Pythagorean Theorem Calculator

Calculate the missing side of a right triangle using the Pythagorean theorem.

By Konstantin Iakovlev · Updated September 2026 · Source: Khan Academy

C

5.0000

Pythagorean Theorem

Formulaa^2 + b^2 = c^2
Calculationc = sqrt(3^2 + 4^2)
Result5.0000

Use the Pythagorean Theorem Calculator above to calculate your results. Enter your values and see instant results — all calculations run in your browser.

Disclaimer: This calculator is for informational purposes only. Results are estimates based on the information you provide and the assumptions described on this page.

How It Works

Finding the unknown side of a right-angled triangle is the everyday job this calculator handles. A geometry student, a carpenter sizing materials for a new roof, and an engineer laying out a structure all face the same question, and the tool answers it instantly. Pinning down the length of a diagonal beam or the distance across a field can save real time and material on a construction project.

The theorem itself 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 two shorter sides, or a² + b² = c². Here a and b are the legs and c is the hypotenuse. Finding a missing side is a matter of rearranging: c = √(a² + b²) when the hypotenuse is unknown, a = √(c² - b²) when one leg is unknown, and b = √(c² - a²) for the other.

This only works on a right-angled triangle, so the relationship breaks down for any other type. The most common slip is mistaking the hypotenuse for a leg, which you avoid by spotting the longest side, opposite the 90-degree angle, before you start. Don't stop at the squared value either; the final square root is what turns the calculation back into an actual length.

Example: Length of a Wheelchair Ramp

  1. 1 A community center is adding a wheelchair ramp. Under the 2010 ADA Standards (405.2 and 405.6), a ramp run can be no steeper than 1:12 and can rise at most 30 inches, so a 2.5-foot rise needs at least 30 feet of horizontal run. The rise is side a, the run is side b, and the sloped surface is the hypotenuse c.
  2. 2 Choose Hypotenuse (c), enter a = 2.5 and b = 30: c = √(2.5² + 30²) = √(6.25 + 900) = √906.25.
  3. 3 The calculator shows c = 30.1040, so the sloped surface is about 30.1 feet long.
  4. 4 The ramp surface is barely longer than its horizontal run because a 1:12 slope is so gentle. The ADA Standards also require a level landing at the top and bottom of each ramp run, which adds to the space the ramp needs.

Source: Khan Academy · Last updated: September 2026

Frequently Asked Questions

What is the Pythagorean theorem? (detailed)
The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (longest side) equals the sum of the squares of the other two sides: a^2 + b^2 = c^2. This only works for right triangles with a 90-degree angle.
How do I find the hypotenuse of a right triangle?
If the two legs are a and b, the hypotenuse c equals the square root of (a^2 + b^2). For a 3-4-5 triangle: c = sqrt(9 + 16) = sqrt(25) = 5. Common Pythagorean triples include 3-4-5, 5-12-13, and 8-15-17.
When do I use the Pythagorean theorem in real life?
Common uses include calculating diagonal distances, determining if a corner is square in construction, finding the distance between two points on a grid, sizing TV screens (measured diagonally), and calculating the length of a ladder needed to reach a height.

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