How to use the vector addition calculator
Add two vectors given magnitude and direction. Enter magnitude a, angle a, magnitude b, angle b in the fields above; the resultant magnitude, resultant direction, x-component, y-component are computed instantly and plotted on the chart so you can see how the answer changes.
Formula
Variables
- A — Magnitude A
- thA — Angle A (°)
- B — Magnitude B
- thB — Angle B (°)
Worked example
With magnitude a = 10, angle a = 0 °, magnitude b = 6, angle b = 60 °, the calculator gives resultant magnitude ≈ 14; resultant direction ≈ 21.78679 °; x-component ≈ 13; y-component ≈ 5.196152.
Frequently asked questions
What is the formula for the vector addition calculation?
Resultant magnitude = hypot(A × cos(thA)+B × cos(thB),A × sin(thA)+B × sin(thB)). Resultant direction (°) = atan2d(A × sin(thA)+B × sin(thB),A × cos(thA)+B × cos(thB)). x-component = A × cos(thA)+B × cos(thB). y-component = A × sin(thA)+B × sin(thB). Here A is magnitude a, thA is angle a (°), B is magnitude b, thB is angle b (°).
What inputs do I need for the vector addition calculator (2d) calculator?
You need magnitude a, angle a in °, magnitude b, angle b in °. Each field is pre-filled with a typical example so you can see how the result responds as you edit the numbers.
How do I use this calculator?
Type values into the input fields. Results and the chart update instantly. Use Reset to restore the example values, Copy results to paste them elsewhere, or Share to copy a link that preserves your inputs.
Is the result exact?
Calculations use standard formulas and double-precision arithmetic, then display about seven significant figures. Real-world measurements carry uncertainty, so treat results as estimates unless your inputs are exact.