Pythagorean Theorem Calculator
Solve right triangle hypotenuse (c) or leg lengths (a, b) using the Pythagorean formula a² + b² = c².
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How to Use the Pythagorean Theorem Calculator
- 1Select which side you want to find: Hypotenuse (c), Leg a, or Leg b.
- 2Enter the lengths of the two known sides.
- 3The calculator applies a² + b² = c² and shows both the exact radical form and decimal value.
- 4Review the area, perimeter, and acute angles.
Formula & How It Works
Pythagorean Equation
In any right-angled triangle, the area of the square whose side is the hypotenuse (c) is equal to the sum of the areas of the squares on the other two legs (a and b).
Worked Examples
Classic 3-4-5 Triangle
Input: a = 3, b = 4
Explanation: 3² + 4² = 9 + 16 = 25. √25 = 5.
Finding Leg a Given Hypotenuse
Input: b = 12, c = 13
Explanation: 13² - 12² = 169 - 144 = 25. √25 = 5.
Frequently Asked Questions
Does the Pythagorean theorem work on all triangles?▼
No, it strictly applies only to right-angled triangles containing a 90-degree angle.
What is a Pythagorean triple?▼
A set of three positive integers that satisfy a² + b² = c², such as (3, 4, 5) and (5, 12, 13).
Can side lengths be in different units?▼
Both side inputs must be in the same unit of measurement (e.g., all inches or all centimeters).
What if the hypotenuse input is smaller than leg b?▼
The hypotenuse must always be strictly longer than either leg. The calculator alerts you if an impossible geometry is entered.
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