Special Right Triangles Calculator — 45-45-90 & 30-60-90 (Free)
Use this free special right triangles calculator for the 45-45-90 and 30-60-90 triangles. Enter any one side and the tool gives the others using the fixed side ratios — in exact radical form and as decimals — with a scaled diagram and the steps.
How to use the calculator
- Choose the triangle type and which side you know.
- Enter that side’s length.
- Read all three sides and the angles, with the diagram.
The special ratios
In a 45-45-90 triangle the sides are in the ratio 1 : 1 : √2 (both legs equal, hypotenuse = leg × √2). In a 30-60-90 triangle they are 1 : √3 : 2 (short leg, long leg = short × √3, hypotenuse = 2 × short). No Pythagorean theorem needed.
Frequently asked questions
What are the side ratios of a 45-45-90 triangle?
1 : 1 : √2. The two legs are equal and the hypotenuse is a leg times √2.
What are the side ratios of a 30-60-90 triangle?
1 : √3 : 2 — the short leg, the long leg (short × √3), and the hypotenuse (2 × short).
Do I need the Pythagorean theorem?
No — the fixed ratios give every side from any one side directly.
Read the full lesson: learn the method step by step.
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