Pythagorean Theorem Calculator
Adjust the inputs below. Results update as you type.
How it works
Pythagorean theorem: a² + b² = c² where c is the hypotenuse (longest side). Solve for unknown: c = √(a²+b²); a = √(c²−b²). Pythagorean triples (integer solutions): 3-4-5, 5-12-13, 8-15-17. Used in construction (squaring corners), navigation (distance), and physics (vector magnitudes). Extends to 3D: space diagonal of a box = √(l²+w²+h²).
Input guidance
- Check units and decimal placement before running calculations.
- For percentage and ratio tasks, define the baseline value clearly.
- Use rounded output carefully and keep full precision for intermediate steps.
The formula
In a right triangle, a² + b² = c², where c is the hypotenuse (opposite the right angle). Solve for any side: c = √(a² + b²) or a = √(c² − b²).
Worked example
With legs 6 and 8: c = √(36 + 64) = √100 = 10.
More examples to test
- Baseline example: solve with clean numbers first to verify formula direction.
- Edge-case example: test near-zero or boundary values to avoid interpretation errors.
How to interpret results
Use outputs as quick checks, then verify with step-by-step work for graded or high-stakes use.
When this can be inaccurate
Errors usually come from unit mismatch, wrong baseline assumptions, or rounding too early in multistep problems.
Change history
- July 2026: Quality-reviewed for publication with formula checks and explanatory copy updates.
Site-wide corrections also appear on the corrections log.
Build math and logic skills with guided lessons
Educational platform recommendation.
Frequently asked questions
When does the Pythagorean theorem apply?+
Only to right triangles — those with a 90° angle. The hypotenuse is always the longest side, opposite the right angle.
How do I find a leg, not the hypotenuse?+
Rearrange: a = √(c² − b²). Subtract the known leg's square from the hypotenuse's square, then take the root.
What is a Pythagorean triple?+
A set of three whole numbers that satisfy a² + b² = c², like 3-4-5 or 5-12-13.
Why do my classroom and calculator results differ?+
Differences usually come from rounding conventions, order-of-operations handling, or different baseline assumptions.
What is the safest way to validate an answer?+
Recompute with units shown and check against a second method or manual arithmetic for critical problems.