Pythagorean Theorem Calculator
Calculate the lengths of sides or hypotenuse of a right triangle using the Pythagorean theorem formula a² + b² = c². Enter any two values to find the third, or calculate the area and perimeter of the triangle.
Calculation Results
| Side (a) | - |
|---|---|
| Side (b) | - |
| Hypotenuse (c) | - |
| Area | - |
| Perimeter | - |
| Angles | - |
About the Pythagorean Theorem
The Pythagorean Theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be written as:
a² + b² = c²
Where:
- a and b are the lengths of the two legs of the triangle
- c is the length of the hypotenuse
How to Use the Calculator
This calculator allows you to find any missing side of a right triangle, as well as calculate the area and perimeter:
- Select what you want to calculate (hypotenuse, side a, side b, area, or perimeter)
- Enter the known values in the appropriate fields
- Click "Calculate" to compute the missing values
Formulas Used
The calculator uses the following formulas:
- Hypotenuse (c): c = √(a² + b²)
- Side (a): a = √(c² - b²)
- Side (b): b = √(c² - a²)
- Area: Area = (a × b) / 2
- Perimeter: Perimeter = a + b + c
- Angles: Angle A = arctan(a/b), Angle B = arctan(b/a)
Applications of the Pythagorean Theorem
The Pythagorean Theorem has numerous practical applications in various fields:
- Construction: Ensuring right angles in buildings and structures
- Navigation: Calculating distances between points
- Physics: Determining resultant forces and vectors
- Computer Graphics: Calculating distances between pixels
- Surveying: Measuring land areas and boundaries
Example Calculations
Here are some common examples of Pythagorean triples (whole number solutions):
- 3-4-5 triangle: 3² + 4² = 5² (9 + 16 = 25)
- 5-12-13 triangle: 5² + 12² = 13² (25 + 144 = 169)
- 8-15-17 triangle: 8² + 15² = 17² (64 + 225 = 289)
- 7-24-25 triangle: 7² + 24² = 25² (49 + 576 = 625)