Skip to main content
PUBLIC.INTERNET
⚡ Instant Access🔒 Privacy First🆓 Always Free📱 Works Everywhere

Pythagoras Instant - Right Triangle Calculator

From construction sites to classroom homework, right triangles are everywhere. Pythagoras Instant is an ultra-fast geometry tool that solves for any side of a right triangle using the Pythagorean theorem (a² + b² = c²). Enter any two known sides and instantly get the missing third side, plus a real-time visualization of the triangle showing all sides, angles, area, and perimeter. Whether you're calculating roof pitch, checking if a corner is square, or solving geometry problems, this free hypotenuse calculator handles it all in your browser. Click common Pythagorean triples like 3-4-5 or 5-12-13 for quick reference, or enter your own measurements for custom calculations. Method details for Pythagorean Theorem Calculator: The result model exposes each formula and equation, applies deterministic calculation steps, uses explicit decimal rounding, and keeps unit assumptions visible so outputs are auditable.

Enter any two sides to calculate the third. Uses the Pythagorean theorem: a² + b² = c²

Common Pythagorean Triples

3 - 4 - 5
Basic
5 - 12 - 13
Common
8 - 15 - 17
Construction
7 - 24 - 25
Advanced
6 - 8 - 10
2× (3-4-5)
9 - 12 - 15
3× (3-4-5)
20 - 21 - 29
Near-equal legs
9 - 40 - 41
Elongated

How to Calculate Triangle Sides

  1. Enter any two sides of your right triangle: Side A and B are the legs (shorter sides), Side C is the hypotenuse (longest side, opposite the right angle)
  2. Leave one field empty for the side you want to calculate the tool automatically solves for it
  3. View the visualization showing your triangle to scale with all measurements, angles, area, and perimeter
  4. Click Pythagorean triples from the reference section to instantly load common examples

Why the Pythagorean Theorem Matters

The Pythagorean theorem states that in a right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides: a² + b² = c². This 2,500-year-old formula is still used daily in construction (checking square corners), navigation (calculating distances), and countless engineering applications. The calculator rearranges the formula automatically: to find c, it computes √(a² + b²); to find a leg, it computes √(c² - b²).

Pythagorean triples are sets of whole numbers that satisfy the theorem perfectly. The most famous is 3-4-5, used by builders for millennia to create perfect right angles. Other useful triples include 5-12-13 and 8-15-17. Any multiple of a triple also works (6-8-10 is just 2× the 3-4-5 triple).

Pro tip: To check if a corner is square, measure 3 units along one wall and 4 units along the other. If the diagonal measures exactly 5 units, your corner is a perfect 90° angle. This '3-4-5 method' has been used since ancient Egypt.