Vector Addition & Subtraction Calculator
Add or subtract two 2D or 3D vectors and instantly get the result vector along with its magnitude (norm), dot product, and the angle between the vectors.
Input
Dimension
Operation
Vector A
Vector B
Result
Result vector A + B
(4, 6)
Magnitude of result vector
7.2111
Angle between A and B
10.3048 °
Dot product A · B
11
Calculation breakdown
| Item | Value |
|---|---|
| Result vector | (4, 6) |
| Magnitude of result vector | 7.2111 |
| Magnitude of vector A | 5 |
| Magnitude of vector B | 2.2361 |
| Dot product A · B | 11 |
| Angle between A and B | 10.3048 ° |
How it works
- Supports 2D (x, y) and 3D (x, y, z) vectors and computes the sum (A+B) or difference (A−B) component by component.
- The magnitude (norm) of the result vector is found as the square root of the sum of the squares of its components.
- The dot product is the sum of the products of the matching components of A and B; the angle is derived from cosθ = (dot product) ÷ (|A| × |B|) and converted to degrees with the inverse cosine.
- When A or B is the zero vector (magnitude 0), the angle is undefined and is shown as "—".
- Components accept negative numbers and decimals. Values are rounded to four decimal places for readability.
- Useful for physics problems such as force composition and displacement, coordinate difference calculations, and math study.
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Vector Addition & Subtraction Calculator