Pythagorean Theorem Calculator

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

By Konstantin Iakovlev · Updated April 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 and does not constitute tax, financial, or legal advice. Results are estimates based on the information you provide and current rates. Always consult a qualified tax professional or financial advisor for advice specific to your situation.

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 in 2026, 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 2026 construction projects.

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: Calculating a Ramp Length for a 2026 Accessibility Project

  1. 1 A community center in Dallas is building a new accessibility ramp. The ramp needs to reach a height of 4 feet (side 'a'), and the horizontal distance from the building to the end of the ramp (side 'b') is 10 feet. We need to find the length of the ramp itself (the hypotenuse, 'c').
  2. 2 Using the formula c = √(a² + b²), we substitute the values: c = √(4² + 10²). This calculates to c = √(16 + 100), which simplifies to c = √116.
  3. 3 The length of the ramp (c) is approximately 10.77 feet.
  4. 4 This calculation ensures the community center orders the correct length of material for the ramp, preventing material waste and ensuring the project stays within its 2026 budget of $15,000 for materials.

Source: Khan Academy · Last updated: April 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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