Right Triangle Solver
Use this pyth theorem calculator to find a missing side of a right triangle. Enter any two known sides, choose which side you want to solve for, and click calculate.
where c is the hypotenuse (the longest side).
What is the Pythagorean theorem?
The Pythagorean theorem is one of the most important formulas in geometry. It applies only to right triangles, which are triangles that contain a 90-degree angle. The theorem states that the square of the hypotenuse equals the sum of the squares of the other two sides:
a2 + b2 = c2
In this formula, side c is always the hypotenuse, and sides a and b are the legs.
How to use this pyth theorem calculator
Step-by-step
- Select the side you want to solve for: a, b, or c.
- Enter the two known side lengths.
- Click Calculate to get the missing side instantly.
If you solve for a leg (a or b), the hypotenuse must be larger than the known leg. The calculator checks that automatically.
Practical examples
Example 1: Find the hypotenuse
If a = 3 and b = 4:
c = √(32 + 42) = √(9 + 16) = √25 = 5
Example 2: Find a leg
If c = 13 and b = 5:
a = √(132 - 52) = √(169 - 25) = √144 = 12
Where this calculator is useful
- Construction and carpentry layout measurements
- Architecture and drafting
- STEM homework and exam prep
- Computer graphics and game development
- Navigation and distance calculations
Common mistakes to avoid
- Using the theorem with non-right triangles.
- Forgetting that c must be the longest side.
- Typing negative values for side lengths.
- Mixing units (for example, inches for one side and feet for another).
Quick reference formulas
- Find hypotenuse: c = √(a2 + b2)
- Find side a: a = √(c2 - b2)
- Find side b: b = √(c2 - a2)
This pyth theorem calculator gives fast, accurate results and helps you understand each step of the calculation so you can apply the method confidently anywhere.