Pythagorean Theorem Calculator
Solve for any missing side of a right triangle using a² + b² = c². Enter any two sides to find the third.
Enter any two sides to solve for the third (leave one empty)
Missing Side
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Triangle Properties
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Pythagorean Theorem
Solve for c: c = √(a² + b²)
Solve for a: a = √(c² − b²)
Solve for b: b = √(c² − a²)
The Pythagorean theorem applies to right triangles only. Side c (the hypotenuse) is always the longest side and is opposite the right angle.
Example 2: a=5, c=13 → b = √(169−25) = √144 = 12
Example 3: b=8, c=10 → a = √(100−64) = √36 = 6
Common Pythagorean Triples
| a | b | c |
|---|---|---|
| 3 | 4 | 5 |
| 5 | 12 | 13 |
| 8 | 15 | 17 |
| 7 | 24 | 25 |
Frequently Asked Questions
Does the Pythagorean theorem work for all triangles?
No, it only works for right triangles (triangles with a 90° angle). For other triangles, use the Law of Cosines: c² = a² + b² − 2ab·cos(C).
How do I know which side is the hypotenuse?
The hypotenuse is always the longest side of a right triangle and is located opposite the 90° angle.
Can the Pythagorean theorem give negative results?
No. If c² − b² or c² − a² is negative, the inputs don't form a valid right triangle (the hypotenuse must be longer than either leg).
What is a Pythagorean triple?
A set of three positive integers (a, b, c) that satisfy a² + b² = c². Examples: (3,4,5), (5,12,13), (8,15,17).
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Last updated: 2026-08-08