How do I know which side is the hypotenuse?
The hypotenuse is the side opposite the right angle. It is always the longest side of a right triangle.
Pythagorean Theorem Calculator
Find a missing side of a right triangle by identifying the hypotenuse first, then solving for a leg or the hypotenuse.
Identify the hypotenuse before choosing a formula
The legs are a and b. The hypotenuse c is opposite the 90 degree angle and is always the longest side of a right triangle.
Pick the missing side
- Identify the right angle.
- Label the hypotenuse.
- Enter the two known sides.
- Choose whether the missing side is a leg or the hypotenuse.
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Right-triangle side formulas
Add squares when finding the hypotenuse; subtract squares when finding a missing leg.
Core theorem
Missing hypotenuse
Missing leg a
Missing leg b
Hypotenuse check
Validation rules
- Use positive side lengths.
- The hypotenuse must be the longest side.
- A known leg must be shorter than the hypotenuse.
- A missing-leg calculation cannot have a negative value under the square root.
Common examples include a ladder against a wall, the diagonal of a rectangle, coordinate-grid distance, and checking whether three lengths form a right triangle.
FAQ
Why does solving for a leg use subtraction?
Because the theorem starts with c^2 = a^2 + b^2. If the hypotenuse and one leg are known, subtract the known leg square from the hypotenuse square before taking the square root.
