Pythagorean Theorem Calculator – Find Sides of a Right Triangle Instantly

Imagine you’re building a garden, designing a ramp, or simply trying to check the length of a diagonal on a rectangular table. You know two sides of a right triangle, but how do you find the third? That’s where a Pythagorean Theorem Calculator comes in. It takes any two sides of a right-angled triangle and instantly calculates the third side using the timeless formula from Greek mathematics. No guessing, no messy manual calculations — just accurate results in seconds.

Why the Pythagorean Theorem is Important

The Pythagorean Theorem is one of the most fundamental principles in mathematics. It states:

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.

Formally:

c² = a² + b²

Where:

• c = hypotenuse
• a, b = the two other sides

Applications:

• Construction and carpentry (calculating diagonal braces or supports)
• Interior design (measuring diagonal distances)
• Navigation and surveying
• Geometry education and homework

Understanding this theorem is critical for anyone working with triangles in practical or academic settings.

How the Calculator Works

1. Select what you know: You can input:
   
   • Two legs (a and b) → find the hypotenuse (c)
     
   • One leg and hypotenuse → find the missing leg
     
2. Input values: Enter the lengths in consistent units (meters, feet, inches, etc.).
   
3. Calculate: The calculator squares the known sides, sums or subtracts as needed, and takes the square root to find the missing side.
   
4. Result: Displays the missing side instantly, with optional rounding for simplicity.
   

Formula Used

• To find the hypotenuse:

  c = √(a² + b²)

• To find a leg (if hypotenuse c is known):

  a = √(c² - b²)
  b = √(c² - a²)

The calculator ensures the result is always positive and checks for valid inputs (e.g., hypotenuse must be the largest side).

Example Calculations

Example 1: Find the hypotenuse

• a = 3 units
• b = 4 units

c = √(3² + 4²) = √(9 + 16) = √25 = 5

Example 2: Find a missing leg

• c = 10 units
• b = 6 units

a = √(10² - 6²) = √(100 - 36) = √64 = 8