Vector Subtraction Calculator

Work out vector subtraction instantly with clear inputs, formula shown and shareable results.

About Vector Subtraction Calculator

Vectors subtract component by component. The result a − b points from the tip of b to the tip of a, and its magnitude is the distance between those two points.

Formula

Vector subtraction

a − b = (a₁ − b₁, a₂ − b₂, a₃ − b₃)

Worked example

With the default values below, Vector Subtraction Calculator returns a − b of (4, 4, -2). Change any input above and every figure here is recalculated in your browser.

Inputs used

Vector a (x, y, z): 5, 7, 2
Vector b (x, y, z): 1, 3, 4

Results

a − b: (4, 4, -2)
|a − b|: 6.00000000
a + b: (6, 10, 6)
a · b: 34.000000

Step by step

1Values used
2Vector subtraction
3a − b= (4, 4, -2)
4|a − b|= 6.00000000
5a + b= (6, 10, 6)
6a · b= 34.000000

Assumptions and limits

The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 8 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

For a = (5,7,2) and b = (1,3,4)?

a − b = (4, 4, −2), of magnitude 6.

Is subtraction commutative?

No. b − a is the same length but points in the opposite direction.