Calculate
Enter any two side lengths
PYTThe reference page asks for any two values and then calculates the missing side. This version keeps the same use case, but updates the solved side, formula steps, and right-triangle diagram live in one place.
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Math calculator
Pythagorean Theorem Calculator
Use a fuller Pythagorean theorem calculator when you want the missing side, the theorem step, and a clear right-triangle diagram together on one page.
How to use this calculator
Pythagorean theorem calculator guide
The Pythagorean theorem connects the three sides of a right triangle through the equation a² + b² = c², where c is the hypotenuse. The reference calculator uses that exact relationship and asks for any two known sides. This version keeps the same geometry logic, but turns it into a live layout with the solved side, equation breakdown, and side-label diagram visible together.
- Use c for the hypotenuse, which is always the longest side in a right triangle and sits opposite the 90-degree angle.
- If the hypotenuse and one leg are known, the missing leg is found with subtraction under the square root rather than addition.
- This theorem is a special case of the law of cosines and is one of the most widely used relationships in basic geometry.
Formula / method
Formula / method
Right-triangle solving follows the Pythagorean theorem, where the squares of the two legs add up to the square of the hypotenuse.
- Use a² + b² = c² when the hypotenuse is unknown.
- Rearrange the same equation when one leg is unknown.
- Area and perimeter are derived from the solved side lengths.
Example calculation
Review the current live example
The example below reflects the current values shown in the calculator above, so it updates as you change the form without altering the calculation logic itself.
Example inputs
Side a3
Side b4
Hypotenuse c5
Example outputs
Right triangle check5.00
Side a3.00
Side b4.00
Hypotenuse c5.00
Disclaimer
Use results as planning guidance only
Results are for reference only. Always verify assumptions, units, and rounding requirements before using an output in school, engineering, or compliance-sensitive work.
- Do not treat calculator output as financial, investment, medical, or legal advice.
- Check assumptions, dates, tax rules, and provider-specific terms before acting on a result.
- Use official documents or professional guidance when the decision has material consequences.
FAQ
Common Pythagorean Theorem questions
Which side is c in the Pythagorean theorem?
c is the hypotenuse, which is the longest side of a right triangle and the side opposite the 90-degree angle.
Can I enter all three sides?
Yes. When all three values are entered, this page checks whether they satisfy a² + b² = c² and tells you whether they form a right triangle.
Why does the calculator reject some side combinations?
If c is not longer than the other leg, or if the three values do not satisfy the theorem, they cannot represent a valid right triangle under the Pythagorean relationship.
Why does this version update live instead of jumping to a result block?
The reference page uses a traditional calculate-and-show flow. Here the solved side, formula steps, and right-triangle diagram stay visible while you adjust the inputs.