Pythagorean Theorem Calculator

Find the missing side (a, b, or c) in a right-angled triangle

Select Side to Find

Choose which side you want to calculate

Pythagorean Theorem

a² + b² = c²
c = √(a² + b²)

Result

Calculated value for side c

Side c =
5
units
Calculation:
c² = a² + b²
c² = 3² + 4²
c² = 9 + 16
c² = 25
c = 5

Right Triangle Diagram

a = 3b = 4c = 5
Finding this side

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About Pythagorean Theorem Calculator

Calculate Missing Sides in Right Triangles

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 squares of the other two sides. This calculator helps you find any missing side when you know the other two.

Features

  • Find any side (a, b, or c)
  • Visual right triangle diagram
  • Step-by-step calculation
  • Highlighted finding side
  • Formula display
  • High precision results
  • Input validation
  • Example values included
  • Real-time updates
  • Clean, modern interface

The Pythagorean Theorem

a² + b² = c²
• a and b are the legs (sides forming the right angle)
• c is the hypotenuse (longest side, opposite right angle)

Formulas

Find c:
c = √(a² + b²)
Find a:
a = √(c² - b²)
Find b:
b = √(c² - a²)

How to Use

  1. Select which side you want to find (a, b, or c)
  2. Enter the values for the two known sides
  3. View the calculated result instantly
  4. Check the step-by-step calculation
  5. Examine the visual triangle diagram

Common Applications

  • Geometry homework and problems
  • Construction and carpentry
  • Navigation and distance calculation
  • Architecture and design
  • Physics and engineering

Famous Example

The 3-4-5 triangle is the most well-known Pythagorean triple: 3² + 4² = 9 + 16 = 25 = 5². Other common triples include 5-12-13, 8-15-17, and 7-24-25.