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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

ItemValue
Result vector(4, 6)
Magnitude of result vector7.2111
Magnitude of vector A5
Magnitude of vector B2.2361
Dot product A · B11
Angle between A and B10.3048 °

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.