Resultant Vector Calculator

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

About Resultant Vector Calculator

The resultant is the vector sum, obtained by adding components independently. Its magnitude is generally less than the sum of the individual magnitudes because the vectors partly cancel.

Formula

Resultant

R = Σvₖ, component by component; |R| = √(Rx² + Ry² + Rz²)

Worked example

With the default values below, Resultant Vector Calculator returns Resultant vector of (4, 3, 6). Change any input above and every figure here is recalculated in your browser.

Inputs used

First vector: 3, 4, 0
Second vector: -1, 2, 5
Third vector: 2, -3, 1

Results

Resultant vector: (4, 3, 6)
Magnitude: 7.81024968
Angle in the xy-plane from the x-axis: 36.869898 °
Elevation above the xy-plane: 50.194429 °

Step by step

1Values used
2Resultant
3Resultant vector= (4, 3, 6)
4Magnitude= 7.81024968
5Angle in the xy-plane from the x-axis= 36.869898 °
6Elevation above the xy-plane= 50.194429 °

Assumptions and limits

The result is derived only from the 3 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 (3,4,0), (−1,2,5) and (2,−3,1)?

The resultant is (4, 3, 6), of magnitude √61 ≈ 7.8102497.

Can the resultant be zero with non-zero vectors?

Yes. Three equal-length vectors at 120° in a plane cancel exactly, which is why balanced forces produce equilibrium.