Pythagorean Theorem Calculator
Find the missing side of a right triangle using a² + b² = c².
Tip: lengths must be positive numbers. To solve for a leg, the hypotenuse must be larger than the known leg.
What Is a Pythag Calculator?
A pythag calculator is a fast tool for applying the Pythagorean theorem to right triangles. If you know any two sides of a right triangle, you can calculate the third side instantly. This is useful for students, builders, engineers, designers, and anyone solving geometry problems in real life.
The theorem is one of the most practical formulas in mathematics:
a² + b² = c²
Here, c is always the hypotenuse (the longest side), and a and b are the two perpendicular legs.
How to Use This Calculator
Step-by-step
- Select which side you want to solve for: a, b, or c.
- Enter the other two known side lengths.
- Click Calculate.
- Read the result and the equation breakdown shown below the form.
Input rules
- All side lengths must be positive values.
- If solving for a or b, side c must be the largest side.
- Decimals are allowed (for example, 7.25).
Worked Examples
Example 1: Find the hypotenuse
If a = 3 and b = 4, then:
c = √(3² + 4²) = √(9 + 16) = √25 = 5
Example 2: Find a leg
If c = 13 and b = 5, then:
a = √(13² − 5²) = √(169 − 25) = √144 = 12
Why This Formula Matters
The Pythagorean theorem appears almost everywhere:
- Construction: Checking square corners and diagonal lengths.
- Navigation: Computing straight-line distance between two points.
- Computer graphics: Distance calculations in 2D and 3D scenes.
- Physics: Combining perpendicular vectors and components.
- Everyday planning: Ladder safety, room layout, and screen size comparisons.
Common Mistakes to Avoid
- Using the theorem on non-right triangles.
- Treating a shorter side as the hypotenuse.
- Forgetting to square values before adding or subtracting.
- Rounding too early in multi-step calculations.
Quick FAQ
Can I use negative numbers?
No. Side lengths represent physical distances and must be positive.
Can this handle decimals?
Yes. The calculator accepts decimal values and returns accurate decimal results.
Does this work for all triangles?
No. It only works for right triangles (triangles with one 90° angle).