**1. Overview**

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

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**

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

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

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.

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