Pythagorean Theorem Calculator
Find the missing side of a right triangle with this free online Pythagorean theorem calculator, plus angles, area, perimeter and exact square-root answers.
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Part of the toolkit
How to use Pythagorean Theorem Calculator
- 1Enter any two sides of the right triangle — legs a and b or the hypotenuse c
- 2Leave the unknown side empty; it's calculated instantly with the working shown
- 3See the angles, area and perimeter, then copy the result
Frequently asked questions
What is the Pythagorean theorem?▾
In a right triangle the square of the hypotenuse equals the sum of the squares of the other two sides: a² + b² = c². A 3-4-5 triangle works because 9 + 16 = 25.
How do I find a missing leg?▾
Rearrange the formula: a = √(c² − b²). With a hypotenuse of 13 and a leg of 5, the other leg is √(169 − 25) = √144 = 12.
What does the exact form like 3√5 mean?▾
When the answer isn't a whole number, it's also shown as a simplified square root. For legs 3 and 6, c = √45 = 3√5 ≈ 6.708.
How are the angles found?▾
With trigonometry: angle α opposite side a is arctan(a / b), and β = 90° − α. In a 3-4-5 triangle they are about 36.87° and 53.13°.
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