Pitagoras (Pythagorean) Theorem Calculator
Find any missing side of a right triangle using the formula a² + b² = c².
Tip: c is always the longest side in a right triangle.
What Is the Pitagoras Theorem?
The Pitagoras theorem (also known as the Pythagorean theorem) is one of the most widely used rules in geometry. It applies only to right triangles, where one angle is exactly 90 degrees. The theorem states:
a² + b² = c²
Here, a and b are the two legs of the triangle, and c is the hypotenuse (the side opposite the right angle and always the longest side).
How This Pitagoras Calculator Works
This calculator lets you solve for any one missing side of a right triangle when the other two sides are known. You can calculate:
- c using c = √(a² + b²)
- a using a = √(c² - b²)
- b using b = √(c² - a²)
The tool includes validation checks, so it warns you if values are invalid (for example, if the hypotenuse is not larger than the known leg).
Step-by-Step Usage
1) Choose what you want to solve
Select whether you want to find side a, side b, or hypotenuse c.
2) Enter the known side values
Provide positive numbers for the two known sides. Leave the unknown side disabled and blank.
3) Click Calculate
The calculator instantly computes the missing side and displays both the result and the formula used. It also fills the missing input field automatically.
Worked Examples
Example A: Find the Hypotenuse
If a = 3 and b = 4, then:
c = √(3² + 4²) = √(9 + 16) = √25 = 5
Example B: Find a Leg
If c = 13 and b = 12, then:
a = √(13² - 12²) = √(169 - 144) = √25 = 5
Common Mistakes to Avoid
- Using the formula for non-right triangles.
- Entering a hypotenuse value that is not the longest side.
- Forgetting to square values before adding/subtracting (if solving manually).
- Using negative lengths (triangle side lengths must be positive).
Where You Can Use It in Real Life
The Pitagoras theorem is useful in many practical situations:
- Construction and carpentry (checking right angles and diagonal measurements)
- Architecture and engineering calculations
- Computer graphics and game development (distance in 2D)
- Navigation, mapping, and surveying
- School homework and exam preparation
Final Thoughts
A good pitagoras calculator saves time and reduces errors, especially when you are working with decimals or repeated calculations. Use this tool whenever you need a quick and accurate right-triangle side calculation.