Pythagorean Theorem Calculator
Use your own numbers after reviewing the formula and worked example.
Quick answer
The Pythagorean theorem applies only to right triangles, with c representing the hypotenuse.
Formula or method
Keep units, percentages and time periods consistent. The formula is useful as a transparent check on the calculator result and helps explain why changing one input changes the answer.
Step-by-step
- Identify the hypotenuse.
- Square known side lengths.
- Add squares to find c or subtract to find a leg.
- Take the positive square root.
Worked example
For legs 3 and 4, c=5. With hypotenuse 13 and one leg 5, the other leg is 12.
How to interpret the result
The formula is specific to right triangles; other triangles require different methods.
When the answer is used for a purchase, loan, payroll decision, construction order, school grade, health estimate or other real-world choice, verify the assumptions that matter in that context. Accurate arithmetic still depends on accurate inputs.
Common mistakes
- Misidentifying the hypotenuse.
- Adding when solving for a leg.
- Using the formula on a non-right triangle.
Frequently asked questions
Which side is c?
The side opposite the 90° angle.
Can it find angles?
Not by itself.
Why use positive square root?
Lengths are positive.