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**1. Overview**

In this quick tutorial, we’ll show how to calculate the distance between two points in Java.

**2. The Math Formula of the Distance**

Let’s say we have two points on a plane: the first point A has the coordinates (x1, y1), and the second point B has the coordinates (x2, y2). We want to calculate AB, the distance between the points.

Firstly, let’s build a right triangle with the hypotenuse AB:

According to the Pythagorean theorem, the sum of the squares of the lengths of the triangle’s legs is the same as the square of the length of the triangle’s hypotenuse: *AB ^{2} = AC^{2} + CB^{2}*.

Secondly, let’s calculate AC and CB.

Obviously:

AC = y2 - y1

Similarly:

BC = x2 - x1

Let’s substitute the parts of the equation:

distance * distance = (y2 - y1) * (y2 - y1) + (x2 - x1) * (x2 - x1)

Finally, from the above equation we can calculate the distance between the points:

distance = sqrt((y2 - y1) * (y2 - y1) + (x2 - x1) * (x2 - x1))

Now let’s move on to the implementation part.

**3. Java Implementation**

**3.1. Using Plain Formula**

Although* java.lang.Math* and *java.awt.geom.Point2D *packages provide ready solutions, let’s firstly implement the above formula as is:

public double calculateDistanceBetweenPoints( double x1, double y1, double x2, double y2) { return Math.sqrt((y2 - y1) * (y2 - y1) + (x2 - x1) * (x2 - x1)); }

To test the solution, let’s take the triangle with legs *3* and *4* (as shown in the picture above). It’s clear that the number *5* is suitable as the value of the hypotenuse:

3 * 3 + 4 * 4 = 5 * 5

Let’s check the solution:

@Test public void givenTwoPoints_whenCalculateDistanceByFormula_thenCorrect() { double x1 = 3; double y1 = 4; double x2 = 7; double y2 = 1; double distance = service.calculateDistanceBetweenPoints(x1, y1, x2, y2); assertEquals(distance, 5, 0.001); }

**3.2. Using ***java.lang.Math* Package

*java.lang.Math*Package

If the result of multiplication in the *calculateDistanceBetweenPoints()* method is too big, overflow can occur. Unlike that, *Math.hypot()* method prevents intermediate overflow or underflow:

public double calculateDistanceBetweenPointsWithHypot( double x1, double y1, double x2, double y2) { double ac = Math.abs(y2 - y1); double cb = Math.abs(x2 - x1); return Math.hypot(ac, cb); }

Let’s take the same points as before and check that the distance is the same:

@Test public void givenTwoPoints_whenCalculateDistanceWithHypot_thenCorrect() { double x1 = 3; double y1 = 4; double x2 = 7; double y2 = 1; double distance = service.calculateDistanceBetweenPointsWithHypot(x1, y1, x2, y2); assertEquals(distance, 5, 0.001); }

**3.3. Using ***java.awt.geom.Point2D* Package

*java.awt.geom.Point2D*Package

Finally, let’s calculate the distance with the *Point2D.distance()* method:

public double calculateDistanceBetweenPointsWithPoint2D( double x1, double y1, double x2, double y2) { return Point2D.distance(x1, y1, x2, y2); }

Now let’s test the method in the same way:

@Test public void givenTwoPoints_whenCalculateDistanceWithPoint2D_thenCorrect() { double x1 = 3; double y1 = 4; double x2 = 7; double y2 = 1; double distance = service.calculateDistanceBetweenPointsWithPoint2D(x1, y1, x2, y2); assertEquals(distance, 5, 0.001); }

**4. Conclusion**

In this tutorial, we’ve shown a few ways to calculate the distance between two points in Java.

As always, the code used in the examples is available over on GitHub.