Special Right Triangles Calculator

Solve the exact side ratios for 45-45-90 and 30-60-90 triangles.

Last updated: June 2026 | By Patchworkr Team

Known Side

Value

Math check: side ratio 1 : 1 : sqrt(2)

Result

Enter a positive side length to complete the triangle.

Ratios

45-45-90: 1 : 1 : sqrt(2)

30-60-90: 1 : sqrt(3) : 2

For a 30-60-90 triangle with short leg 5, the long leg is 5 sqrt(3) = 8.660254 and the hypotenuse is 10.

For a 45-45-90 triangle with a leg of 5, the other leg is also 5 and the hypotenuse is 5 sqrt(2).

These ratios are exact. The calculator uses them directly instead of approximating the triangle numerically first.

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