Pythagorean Theorem Calculator
By Santaji GadepatilinUpdated October 27, 2026
Hypotenuse c (cm) vs Side a (cm) — other inputs held at your current values.
How to use this calculator
Enter any two sides of a right-angled triangle. The third side is calculated straight away. The two shorter sides (a and b) meet at the right angle; the hypotenuse (c) is the longest side, opposite the right angle.
Each side has its own unit, so you can enter a in metres and b in feet if you need to.
The formula
a² + b² = c²
- Hypotenuse: c = √(a² + b²)
- Missing side: a = √(c² − b²)
Worked example
A ladder reaches 6 m up a wall with its foot 2.5 m from the wall. How long is the ladder?
c = √(6² + 2.5²) = √(36 + 6.25) = √42.25 = 6.5 m
Common Pythagorean triples
| a | b | c |
|---|---|---|
| 3 | 4 | 5 |
| 5 | 12 | 13 |
| 8 | 15 | 17 |
| 7 | 24 | 25 |
| 20 | 21 | 29 |
Any multiple of a triple also works — 6-8-10 and 30-40-50 are both right triangles.
Practical uses
- Checking a right angle on site. Builders mark 3 units on one side and 4 on the other; if the diagonal is exactly 5, the corner is square.
- Screen sizes. A TV’s size is its diagonal. A screen 120 cm wide and 67.5 cm tall has a diagonal of about 137.7 cm (54 inches).
- Distance on a map. Moving 3 km east and 4 km north puts you 5 km from where you started in a straight line.
Frequently asked questions
What is the Pythagorean theorem?
In a right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides — a² + b² = c².
How do I find a missing short side?
Rearrange to a = √(c² − b²). Press × on side a, then enter b and c. The hypotenuse must be the longest side.
What are Pythagorean triples?
Whole-number sets that satisfy the theorem, such as 3-4-5, 5-12-13, 8-15-17 and 7-24-25.