Pythagorean Theorem Calculator guide
Pythagorean Theorem Calculator: a² + b² = c²
Use our Pythagorean theorem calculator to find the hypotenuse or a missing side of a right-angled triangle, with step-by-step working.
By the AllCalculator editorial teamUpdated 16 October 20261 min read
Pythagoras' theorem is one of the most useful results in maths. In any right-angled triangle, a² + b² = c², where c is the hypotenuse. Our Pythagorean Theorem Calculator uses it to find a missing side.
How to use the calculator (Pythagorean Theorem Calculator)
- Choose whether to find the hypotenuse or a shorter side.
- Enter the two sides you know.
You'll see the answer with each step of the working.
The formulas
- Hypotenuse: c = √(a² + b²)
- Shorter side: b = √(c² − a²)
The hypotenuse is always the longest side, opposite the right angle.
A worked example
With the calculator's default settings, sides of 3 and 4:
- 3² = 9 and 4² = 16
- 9 + 16 = 25
- c = √25 = 5
That's a Pythagorean triple: three whole numbers that fit the theorem.
Common Pythagorean triples
| a | b | c |
|---|---|---|
| 3 | 4 | 5 |
| 5 | 12 | 13 |
| 8 | 15 | 17 |
| 7 | 24 | 25 |
Multiples work too, such as 6, 8, 10.
Frequently asked questions
How is it used in real life?
Builders use the 3-4-5 rule to check corners are square. It also gives straight-line distances, such as the diagonal of a screen or a ladder against a wall.
Does it work for other triangles?
No, only right-angled ones. For others, use the cosine rule in our Triangle Calculator.
To find the angles too, try our Right Triangle Calculator.
Sources and further reading
- GOV.UK: National curriculum in England – mathematicsgov.uk
- Wolfram MathWorld: Pythagorean theoremmathworld.wolfram.com
Links open official and independent websites in a new tab.
This guide is general information to help you understand your options. It isn't financial, tax, legal or building advice and doesn't take your personal circumstances into account. Figures were checked when the guide was last updated and can change, so confirm anything important with GOV.UK, HMRC, a regulated adviser or a qualified tradesperson.