Vector Addition Calculator
Enter two vectors and choose add or subtract.
This result is an estimate only. Double-check important figures before relying on them.
How it is calculated
- A + B = (a₁ + b₁, a₂ + b₂, …)
- A − B = (a₁ − b₁, a₂ − b₂, …)
- Magnitude = √(sum of the squares of the components)
For the length of one vector, use the vector magnitude calculator.
Worked example
(1, 2, 3) + (4, 5, 6):
- Result = (5, 7, 9)
- Magnitude = 12.4499
Why your number may differ
Vectors must have the same number of components. Results are rounded to 6 decimal places.
Frequently asked questions
How do I add vectors?
Add the matching components. (1, 2, 3) + (4, 5, 6) = (5, 7, 9).
How do I subtract vectors?
Subtract the matching components. A − B points from B to A.
What is the resultant?
The single vector you get by combining the others, such as the total force from two forces.