Pythagorean Theorem Calculator
Enter two sides of a right triangle to calculate the missing side.
Pythagorean Theorem Calculator
A Pythagorean Theorem Calculator is a math tool used to calculate the missing side of a right-angled triangle using the famous Pythagorean theorem. This calculator is widely used by students, teachers, engineers, architects, and anyone working with right triangles.
Instead of performing manual square and square-root calculations, the calculator delivers fast and accurate results.
What Is the Pythagorean Theorem?
The Pythagorean theorem is a fundamental rule in geometry that applies only to right-angled triangles. It states that:
a² + b² = c²
Where:
- a and b are the two shorter sides (legs)
- c is the longest side (hypotenuse)
This formula allows you to calculate the length of one side when the other two sides are known.
What a Pythagorean Theorem Calculator Can Calculate
A Pythagorean theorem calculator can calculate:
- The hypotenuse when both legs are known
- A missing leg when the hypotenuse and one leg are known
The calculator automatically rearranges the formula to suit your input.
Pythagorean Theorem Formulas
The calculator uses the following formulas:
- Hypotenuse: c = √(a² + b²)
- Leg a: a = √(c² − b²)
- Leg b: b = √(c² − a²)
These formulas ensure accurate results for all right-triangle calculations.
How to Use a Pythagorean Theorem Calculator
Using a Pythagorean theorem calculator is simple:
- Enter the known side lengths
- Select which side you want to calculate
- Click calculate
- View the result instantly
The calculator handles all squaring and square-root operations for you.
Pythagorean Theorem Calculator Examples
Example 1: Finding the Hypotenuse
Leg a = 3
Leg b = 4
c = √(3² + 4²) = √25 = 5
Example 2: Finding a Missing Leg
Hypotenuse = 13
Leg b = 5
a = √(13² − 5²) = √144 = 12
These examples show how the calculator simplifies geometry problems.
Why Use a Pythagorean Theorem Calculator?
A Pythagorean theorem calculator is useful because it:
- Saves time on manual calculations
- Reduces math errors
- Helps students understand geometry concepts
- Supports homework and exam preparation
- Applies to real-world measurements
It is ideal for both learning and professional use.
Real-World Applications of the Pythagorean Theorem
The Pythagorean theorem is used in many real-life situations, including:
- Construction and architecture
- Land surveying
- Navigation and mapping
- Engineering design
- Computer graphics
A calculator makes these applications faster and more accurate.
Pythagorean Theorem vs Distance Formula
The distance formula in coordinate geometry is based on the Pythagorean theorem. Both use the same principle of finding distance using squared values.
Summary
A Pythagorean Theorem Calculator is a reliable and efficient tool for solving right-triangle problems using the formula:
a² + b² = c²
Whether you are a student learning geometry or a professional working with measurements, this calculator provides accurate results quickly and easily.