Pythagorean Theorem Calculator

Find the missing side of a right triangle or verify if three sides form a right triangle.

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1. Select the mode: find a missing side or verify if three sides form a right triangle. 2. In solve mode, enter two known sides and select which side to find (a, b, or hypotenuse c). 3. View the missing side length calculated using the Pythagorean theorem. 4. In verify mode, enter all three sides to check if they satisfy a^2 + b^2 = c^2. 5. Review the step-by-step calculation showing each stage of the formula. 6. Click the copy button to copy the result.

About This Tool

The Pythagorean Theorem Calculator applies the fundamental relationship a^2 + b^2 = c^2 to solve for any missing side of a right triangle. Enter any two sides - whether two legs or one leg and the hypotenuse - and the tool instantly calculates the missing measurement. It also computes the area, perimeter, and all three angles of the resulting right triangle.

In addition to solving for missing sides, the calculator includes a verification mode where you enter all three side lengths and the tool checks whether they satisfy the Pythagorean theorem. This is handy for confirming measurements in construction, carpentry, or any real-world scenario where you need to verify a right angle. The tool highlights whether the sides form a valid right triangle and shows the margin of error if they do not.

The Pythagorean theorem is one of the most widely used formulas in mathematics, engineering, physics, and everyday life. From calculating diagonal screen sizes and determining distances on a map to laying out foundations and building staircases, this calculator saves time and eliminates arithmetic mistakes. Results include step-by-step workings so students can follow along and learn the process.

Formula / How It Works

a^2 + b^2 = c^2 | c = sqrt(a^2 + b^2) | a = sqrt(c^2 - b^2)

Frequently Asked Questions

The Pythagorean theorem states 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: a^2 + b^2 = c^2.
Enter the two legs (a and b) and the calculator computes the hypotenuse as c = sqrt(a^2 + b^2). For example, if a = 3 and b = 4, then c = sqrt(9 + 16) = sqrt(25) = 5.
Yes. If you know the hypotenuse c and one leg b, the missing leg is a = sqrt(c^2 - b^2). The calculator handles this automatically when you leave one leg blank and fill in the other leg and hypotenuse.
Switch to verification mode and enter all three side lengths. The calculator checks whether the square of the longest side equals the sum of the squares of the other two. If the equation holds, the sides form a right triangle.
Pythagorean triples are sets of three positive integers that satisfy a^2 + b^2 = c^2. Common examples include (3, 4, 5), (5, 12, 13), (8, 15, 17), and (7, 24, 25). Any multiple of a triple is also a triple.

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