrees or radians. All angle inputs and results will use the mode you pick.
Leg (a): Enter the length of one of the two equal sides of the triangle.
Base (b): Enter the length of the bottom side, which is the unequal side of the triangle.
Vertex Angle (β): Enter the angle at the top of the triangle where the two equal legs meet.
Base Angle (α): Enter one of the two equal angles at the bottom of the triangle.
Height to Base (hb): Enter the straight-down distance from the top vertex to the base.
Height to Leg (ha): Enter the distance from a base corner straight across to the opposite equal leg.
Area (K): Enter the total space inside the triangle if you already know it.
Perimeter (P): Enter the total distance around all three sides if you already know it.
Calculate: Click this button to solve the triangle. All results, a diagram, and an angle chart will appear below.
Reset: Click this button to clear all inputs and start over with default sample values.
What Is an Isosceles Triangle?
An isosceles triangle is a triangle that has two sides of equal length. These equal sides are called legs, and the third side is called the base. The two angles at the base are always equal to each other. The angle at the top, where the two legs meet, is called the vertex angle.
Key Properties of Isosceles Triangles
- Two sides (legs) are always the same length.
- The two base angles are always equal.
- All three angles add up to 180°.
- The height drawn from the vertex to the base splits the base into two equal halves. This means the height is also the line of symmetry.
- If all three sides happen to be equal, the triangle is also equilateral.
How to Calculate an Isosceles Triangle
You only need two known values to find everything else about an isosceles triangle. For example, if you know the leg and the base, you can find all the angles, the height, the area, and the perimeter. Here are the most common formulas:
- Height to base: h = √(a² − (b/2)²), where a is the leg and b is the base. This uses the same principle as the Pythagorean theorem.
- Area: K = ½ × b × h
- Perimeter: P = 2a + b
- Base angle: α = arccos(b / (2a))
- Vertex angle: β = 180° − 2α
When solving triangles using side and angle relationships, the Law of Cosines Calculator is especially helpful for finding a missing side when you know two sides and the included angle, while the Law of Sines Calculator works well when you know an angle and its opposite side.
Where Are Isosceles Triangles Used?
Isosceles triangles show up in many places. Builders use them in roof designs and bridge supports. Engineers use them in trusses and structural frames. They also appear in road signs, logos, and art. In math class, they are one of the first triangle types students learn about because their symmetry makes them easier to work with.