Physics Figures Vector Diagram Generator
ABCR

Vector addition diagrams, drawn to scale head to tail

The Vector Diagram Generator draws up to three vectors to scale, head to tail, on a grid where one square is a magnitude of 1, with their resultant from the first tail to the last tip. You give each vector its magnitude, from 0.5 to 12 squares, and its direction in degrees counterclockwise from the right, and the generator tells you the resultant’s magnitude and direction for your answer key.

It doesn’t say what the vectors are, so the same figure works for displacement, velocity and force problems. Draw any vector or the resultant dashed, or leave it off for students to draw in, and mark angles or show components for questions on resolving vectors.

What you can set

  • Up to three vectors, each with its magnitude in grid squares (0.5 to 12) and its direction
  • Each vector and the resultant drawn solid, dashed or left off, with its own label
  • For any arrow at an angle, an angle mark from the horizontal or vertical, and its x and y components
  • A grid, one square per unit of magnitude, and plain x and y axes through the first tail
  • Mirror, to flip the figure left to right, and color for slides

Copying, printing and sharing

Copy the figure straight into a test, worksheet or slide, or download it as a PNG or SVG. Printing the page prints just the figure. Share link copies the page’s address with your settings in it, so anyone who opens it sees this exact figure, and presets save settings you use often in your browser. It’s free, with no sign-up.

Example figures

Frequently asked questions

How do you add vectors head to tail?

Draw the first vector, then start the second at the first one’s tip (its head), and so on. The resultant runs from the first vector’s tail to the last vector’s tip. With A 4 squares to the right and B 3 squares up, the resultant is 5 squares long, about 36.9° above the horizontal.

How do you find a vector’s components?

A vector of magnitude A at angle θ above the horizontal has an x-component of A cos θ and a y-component of A sin θ. Turn on Show its components to draw them as thinner dashed arrows, along the horizontal and then up or down to the tip.

Can I subtract vectors?

There’s no subtraction setting, but A − B is A + (−B): add B with its direction turned around 180° and label it −B. The resultant is then A − B.

Can I leave the resultant for students to draw?

Yes. Set the resultant’s arrow to Left off. It isn’t drawn, but the Resultant settings still show its magnitude and direction for your key. Any vector can be left off the same way, leaving a gap in the chain for students to fill in.

What does one grid square stand for?

A magnitude of 1. The grid has no numbers, so you say what a square is worth, like 1 m, 1 m/s or 10 N. It’s lined up with the first tail, so tips land on grid points whenever the magnitudes and angles allow.

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