BYTETOOLS

Pythagorean Theorem Calculator

Solve the Pythagorean theorem: enter any two sides of a right triangle to find the third, plus the area. Free a² + b² = c² calculator with steps.

3
Side a
4
Side b
5
Hypotenuse c
6
Area

How it was solved

c = √(a² + b²) = √(3² + 4²) = 5

Area = ½ · a · b = 6

  • Finds any missing side of a right triangle
  • Solves for a leg or the hypotenuse
  • Also computes the triangle area
  • Shows the exact formula used
  • Validates that c is the longest side
  • Runs entirely in your browser

How to use the Pythagorean Theorem Calculator

  1. 1

    Choose which side you want to solve for: c, a or b.

  2. 2

    Enter the two known sides of the right triangle.

  3. 3

    Read the missing side and the triangle's area instantly.

  4. 4

    Review the worked formula to check your calculation.

About the Pythagorean Theorem Calculator

The ByteTools Pythagorean Theorem Calculator finds the missing side of a right triangle using a² + b² = c². Enter any two of the two legs a and b or the hypotenuse c, and it returns the third side along with the triangle's area and the exact formula used.

It is built for geometry students, carpenters, and DIY builders squaring up a frame or checking a diagonal. Whether you need the hypotenuse from two legs or a leg from the hypotenuse, the calculator picks the correct rearrangement of the theorem for you.

All maths runs locally in your browser with JavaScript, so nothing is uploaded or stored. It also validates that the hypotenuse is the longest side, catching impossible inputs before they give a wrong answer.

Frequently asked questions

What is the Pythagorean theorem?

The Pythagorean theorem states that in a right triangle, the square of the hypotenuse equals the sum of the squares of the two legs: a² + b² = c². It only applies to right triangles, where one angle is exactly 90 degrees.

How do you find the hypotenuse?

Square both legs, add them together, and take the square root: c = √(a² + b²). For example, legs of 3 and 4 give a hypotenuse of 5, because √(9 + 16) = √25 = 5. This is the classic 3-4-5 right triangle.

How do you find a missing leg?

Rearrange the formula to a = √(c² − b²). Subtract the known leg's square from the hypotenuse's square, then take the square root. The hypotenuse must be longer than the leg, or no right triangle exists.

How do you find the area of a right triangle?

The area equals one-half times the two legs multiplied together, since the legs are perpendicular. For legs of 3 and 4, the area is ½ × 3 × 4 = 6. The calculator shows this automatically once both legs are known.

What is a Pythagorean triple?

A Pythagorean triple is a set of three whole numbers that satisfy a² + b² = c², such as 3-4-5, 5-12-13 and 8-15-17. These appear often in geometry problems because every side comes out as a clean integer.

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