Pythagorean Theorem Calculator
Enter any two sides of a right triangle to solve for the third.
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Request a ToolHow to Use the Pythagorean Theorem Calculator
This calculator solves for any missing side of a right triangle using the equation a^2 + b^2 = c^2.
- Enter two known sides. Type the values you know into the a, b, or c fields. Leave the unknown side empty.
- Read the result. The calculator instantly computes the missing side and shows the formula used, along with all three side values.
- Copy or share. Use the buttons on the result card to copy the answer or share a link with your inputs pre-filled.
You can solve for the hypotenuse (c) by entering both legs (a and b), or solve for a missing leg by entering the hypotenuse and the other leg. Results update live as you type.
About the Pythagorean Theorem
The Pythagorean theorem is one of the most fundamental relationships in geometry. It states that in any right triangle, the square of the hypotenuse (the side opposite the 90-degree angle) equals the sum of the squares of the other two sides. Written as a^2 + b^2 = c^2, this formula has been proven in hundreds of ways since ancient times. It is the foundation for distance calculations in coordinate geometry, construction measurements, and navigation. The theorem only applies to right triangles. For other triangle types, use the Law of Cosines instead.
Frequently Asked Questions
What is the Pythagorean theorem formula?
The formula is a^2 + b^2 = c^2, where a and b are the two legs of a right triangle and c is the hypotenuse. To find c, calculate the square root of (a^2 + b^2). To find a missing leg, rearrange to a = sqrt(c^2 - b^2).
Can I solve for a leg instead of the hypotenuse?
Yes. Enter the hypotenuse (c) and one leg, then leave the other leg empty. The calculator rearranges the formula automatically. For example, if c = 13 and b = 5, it finds a = sqrt(169 - 25) = 12.
Does this work for non-right triangles?
No. The Pythagorean theorem only applies to right triangles (triangles with a 90-degree angle). For other triangles, use the Law of Cosines calculator, which generalizes this relationship to any triangle.