Calculate the distance between two points in a 2D Cartesian coordinate system.
Enter coordinates to see the length.
Understanding the Line Segment Length Calculator
This calculator computes the length of a line segment defined by two points in a two-dimensional Cartesian plane. The Cartesian plane is a fundamental concept in mathematics, used to represent points and geometric shapes using ordered pairs of numbers (coordinates).
The Mathematics Behind the Calculation
The distance between two points $(x_1, y_1)$ and $(x_2, y_2)$ in a Cartesian plane is found using the distance formula, which is derived from the Pythagorean theorem.
Imagine a right-angled triangle where the line segment between the two points is the hypotenuse. The lengths of the other two sides (the legs) are the absolute differences in the x-coordinates and the y-coordinates.
The horizontal leg has a length of $|x_2 – x_1|$.
The vertical leg has a length of $|y_2 – y_1|$.
According to the Pythagorean theorem, for a right-angled triangle with legs 'a' and 'b' and hypotenuse 'c', we have $a^2 + b^2 = c^2$.
Since squaring a number makes it positive, the absolute value signs are redundant:
$(x_2 – x_1)^2 + (y_2 – y_1)^2 = \text{Length}^2$
To find the length, we take the square root of both sides:
Length = $\sqrt{(x_2 – x_1)^2 + (y_2 – y_1)^2}$
How to Use the Calculator
Simply enter the x and y coordinates for both of your points into the designated fields. Click the "Calculate Length" button, and the tool will display the exact length of the line segment connecting these two points.
Use Cases
This calculator is useful in various fields:
Mathematics and Geometry: Verifying calculations, understanding distances, and in coordinate geometry problems.
Engineering and Architecture: Calculating distances for structural elements or site layouts.
Computer Graphics: Determining distances between pixels or objects on a screen.
Navigation and Surveying: Estimating distances on maps or terrain models.
Physics: Calculating displacement or distances in projectile motion or other scenarios.
Example Calculation
Let's calculate the distance between Point 1 at (3, 7) and Point 2 at (9, 2).
The calculator will provide this result when you input these values.
function calculateLineSegmentLength() {
var x1 = parseFloat(document.getElementById("x1").value);
var y1 = parseFloat(document.getElementById("y1").value);
var x2 = parseFloat(document.getElementById("x2").value);
var y2 = parseFloat(document.getElementById("y2").value);
var resultDiv = document.getElementById("result");
// Check if all inputs are valid numbers
if (isNaN(x1) || isNaN(y1) || isNaN(x2) || isNaN(y2)) {
resultDiv.textContent = "Please enter valid numbers for all coordinates.";
resultDiv.style.backgroundColor = "#dc3545"; /* Red for error */
return;
}
var deltaX = x2 – x1;
var deltaY = y2 – y1;
var lengthSquared = Math.pow(deltaX, 2) + Math.pow(deltaY, 2);
var length = Math.sqrt(lengthSquared);
resultDiv.textContent = "Length: " + length.toFixed(4); // Displaying up to 4 decimal places
resultDiv.style.backgroundColor = "var(–success-green)"; // Reset to success color
}