The Pythagorean Theorem Calculator is the essential tool for solving right triangles. Whether you need to find the length of the hypotenuse or one of the legs, this calculator applies the famous $a^2 + b^2 = c^2$ equation instantly. It’s perfect for checking homework, construction projects, or any scenario involving 90-degree angles.
Features
Two-Way Solution: Calculate the Hypotenuse (c) given legs, or find a missing Leg (a or b) given the hypotenuse.
Step-by-Step Proof: Shows the squared values and the final square root calculation.
Visual Diagram: Draws the right triangle to scale, helping you visualize the side lengths.
Precision: Provides accurate results up to 4 decimal places.
How to Use This Calculator
Select Mode: Choose “Hypotenuse (c)” if you know both legs, or “Leg (a or b)” if you know the hypotenuse.
Input Values: Enter the lengths of the known sides.
Calculate: Click the button to get the missing side length.
Review: See the algebraic working displayed below the result.
Formulas
The calculator uses the following mathematical principles:
Find Hypotenuse: $$ c = \sqrt{a^2 + b^2} $$
Find Leg a: $$ a = \sqrt{c^2 – b^2} $$
Find Leg b: $$ b = \sqrt{c^2 – a^2} $$
Practical Applications
Construction: Squaring corners for framing or laying tile.
Navigation: Calculating the direct distance (as the crow flies) when moving north/south and east/west.
Screen Sizing: Determining diagonal screen inches from width and height.
Tips for Success
Hypotenuse is Longest: The hypotenuse (c) must always be longer than either leg. If your input violates this, the calculator will warn you.
Right Triangles Only: This theorem only applies to triangles with a 90-degree angle.
Units: Keep your units consistent (e.g., don’t mix feet and inches).
Frequently Asked Questions (FAQ)
What is the Pythagorean Theorem?
It states that in a right-angled triangle, the square of the hypotenuse equals the sum of the squares of the other two sides ($a^2 + b^2 = c^2$).
Why is it useful?
It connects geometry and algebra, allowing calculation of distances without measuring them directly.
Final Words
Simple, timeless, and effective. The Pythagorean Theorem Calculator brings ancient Greek mathematics to your fingertips, ensuring you never have to guess a diagonal measurement again.
