Maths / Geometry
Pythagorean Theorem Calculator
Find the missing side of a right triangle from any two sides, with the working shown step by step, a drawing to scale, and the angles, area, and perimeter.
Pythagorean Theorem Calculator: The Pythagorean theorem says that in a right 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. Given both legs, the calculator adds their squares and takes the square root; given a leg and the hypotenuse, it subtracts. The angles come from the arctangent of the two legs. Runs 100% locally in your browser with zero server file uploads.
- Category
- School & study tools
- Runs
- In your browser
- Cost
- Free · no sign-up
- Availability
- Ready to use
Runs entirely in your browser
Enter any two sides and leave the third empty.
- c² = a² + b²
- c² = 3² + 4² = 9 + 16 = 25
- c = √25 = 5
Using it in real life
Builders check a corner is square by marking 3 m along one wall and 4 m along the other: if the diagonal between the marks is exactly 5 m, the corner is 90°. The same sum finds the length of a ladder needed to reach a height from a given distance, or a TV's diagonal from its width and height.
For a right triangle's area from its legs alone, the right triangle calculator is quicker; for roots on their own, the square root calculator.
Why it is true
Arrange four copies of the triangle inside a square with sides a + b, leaving a tilted square of side c in the middle. The big square's area is (a + b)², which equals the four triangles, 2ab, plus c². Expanding gives a² + 2ab + b² = 2ab + c², so a² + b² = c².
How to use it
- Enter any two of the three sides and leave the third empty.
- Read the missing side and the steps that found it.
- Use the angles, area, and perimeter shown below the drawing.
Privacy & limitations
Everything is worked out in your browser.
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Frequently asked questions
Which side is the hypotenuse?
The longest side, opposite the right angle. It must be longer than either leg, so a leg of 5 and a hypotenuse of 5 has no answer.
What are Pythagorean triples?
Whole-number sides that fit the theorem, such as 3, 4, 5; 5, 12, 13; and 8, 15, 17. Builders use 3, 4, 5 to check that a corner is square.
Does it work for any triangle?
Only for right triangles. For others, the law of cosines adds a correction: c² = a² + b² − 2ab·cos C, which becomes the Pythagorean theorem when C is 90°.
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