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Vector Math

Vector Addition Calculator

Combine vectors of any dimension by adding or subtracting their components and see the result instantly.

vector additionvector subtractioncomponents
Vector Addition & Subtraction

Add or subtract vectors component-wise in any dimension.

Dimension
3
A + B
(3, -1, 4)
A − B
(1, 7, -6)

Component addition

(a₁, a₂, …, aₙ) ± (b₁, b₂, …, bₙ) = (a₁ ± b₁, a₂ ± b₂, …, aₙ ± bₙ)

The calculator also reports the dimension so you can verify both vectors share the same length before proceeding.

How to use

  1. Enter vector A as comma- or space-separated components.
  2. Enter vector B using the same dimension.
  3. Review A + B and A − B beneath the inputs.

Example

Input: A = (2, 3, −1), B = (1, −4, 5)

Output: A + B = (3, −1, 4), A − B = (1, 7, −6)

Student-friendly breakdown

This walkthrough emphasizes the most searched ideas for Vector Addition Calculator: vector calculator, vector addition calculator, dot product calculator, cross product calculator. Start with the formula above, then follow the guided steps to double-check your work. For quick revision, highlight the givens, plug into the equation, and finish by verifying your units.

Need more support? Use the links below to open the long-form guide, browse additional examples, or hop into adjacent calculators within the same topic — each one is a quick way to double-check your work or handle a related question without starting from scratch.

Step-by-step guideSee instructions, classroom tips, and practice prompts.Worked examplesReview the walk-through example plus try-it-yourself prompts.Category hubBrowse every tool in this category from one page.Dot Product CalculatorFinds the scalar product plus the angle between vectors.Cross Product CalculatorComputes the vector cross product in three dimensions.

Deep dive & study plan

Vector Addition Calculator: Performs vector addition and subtraction component-wise. It's built around vector addition, vector subtraction, components, so you can go from a raw question to a checked answer without switching tools.

The math behind it: The calculator also reports the dimension so you can verify both vectors share the same length before proceeding. The core relationship is (a₁, a₂, …, aₙ) ± (b₁, b₂, …, bₙ) = (a₁ ± b₁, a₂ ± b₂, …, aₙ ± bₙ), shown above the calculator so you can see exactly how your inputs turn into the result.

To use it well: (1) Enter vector A as comma- or space-separated components. (2) Enter vector B using the same dimension. (3) Review A + B and A − B beneath the inputs. Keep your units consistent as you go, and re-run a case you already know the answer to — it's the fastest way to catch a typo before it throws off a result you're relying on.

Worked example: entering A = (2, 3, −1), B = (1, −4, 5) returns A + B = (3, −1, 4), A − B = (1, 7, −6). Try swapping in your own numbers next, especially a case you're unsure about, before you use this for something that matters.

Quick retention checklist

  • Speak the formula aloud (or annotate it) so the relationships stick.
  • Write each step in your own words and compare with the numbered list above.
  • Swap in new numbers for the Example to make sure the calculator (and your logic) handles edge cases.
  • Check at least one related calculator below — it's the fastest way to confirm your numbers still line up from a different angle.

FAQ & notes

Can I mix spaces and commas?

Yes. The parser accepts either separator as long as the dimension matches for both vectors.

Does it handle 2D vectors?

Absolutely—enter as many components as you need, including two-dimensional vectors.

What formula does the Vector Addition Calculator use?

The calculator also reports the dimension so you can verify both vectors share the same length before proceeding.

How do I use the Vector Addition Calculator?

Enter vector A as comma- or space-separated components. Enter vector B using the same dimension. Review A + B and A − B beneath the inputs.