Pythagorean Theorem Calculator
Calculate missing side of a right triangle.
Right Triangle Sides
Formula:
c = √(a² + b²) = √(3² + 4²)
Result
Side C
5.0000
units
Triangle Sides
a = 3
b = 4
c = 5.0000
Verification:
a² + b² = c²
(3)² + (4)² = (5.0000)²
25.0000 = 25.0000 ✓
About This Calculator
The Pythagorean Theorem Calculator helps you find the length of a missing side in a right triangle using the famous Pythagorean theorem. The theorem states that in a right triangle, the square of the hypotenuse equals the sum of squares of the other two sides.
This calculator can solve for any side (a, b, or c) given the other two sides. Side c is the hypotenuse (the side opposite the right angle), while sides a and b are the legs of the triangle.
Formula & Calculation Method
Pythagorean Theorem:
Theorem:
a² + b² = c²
where:
a, b = legs of the right triangle
c = hypotenuse (longest side, opposite the right angle)
Solving for sides:
c = √(a² + b²)
a = √(c² - b²)
b = √(c² - a²)
The Pythagorean theorem applies only to right triangles (triangles with a 90-degree angle). The hypotenuse (c) is always the longest side and is opposite the right angle.
How to Use This Calculator
- Select Side to Solve: Choose which side you want to calculate (a, b, or c).
- Enter Known Sides: Input the lengths of the two known sides.
- View Results: See the calculated length of the missing side.
- Verify: Ensure the triangle is valid (hypotenuse must be longest side).
Frequently Asked Questions
What is the Pythagorean theorem?
The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (longest side) equals the sum of squares of the other two sides: a² + b² = c². It only applies to right triangles (triangles with a 90° angle).
Which side is the hypotenuse?
The hypotenuse (c) is the longest side of a right triangle and is opposite the right angle. It is always the side you solve for when you know the two legs, or the side you need to know when solving for a leg.
Can I use this for non-right triangles?
No, the Pythagorean theorem only applies to right triangles. For other triangles, you would use the Law of Cosines or Law of Sines.
What if I get an error calculating a leg?
If you're solving for side a or b and get an error, it means the hypotenuse (c) must be greater than the other known leg. The hypotenuse is always the longest side in a right triangle.
Calculator by
NumCalculators Editorial Team
Multi-disciplinary Expert Team