The Pythagorean theorem helps calculate a missing side of a right triangle. It is useful in geometry, construction measurements, design layouts, and distance calculations. A Pythagorean theorem calculator can quickly evaluate the formula once you know two side lengths.
What is the Pythagorean theorem?
For a triangle containing a 90-degree angle, the theorem states:
a² + b² = c²
Here, a and b are the two legs meeting at the right angle, while c is the hypotenuse, the side opposite the right angle and the longest side of a nondegenerate right triangle.
How to find the hypotenuse
Use c = √(a² + b²). If a = 3 and b = 4, then c = √(9 + 16) = √25 = 5. This is the familiar 3–4–5 right triangle.
How to find a missing leg
When the hypotenuse and one leg are known, rearrange the formula. For example, b = √(c² − a²). If c = 13 and a = 5, then b = √(169 − 25) = √144 = 12.
How to use the online calculator
- Open the Pythagorean Theorem Calculator.
- Identify the two known sides and the missing side.
- Enter the available measurements in the corresponding fields.
- Calculate the unknown side and review the result.
- Check that all measurements use the same unit, such as centimetres or metres.
Practical example: measuring a diagonal
A rectangular surface measures 6 metres by 8 metres. Its diagonal is √(6² + 8²) = √100 = 10 metres. This can help when checking rectangular layouts or estimating a straight-line distance across a flat surface.
Common right-triangle side lengths
| Leg a | Leg b | Hypotenuse c |
|---|---|---|
| 3 | 4 | 5 |
| 5 | 12 | 13 |
| 8 | 15 | 17 |
| 7 | 24 | 25 |
Important limitations
The theorem applies to right triangles only. It does not directly determine a side of an arbitrary triangle without additional information. For a valid nondegenerate right triangle, the hypotenuse must be longer than either leg.
Frequently asked questions
Can I use the theorem on any triangle?
No. The standard Pythagorean equation applies to triangles with a 90-degree angle.
What if the answer contains a square root?
You can leave it in exact radical form or use a decimal approximation appropriate for your task.
How do I identify the hypotenuse?
It is the side opposite the right angle.
Does the formula work with feet and inches?
Yes, as long as both input lengths are converted into the same unit before calculating.
Use the Pythagorean theorem calculator to check your next right-triangle problem.
Moiz Ahmad is a digital marketer and SEO expert based in Dera Ismail Khan, Pakistan. With over 6 years of experience in SEO, WordPress development, and digital strategy, he has helped 30+ businesses rank on Google’s first page. He is the founder of DigiTechPak and Moiz Blogger. Connect: LinkedIn | Twitter | Moiz Blogger