Pythagorean Theorem Calculator

Pythagorean Theorem – Quick Cheat Sheet

Right triangle only: the angle between legs a and b is 90°.
Core formula: a² + b² = c² (c is the hypotenuse; opposite the right angle).
Solve for c: c = √(a² + b²).
Solve for a: a = √(c² − b²) (requires c > b).
Solve for b: b = √(c² − a²) (requires c > a).
Pythagorean triples: (3,4,5), (5,12,13), (8,15,17), (7,24,25), (9,40,41)...
Units: keep the same unit for all sides; output uses the same unit.
Validation: sides must be non-negative; when solving a leg, c must be larger than the known leg.

Tips & notes

If you enter all three sides, the tool verifies the identity within a small numerical tolerance.
Use the “Decimals” control to set precision (0–12 places).
Works for any consistent unit system (metric or imperial).