2D Distance Calculator
Calculate the straight-line distance between two points in a 2D coordinate system. The distance between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by the formula: $D = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$.
Understanding the Distance Formula
The distance formula is derived from the Pythagorean theorem, which states that for a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
Given two points, $P_1 = (x_1, y_1)$ and $P_2 = (x_2, y_2)$, we can form a right-angled triangle where the distance between the two points, $D$, is the hypotenuse. The other two sides are the horizontal distance, $|x_2 - x_1|$, and the vertical distance, $|y_2 - y_1|$.
The Pythagorean theorem, $a^2 + b^2 = c^2$, becomes: $(x_2 - x_1)^2 + (y_2 - y_1)^2 = D^2$
Solving for $D$ gives us the distance formula: $D = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$
How This Tool Works
This tool operates entirely within your browser using JavaScript. When you click "Calculate Distance," it retrieves the four coordinate values you've entered. It then performs the following steps:
- Parses the input values as numbers.
- Calculates the difference between the x-coordinates and the y-coordinates.
- Squares each difference.
- Adds the two squared differences together.
- Takes the square root of the sum to find the final distance.
All calculations are performed client-side, ensuring your data remains private and is never sent to a server.