Isosceles Triangle Calculator: Area, Height & Angles Made Easy (2026)
Calculate all properties of an isosceles triangle. Find area, height, base, legs, angles, and perimeter from any known dimensions with our free calculator.
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Put these formulas into practice with our instant, step-by-step Isosceles Triangle Calculator.
An isosceles triangle is a triangle with at least two sides of equal length, making it one of the most common and useful triangle types in geometry. From roof trusses to flag designs, isosceles triangles appear everywhere in both nature and human-made structures. Our free isosceles triangle calculator lets you enter any two known dimensions and instantly compute all remaining properties.
Key Takeaway
An isosceles triangle has two equal sides (legs) and two equal base angles. Our calculator computes area, height, perimeter, and all angles from any two known values.
What is an Isosceles Triangle?
An isosceles triangle is defined as a triangle with at least two sides of equal length. The two equal sides are called legs, and the third side is called the base. The angles opposite the equal sides (called base angles) are also equal.
Every equilateral triangle (where all three sides are equal) is also an isosceles triangle, but not every isosceles triangle is equilateral. The isosceles triangle has exactly one line of symmetry: the altitude from the apex (the vertex between the two legs) to the base.
Formulas for Isosceles Triangle Calculations
Height: h = √[l² - (b/2)²]
Perimeter: P = b + 2l
Base angle: α = arctan(2h / b)
Apex angle: θ = 180° - 2α
Where b is the base, l is the leg length, and h is the height from the apex to the base.
How to Use the Isosceles Triangle Calculator
Our calculator accepts the base and leg length as inputs and computes all remaining properties:
- Enter the base length
- Enter the leg length (must be greater than half the base)
- View all computed results: height, area, perimeter, base angle, and apex angle
- Copy the results to your clipboard
Worked Example
Isosceles Triangle with Base = 8, Leg = 5
| Property | Calculation | Result |
|---|---|---|
| Height | √(5² - 4²) = √9 | 3 |
| Area | (8 × 3) / 2 | 12 |
| Perimeter | 8 + 5 + 5 | 18 |
| Base angle | arctan(3/4) | 36.87° |
| Apex angle | 180° - 2(36.87°) | 106.26° |
Real-World Applications
- Architecture: Roof trusses, gables, pediments, and A-frame structures
- Engineering: Bridge supports and load distribution
- Flags: Many national flags feature isosceles triangles
- Sports: Basketball key area and field markings
- Art: Symmetrical designs and patterns
Frequently Asked Questions
What are the base angles?
The base angles are the two angles opposite the equal sides. In an isosceles triangle, the base angles are always equal. If the apex angle is θ, each base angle is (180° - θ)/2.
Can an isosceles triangle be a right triangle?
Yes. A right isosceles triangle has a 90° apex angle and two 45° base angles. The legs are equal, and the hypotenuse is leg × √2.
Try our isosceles triangle calculator to compute all properties instantly, or explore our equilateral triangle calculator and right triangle calculator for more triangle computations.