Right Triangle Calculator
Use the Pythagorean theorem: a2 + b2 = c2, where c is the hypotenuse.
What Is the Pythagorean Theorem?
The Pythagorean theorem is one of the most important equations in geometry. It applies to right triangles (triangles with one 90° angle) and connects the three side lengths. If the two shorter sides are a and b, and the longest side (the hypotenuse) is c, then:
a2 + b2 = c2
This formula lets you find a missing side length when two sides are known. It is widely used in algebra, trigonometry, physics, construction, engineering, and computer graphics.
How to Use This Pythagorean Theorem Equation Calculator
- Select which side you want to calculate: a, b, or c.
- Enter the other two known side lengths.
- Click Calculate to get the missing value instantly.
- Use Reset to clear all fields and start over.
The calculator also validates your input. If you are solving for a leg (a or b), the hypotenuse must be greater than the known leg.
Formula Variations
Find the hypotenuse
When you know both legs:
c = √(a2 + b2)
Find a leg
When you know one leg and the hypotenuse:
a = √(c2 - b2) or b = √(c2 - a2)
Worked Examples
Example 1: Solve for c
If a = 6 and b = 8, then: c = √(62 + 82) = √(36 + 64) = √100 = 10.
Example 2: Solve for a
If c = 13 and b = 5, then: a = √(132 - 52) = √(169 - 25) = √144 = 12.
Common Mistakes to Avoid
- Using the theorem on non-right triangles.
- Forgetting that c is always the longest side.
- Entering negative lengths (side lengths must be positive).
- Mixing units, such as centimeters and meters, in the same calculation.
Real-World Uses
The Pythagorean theorem appears in practical situations whenever right angles are involved:
- Finding ladder length against a wall.
- Calculating diagonal distance across a room or screen.
- Surveying and land measurement.
- Vector magnitude in physics and engineering.
- Game development and 2D/3D coordinate systems.
Final Thoughts
A reliable Pythagorean theorem equation calculator saves time and reduces math errors. Whether you are studying geometry or solving a practical measurement problem, this tool gives a quick and accurate way to find missing right-triangle sides.