# Distance between vectors

Online calculator for calculating the distance between vectors with 4 elements

## Calculate vector distance

This function calculates the distance between two vectors. To perform the calculation, enter the vectors whose distance is to be calculated and click the Calculate button. Empty fields are counted as 0.

Vector distance calculator

 Vector 1 Vector 2 Result * = Decimal places 0 1 2 3 4 6 8 10

## Formulas for the distance between two points

To find the distance between two vectors, use the distance formula.

$$d=\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2 + (z_2-z_1)^2}$$

In the formula the $$x$$ and $$y$$ vectors stand for the position in a vector space.

### Example

The following example calculates the distance between points $$(0, -2, 7)$$ und $$(8, 4, 3)$$.

$$d=\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2 + (z_2-z_1)^2}$$

$$d=\sqrt{(8-0)^2 + (4-(-2))^2 + (7-3)^2}$$

$$d=\sqrt{(8)^2 + (6)^2 + (4)^2}$$

$$d=\sqrt{64 + 36 +16}$$

$$d=\sqrt{116} = 10,77$$

The distance between the points $$(0, -2, 7)$$ and $$(8, 4,3)$$ is $$10,77$$