Distance between vectors

Online calculator for calculating the distance between vectors with 2 elements

Calculate vector distance

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


Vector distance calculator

Vector 1Vector 2Result
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Decimal places

More vector functions for 2 elements

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

Vector functions for 3 or 4 elements

Formulas for the distance between two points

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

! In this general example, the calculation is based on vectors with 3 elements.

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

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 \((0, -2, 7)\) and \((8, 4, 3)\).

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

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

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

\(d=\sqrt{64 + 36 +16}\)

\(d=\sqrt{116} = 10,77\)

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

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