# Square of the vector distance

Online calculator for calculating the square of the distance between vectors with 2 elements

Enter the two vectors whose distance is to be calculated. Then press the Caculate button.

Square vector distance calculator

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

### More vector functions for 2 elements

 Addition Subtraction Multiplication Scalar Multiplication Division Scalar-Division Scalar Product Interpolation Distance Distance Square Normalization Length

## Description and formulas of the quadratic vector distance

To find the distance or its square between two vectors, use the distance formula.

$$d^2=(x_2-x_1)^2 + (y_2-y_1)^2 + (z_2-z_1)^2$$

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

### Example

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

$$d^2=(x_2-x_1)^2 + (y_2-y_1)^2 + (z_2-z_1)^2$$

$$d^2=(8-0)^2 + (4-(-2))^2 + (7-3)^2$$

$$d^2=(8)^2 + (6)^2 + (4)^2$$

$$d^2=64 + 36 +16$$

$$d^2=116$$

The square of the distance between the points $$(0, -2, 7)$$ and $$(8, 4, 3)$$ is $$116$$