Pythagorean Theorem Calculator - Free Online Right Triangle Calculator
Pythagorean Theorem Calculator
Calculate the missing side of a right triangle using a² + b² = c². Enter any two sides to find the third.
Tip: Enter any two values and leave the third blank. The hypotenuse (c) is always the longest side opposite the right angle.
How to use this calculator
📐 How to Use the Pythagorean Theorem Calculator
- Enter any two known side lengths of your right triangle
- Leave the unknown side blank
- Click "Calculate Missing Side" or press Enter
- View the step-by-step solution and all triangle properties
- The calculator automatically validates that c is the longest side (hypotenuse)
📏 The Pythagorean Theorem
In a right triangle, the square of the hypotenuse equals the sum of squares of the other two sides:
a² + b² = c²
Where:
- • a = One leg (adjacent side)
- • b = Other leg (opposite side)
- • c = Hypotenuse (longest side, opposite the right angle)
🌟 Real-World Examples
Example 1: Ladder Against a Wall
A 10-foot ladder leans against a wall, reaching 8 feet high. The base is √(10² - 8²) = 6 feet from the wall.
Example 2: TV Screen Size
A TV with 40" width and 30" height has a diagonal of √(40² + 30²) = 50 inches.
Example 3: Construction Square
To check if a corner is square, measure 3 feet along one wall, 4 feet along the other. The diagonal should be exactly 5 feet (3-4-5 triangle).
💡 Special Right Triangles
Common Pythagorean Triples:
- • 3-4-5 (and multiples: 6-8-10, 9-12-15)
- • 5-12-13
- • 8-15-17
- • 7-24-25
Special Angles:
- • 45-45-90: sides in ratio 1:1:√2
- • 30-60-90: sides in ratio 1:√3:2
⚠️ Common Mistakes to Avoid
- • The hypotenuse (c) is always the longest side - opposite the right angle
- • This theorem only works for right triangles (90° angle)
- • Don't forget to square root the final result when solving for a side
- • Check that your answer makes sense - the hypotenuse must be longer than either leg
- • Remember: a² + b² = c², not a + b = c
About this calculator
Calculate missing sides of right triangles using the Pythagorean theorem. Find hypotenuse or legs with our free visual calculator and step-by-step solutions.
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