Advanced Isosceles Triangle Calculator

Case	Equal Side	Base	Height	Area	Perimeter	Vertex Angle
Classroom Example A	10	12	8	48	32	73.7398°
Classroom Example B	13	10	12	60	36	45.2397°
Classroom Example C	9	14	5.6569	39.5983	32	102.6356°

Formula Used

Height from equal side and base: h = √(a² − b²/4)

Area: A = (b × h) / 2

Perimeter: P = 2a + b

Vertex angle from equal side and base: θ = 2 × asin(b / 2a)

Base angle: α = (180 − θ) / 2

Equal side from base and height: a = √(h² + b²/4)

Inradius: r = 2A / P

Circumradius: R = a²b / 4A

These relationships come from symmetry and the Pythagorean theorem. Splitting the base creates two right triangles. That makes missing lengths and angles easier to compute.

How to Use This Calculator

Select the input mode that matches your known values.
Enter the related measurements in the visible fields.
Use consistent units for every length entry.
Click Calculate Triangle to solve the shape.
Review results above the form after submission.
Use the CSV or PDF buttons to export results.
Check the graph for a quick visual comparison.
Compare your answer with the example table below.

Frequently Asked Questions

1. What is an isosceles triangle?

An isosceles triangle has two equal sides. The angles opposite those equal sides are also equal. Its symmetry makes many calculations simpler.

2. Which inputs are enough to solve it?

You can solve it using equal side and base, equal side and height, equal side and vertex angle, or base and height. Each mode here uses one valid pair.

3. Why must the base be smaller than twice the equal side?

If the base reaches twice the equal side, the triangle collapses into a straight line. A valid isosceles triangle needs a positive height.

4. Does the calculator need matching units?

Yes. Enter all lengths in one unit system. For example, keep every length in centimeters, meters, or inches. Mixed units produce incorrect results.

5. What does the vertex angle mean?

The vertex angle sits between the two equal sides. The other two angles are the base angles. They are always equal in an isosceles triangle.

6. What is the difference between inradius and circumradius?

Inradius measures the radius of the inscribed circle touching all sides. Circumradius measures the radius of the outer circle passing through all vertices.

7. Can I use decimals?

Yes. The calculator accepts decimal values for lengths and angles. That helps when working with measured data, design values, or rounded homework answers.

8. What does the graph show?

The graph compares the main computed outputs. It helps you inspect how side length, area, perimeter, angles, and radii relate in one solved triangle.