Vector Addition Calculator
Add two or more vectors component-wise in any dimension and show the resultant.
About Vector Addition Calculator
Vector addition sums corresponding components: (A+B)ᵢ = Aᵢ + Bᵢ. Both vectors must have the same dimension. The resultant's magnitude is computed as the Euclidean norm.
Formula
Component-wise Addition
(A + B)ᵢ = Aᵢ + Bᵢ
- A
- First vector
- B
- Second vector
Worked example
With the default values below, Vector Addition Calculator returns A + B of [5, 7, 9]. Change any input above and every figure here is recalculated in your browser.
Inputs used
- Vector A (comma or space separated)
- 1, 2, 3
- Vector B (comma or space separated)
- 4, 5, 6
Results
- A + B
- [5, 7, 9]
- Magnitude of Result
- 12.449900
Step by step
- 1Vector A= [1, 2, 3]
- 2Vector B= [4, 5, 6]
- 3A + B= [5, 7, 9]
- 4||A + B||= 12.4499
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 6 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
Do vectors need to be the same dimension?
Yes. You can only add vectors of the same dimension — each component is summed with its counterpart.
Is vector addition commutative?
Yes. A + B = B + A, just like scalar addition.