Pythagorean Theorem Calculator

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

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

This Pythagorean Theorem Calculator helps you quickly find the length of an unknown side of a right-angled triangle. Whether you're a student tackling geometry, a carpenter estimating materials for a new roof in 2026, or an engineer designing structures, this tool simplifies complex calculations. Knowing the precise length of a diagonal beam or the distance across a field can save significant time and resources in 2026 construction projects.

The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. This is expressed by the formula a² + b² = c², where 'a' and 'b' are the lengths of the two shorter sides (legs) and 'c' is the length of the hypotenuse. To find a missing side, you simply rearrange the formula: if 'c' is missing, c = √(a² + b²); if 'a' is missing, a = √(c² - b²); and if 'b' is missing, b = √(c² - a²).

Always ensure you are working with a *right-angled* triangle; the theorem does not apply to other triangle types. A common mistake is confusing the hypotenuse with one of the legs, so always identify the longest side first or the side opposite the 90-degree angle. Remember to take the square root at the final step to get the actual length, not the squared value.

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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