Vector Addition Simulator
Drag vectors on a grid, add them tip to tail and see the sum, its magnitude, angle and components.
Drag the arrow heads to change the vectors. Switch to tip-to-tail to see how the sum is built, and show the components.
About the Vector Addition Simulator
Free vector addition simulator. Drag vectors on a grid, add them tip to tail and see the sum, its magnitude, angle and components. Drag, change the sliders and see the result live. No sign-up, works on phone and computer. Built for math, the vector addition simulator runs instantly in your browser: change a setting or drag an object and the result updates at once, so you learn by trying things out rather than only reading about them.
Drag vectors on a grid, add them tip to tail and see the sum, its magnitude, angle and components. Use it to explore math ideas at your own pace, then check what you found against the key ideas further down this page.
How to use the Vector Addition Simulator
- Use the controls to change Draw, Components, Vectors. The simulation reacts instantly.
- Pick an option such as Tip to tail, From origin, Off, Show x and y to switch modes or load an example.
- Press "Reset" to start, reset or change what is happening.
- Where you see a glowing handle, object, weight or atom, drag it with your mouse or finger. Everything responds in real time.
- Watch the readouts and graphs update as you experiment, and compare what you see with the key ideas below.
Things to try
- Make two vectors that cancel out.
- Show the components of the sum.
- Add a third vector.
Key ideas you can learn
- Add vectors by placing them tip to tail.
- The sum goes from the start of the first to the end of the last.
- Add the x parts and the y parts separately.
- Magnitude = √(x² + y²).
Where this is used in the real world
Pilots, sailors and engineers combine velocities and forces this way.
Who is this simulation for?
Algebra, geometry, trigonometry and calculus students, teachers preparing demonstrations, and self-learners who want to see the maths move.
For teachers: project it on the board, let students predict what will happen, then run it together. For students: change one thing at a time and write down what changes.
Frequently asked questions
How do you add two vectors?
Add their x-components and their y-components separately, or draw them tip to tail.
How do I find the angle of a vector?
Use the tangent: angle = arctan(y ÷ x).
Is the Vector Addition Simulator free to use?
Yes. It is completely free, with no signup, no download and no ads inside the simulation. It runs in your web browser.
Does the Vector Addition Simulator work on a phone or tablet?
Yes. It uses touch as well as the mouse, so you can drag objects with your finger. A larger screen makes the controls easier to see.