Free Pythagorean Theorem Calculator - a² + b² = c²
Calculate the missing side of any right triangle. Best free Pythagorean calculator 2025 - enter any two sides to find the third.
Quick Answer
The Pythagorean theorem states a² + b² = c², where c is the hypotenuse (longest side) and a, b are the other two sides of a right triangle. To find c: c = √(a² + b²). To find a leg: a = √(c² - b²). Example: sides 3 and 4 give hypotenuse √(9+16) = √25 = 5. Calculate at practicalwebtools.com.
Key Facts about Pythagorean Theorem Calculator:
- Pythagorean theorem: a² + b² = c²
- c is always the hypotenuse (longest side, opposite right angle)
- Only works for right triangles (one 90° angle)
- Famous triples: 3-4-5, 5-12-13, 8-15-17, 7-24-25
- Used in construction, navigation, physics, gaming
- Named after Greek mathematician Pythagoras (c. 570-495 BC)
- Converse: if a² + b² = c², the triangle is right
Why Use Our Pythagorean Theorem Calculator?
Solve right triangles:
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How to Pythagorean Theorem Calculator in 3 Easy Steps
Use the theorem:
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Frequently Asked Questions
Everything you need to know about our pythagorean theorem calculator
What is the Pythagorean theorem?
a² + b² = c² for right triangles, where c is the hypotenuse.
In a right triangle, the square of the hypotenuse equals the sum of squares of the other two sides: a² + b² = c², where c is the longest side opposite the right angle.
How do I find the hypotenuse?
c = √(a² + b²). For 3 and 4: √(9+16) = 5.
Square both legs (a and b), add them, then take the square root. c = √(a² + b²). For legs 3 and 4: c = √(9+16) = √25 = 5.
How do I find a leg?
a = √(c² - b²). If c=5, b=4: √(25-16) = 3.
Square the hypotenuse, subtract the square of the known leg, take square root. a = √(c² - b²). If c=5 and b=4: a = √(25-16) = √9 = 3.
What are Pythagorean triples?
Integer sets satisfying a² + b² = c²: 3-4-5, 5-12-13, 8-15-17.
Sets of three integers that satisfy a² + b² = c². Common ones: 3-4-5, 5-12-13, 8-15-17, 7-24-25. Any multiple also works (6-8-10, etc.).
Still have questions? Try the tool yourself!
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