Pythagorean Theorem Calculator: Find Missing Side
Solve right triangles using the Pythagorean theorem. Find the hypotenuse or a missing leg.
Pythagorean Theorem
Calculate the hypotenuse of a right triangle (a² + b² = c²)
Quick Tips
- • Works only for right triangles (one 90° angle)
- • Use the same units for both sides
- • Classic example: 3-4-5 triangle
What is the Pythagorean Theorem?
The Pythagorean theorem applies only to right triangles (one 90° angle). It relates the two legs (a, b) to the hypotenuse (c), which is the longest side opposite the 90° angle.
Formula
a² + b² = c²
To find the hypotenuse: c = √(a² + b²)
To find a missing leg: a = √(c² − b²) or b = √(c² − a²)
How to Use This Calculator
- 1Enter side a and side b (the two legs).
- 2Click calculate to get c (hypotenuse).
- 3If you know c and one leg, use the leg formula to get the missing side.
- 4Make sure units match (cm with cm, m with m).
Common Examples
| a | b | c (hypotenuse) | Notes |
|---|---|---|---|
| 3 | 4 | 5 | Classic 3-4-5 triangle |
| 5 | 12 | 13 | Classic 5-12-13 triangle |
| 6 | 8 | 10 | Scaled 3-4-5 triangle |
Right Triangle Diagram
Common Mistakes
- Using the theorem on a triangle that is not a right triangle.
- Mixing units (cm and m in the same calculation).
- Forgetting to square a and b before adding.
- Accidentally treating c as a leg (c must be opposite the 90° angle).
Pythagorean Theorem FAQs
What is the Pythagorean theorem used for?
It’s used to find a missing side of a right triangle using a² + b² = c².
Does it work for all triangles?
No. It only works for right triangles (one angle must be 90°).
Which side is the hypotenuse (c)?
The hypotenuse is the longest side, opposite the 90° angle.
How do I find the hypotenuse?
Use c = √(a² + b²).
How do I find a missing leg?
Rearrange: a = √(c² − b²) or b = √(c² − a²).
What if c is smaller than a or b?
Then the inputs don’t make a valid right triangle because c must be the largest side.
Can I use decimals or fractions?
Yes. The formula works with decimals and fractions.
Why do I get an error with negative inside the square root?
That usually means you entered values that can’t form a right triangle (like c too small).
Does unit matter (cm, m, inches)?
Units don’t matter as long as you use the same unit for all sides.
How can I check if a triangle is right-angled?
If a² + b² equals c² (with c as the largest side), it’s a right triangle.