Pythagorean Theorem Calculator — How to Find a Missing Side
Solve for missing side a, b, or c in a right triangle with a² + b² = c². Example: a = 3, b = 4 → c = 5. Enter two known positive sides; rejects impossible leg/hypotenuse pairs. Browser learning tool.
How it works
Choose which side is missing. Enter the other two positive lengths. For c, inputs are legs a and b; for a, inputs are b and c; for b, inputs are a and c. Returns the positive square-root solution.
Formula
Pythagorean theorem a² + b² = c²:
- Missing c: c = √(a² + b²).
- Missing a: a = √(c² − b²) with c > b > 0.
- Missing b: b = √(c² − a²) with c > a > 0.
- Only real positive lengths; not a full trigonometry suite.
Example
Example: a = 3, b = 4 → c = 5.
When to use it
- Geometry homework: find a missing right-triangle side.
- Quick check of 3-4-5 style triples.
- Estimate diagonal length from two orthogonal legs.
Frequently asked questions
Which inputs when solving for c?
Enter legs a and b as the two known sides.
Why reject c ≤ a?
A hypotenuse must be strictly longer than each leg.
Are units required?
No — keep both known sides in the same unit.
Does this handle obtuse triangles?
No — only the right-triangle relation a²+b²=c².
Related tools
Questions or feedback
Something unclear, broken, or missing? Draft a message below — we read every note about these tools.