About the Pythagorean Theorem Calculator
What is the Pythagorean Theorem Calculator?
The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) equals the sum of the squares of the other two sides: a² + b² = c². It is one of the most used results in geometry, construction, navigation and physics.
Choose whether to find the hypotenuse or a missing leg, then enter the two known sides. The calculator also gives the triangle's area, its perimeter and the two acute angles, so you get the complete solution of the triangle.
How to use the Pythagorean Theorem Calculator
- Find (sample: Hypotenuse c (from legs a and b))
- Leg a (sample: 3)
- Leg b (when finding the hypotenuse) — used when finding the hypotenuse. (sample: 4)
- Hypotenuse c (when finding a leg) — used when finding a leg; it must be longer than leg a. (sample: 5)
- Press Solve Triangle (results also refresh as you type). The result card shows the Missing Side, along with Area, Perimeter, Angle opposite a and Angle opposite b.
Formula used
c = √(a² + b²) and b = √(c² − a²)
- a, b = the two legs (the sides forming the right angle)
- c = the hypotenuse, the longest side
The angle opposite a is tan⁻¹(a ÷ b), and the two acute angles always add up to 90°.
Worked example
These are the sample values already filled in the calculator above, and the result it returns for them:
| Input | Sample value |
|---|---|
| Find | Hypotenuse c (from legs a and b) |
| Leg a | 3 |
| Leg b (when finding the hypotenuse) | 4 |
| Hypotenuse c (when finding a leg) | 5 |
| Result | Value |
|---|---|
| Hypotenuse c | 5 |
| Area | 6 |
| Perimeter | 12 |
| Angle opposite a | 36.8699° |
| Angle opposite b | 53.1301° |
Tips for using the Pythagorean Theorem Calculator
- Well-known whole-number triples: 3-4-5, 5-12-13, 8-15-17 and 7-24-25. Any multiple, such as 6-8-10, also works.
- Builders use the 3-4-5 rule to set out a right angle: mark 3 m and 4 m along two lines; the diagonal between the marks should be exactly 5 m.
- Ladder problems: a 5 m ladder with its foot 3 m from a wall reaches √(25 − 9) = 4 m up the wall.