Pythagorean Theorem Calculator
Solve the Pythagorean theorem (a² + b² = c²) with a right-triangle solver for missing sides, area and perimeter in any unit.
a² + b² = c²
Enter any two sides to find the third
Enter any two sides to calculate the third side, area and perimeter.
Last updated: February 2026
How this calculator is verified
Checked by Rahim Virani on
- a^2 + b^2 = c^2 verified with a 3-4-5 triangle
- Degenerate and negative side lengths rejected with a clear message
- Units held consistent: mixed unit input is refused rather than silently converted
The full verification method is on our how we verify page. Found an error? Tell us and we will re-check it.
When to Use This Calculator
The Pythagorean theorem — a² plus b² equals c² — is one of the most searched maths tools in the world, used wherever a right angle meets a measurement. Students from Class 8 onwards verify homework and board-exam answers, while carpenters, masons and electricians in India use it on site to check whether a corner is square: a 3-4-5 triangle confirms a perfect 90 degrees. It also solves practical length problems — the shortest distance across a rectangular field, the length of a ladder needed to reach a window, or the diagonal of a TV screen or wall panel. Enter any two sides and the calculator returns the third, or enter both shorter sides to get the hypotenuse directly.
How to Use This Calculator
- Step 1: Enter any two of the three side lengths — two legs, or one leg and the hypotenuse.
- Step 2: Pick the unit you want to work in, such as metres, centimetres or feet.
- Step 3: The missing side is calculated automatically, along with the area and perimeter.
- Step 4: Verify the result by checking that a squared plus b squared equals c squared.
Worked Example
A 6-metre and 8-metre pair of legs gives a hypotenuse of 10 metres, because 36 plus 64 is 100 and its square root is 10. The area is half of 6 times 8, which is 24 square metres, and the perimeter is 6 plus 8 plus 10, or 24 metres. If only the hypotenuse of 13 and one leg of 5 were known, the missing leg works out to 12, since 169 minus 25 is 144. The unit selector changes how the results are labelled — enter 3 and 4 in feet and the calculator reports the 5-foot hypotenuse, area of 6 ft² and perimeter of 12 ft.
Tips and Common Mistakes
- •Tip 1: The theorem applies only to right triangles, so confirm the 90-degree corner before using it.
- •Tip 2: The hypotenuse is always the longest side and lies opposite the right angle; entering it shorter than a leg shows an error message instead of a result.
- •Tip 3: Use it to check rectangular layouts, such as confirming that a corner is square by measuring the diagonal.
- ✗Mistake 1: Using the theorem on a triangle that is not right-angled, where the relation a squared plus b squared equals c squared fails.
- ✗Mistake 2: Adding the two sides first and then squaring the sum; each side must be squared separately before adding.
Expert Note
The Pythagorean theorem is a staple of CBSE Class 10 board exams and JEE mains. Students should memorise the 3-4-5, 5-12-13, and 8-15-17 Pythagorean triples for quick mental checks. The calculator also computes area and perimeter, which are frequently tested alongside the theorem in geometry problems.
Sources and References
- •Euclid's Elements, Book I, Proposition 47
- •NCERT Class 10 Mathematics, Chapter 6: Triangles
- •Britannica: Pythagorean theorem proof and history
Official sources are linked so you can confirm the current rate yourself. Check the linked page for the latest notification before relying on these figures.
Frequently Asked Questions
What is the Pythagoras calculator?
It solves the Pythagoras theorem (a² + b² = c²) for any right triangle. Enter any two sides — the two shorter sides or one short side plus the hypotenuse — and it finds the missing side, along with the area and perimeter.
How do I find the hypotenuse?
Enter the two shorter sides (a and b) and leave the hypotenuse blank. The calculator applies c = √(a² + b²). For sides of 3 and 4, the hypotenuse is √(9 + 16) = 5.
How do I find a missing short side?
Enter the hypotenuse and one short side. The calculator rearranges the theorem to a = √(c² − b²). For a hypotenuse of 5 and one side of 3, the other side is √(25 − 9) = 4.
When is the Pythagoras theorem used in real life?
Anywhere a right angle is involved — ladder heights, TV and screen sizes, roof pitches, navigation distances and construction layouts all use a² + b² = c² to find an unknown length.
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