Pythagorean Theorem Calculator
Enter any two sides of a right triangle to instantly find the third
What is the Pythagorean Theorem?
The Pythagorean theorem states that in a right‑angled triangle, the square of the length of the hypotenuse (c) equals the sum of the squares of the other two sides (a and b). This fundamental relation is written as:
a² + b² = c²
How to Use This Calculator
- Enter exactly two side lengths of your right triangle into the input fields above. You can fill any combination (two legs, or one leg and the hypotenuse).
- Click “Calculate Missing Side”. The tool automatically determines which side is missing and computes it using the Pythagorean formula.
- The result appears in the blue box, showing the missing side length rounded to a reasonable number of decimal places.
- Use “Clear All” to reset the fields and try another triangle.
Note: The calculator works with any positive number. If you enter invalid data (e.g., three sides, negative, zero, or non‑triangle values), it will show a helpful error message.
Example Calculations
1. Find the Hypotenuse
Legs: a = 3, b = 4
Calculation: c = √(3² + 4²) = √(9 + 16) = √25 = 5
2. Find a Missing Leg
Hypotenuse: c = 13, one leg: a = 5
Calculation: b = √(c² − a²) = √(169 − 25) = √144 = 12
Frequently Asked Questions
Only on right triangles (one 90° angle). The formula relates the three sides, allowing you to find any one side if the other two are known.
Yes – enter the legs into a and b, leave c empty, and the calculator will compute the hypotenuse automatically.
Enter the known leg and the hypotenuse, leaving the other leg field blank. The calculator uses the rearranged formula leg = √(c² − known leg²).
Absolutely – you can enter values like 3.5 or 7.2. The answer will be accurate and displayed with appropriate precision.
