2D Vector Calculator

Add, subtract, and project 2D vectors

About this calculator

The 2D Vector Calculator adds, subtracts, or projects two vectors A and B. Every result includes the resultant components, its magnitude, its direction in degrees, and the dot product A · B; projection mode also reports the vector projection projᵦA = ((A·B)/(B·B))·B and the signed scalar projection (A·B)/|B|. Projecting onto the zero vector is flagged as undefined, and a zero resultant has no direction.

How to use the 2D Vector Calculator calculator

  1. Enter the measurements you know into the input fields.
  2. Read the computed properties — they update instantly as you type.
  3. Compare the diagram with your figure to confirm the setup is right.
  4. Copy the page URL to share the exact calculation.

Common examples

  • A(3, 4) + B(1, 2) → (4, 6), magnitude ≈ 7.2111, direction ≈ 56.31°, dot product 11
  • A(5, 5) − B(2, 1) → (3, 4), magnitude 5, direction ≈ 53.13°
  • Project A(4, 2) onto B(3, 4) → (2.4, 3.2), scalar projection 4
  • Project A(3, 4) onto (1, 0) → (3, 0): the projection onto the x-axis keeps only the x-component

Frequently asked questions

How does the 2D Vector Calculator calculator work?

Enter the known measurements of your figure and the calculator applies the standard geometric formulas to find the remaining properties, alongside a diagram that reflects your numbers. All values are computed with high-precision arithmetic.

When would I use the 2D Vector Calculator calculator?

It helps with geometry homework, technical drawing, construction and DIY layout, and any situation where you know some measurements of a shape and need the rest.

How accurate are the results?

Formulas are evaluated at 30 significant digits of precision internally, including roots and trigonometric functions. Displayed values are rounded for readability, but the underlying computation does not accumulate floating-point drift.

Can I share a specific calculation with someone else?

Yes. Every value you enter updates the URL, so copying the address bar and sharing the link reopens the exact same figure and results for whoever clicks it.