Right Triangle Calculator
Use this quick Pythagorean theorem tool to solve for any side of a right triangle. Enter two known sides, choose what to solve for, and click calculate.
Formula: a2 + b2 = c2 (where c is the longest side).
What Is the Pythagorean Theorem?
The Pythagorean theorem is one of the most important formulas in geometry. It applies to right triangles, which are triangles that contain one 90-degree angle. The theorem says:
a2 + b2 = c2
Here, a and b are the two shorter sides (called legs), and c is the longest side (the hypotenuse). If you know any two sides of a right triangle, you can always calculate the third.
How to Use This Pythagoras Calculator
- Choose what side you want to solve for: a, b, or c.
- Enter the two known side lengths.
- Click Calculate.
- Read the result and formula breakdown in the result box.
Tip: all side lengths should be positive numbers. If you are solving for a leg (a or b), the hypotenuse must be larger than the known leg.
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 Missing Leg
If c = 13 and b = 5, then:
a = √(132 - 52) = √(169 - 25) = √144 = 12
Why This Formula Matters
The theorem appears everywhere: construction, architecture, physics, engineering, navigation, game development, and even everyday DIY projects. Any time you need to find diagonal distance from horizontal and vertical components, the Pythagorean theorem is usually the fastest route.
Common Uses
- Checking if corners are square in carpentry
- Computing shortest path distances on a grid
- Determining TV or monitor diagonal size from width and height
- Calculating slope lengths in roof design
- Solving 2D vector magnitude problems
Common Mistakes to Avoid
- Using the formula on non-right triangles
- Mixing units (for example, inches and centimeters in the same equation)
- Forgetting that c is always the longest side
- Entering negative values for side lengths
- Rounding too early during multi-step calculations
Quick Reference
Find Hypotenuse
c = √(a2 + b2)
Find Leg a
a = √(c2 - b2)
Find Leg b
b = √(c2 - a2)
Final Thoughts
A good Pythagoras calculator saves time and reduces arithmetic mistakes, especially when you are handling repeated geometry problems. Use it to validate homework, speed up engineering sketches, or double-check real-world measurements before cutting material. The key is simple: enter two known sides, choose the unknown side, and let the math do the heavy lifting.