Draw root locus plots online
This free online root locus plotter shows where the closed-loop poles of a system move as a gain K is varied. Enter the open-loop transfer function and it draws every branch, with asymptotes, breakaway points, and imaginary-axis crossings.
What is a root locus?
The root locus is the set of paths traced by the closed-loop poles of a feedback system as a single gain K varies from 0 to infinity. The poles are the roots of the characteristic equation D(s) + K·N(s) = 0.
It is a classic design tool: by reading where the branches go, you can choose a gain that places the closed-loop poles for a desired damping ratio, settling time, and stability margin — without repeatedly solving the polynomial by hand.
How to draw a root locus from a transfer function
- Enter the open-loop transfer function H(s) = N(s) / D(s).
- Branches start at the open-loop poles (✕) at K = 0 and end at the zeros (○) or run to infinity along the asymptotes.
- Read the marked breakaway/break-in points and the imaginary-axis crossings, where the gain K for marginal stability is labelled.
- Hover or click a branch to see the gain K and damping ratio ζ at that closed-loop pole.
Frequently asked questions
- What is a root locus?
- A root locus shows how the closed-loop poles of a system move through the s-plane as a gain K varies from 0 to infinity. It helps you choose K for a desired transient response and stability.
- How do you plot a root locus?
- Enter the open-loop transfer function. The tool finds the roots of D(s) + K·N(s) for many values of K and connects them into branches, which start at the open-loop poles and end at the zeros or run to infinity.
- What are asymptotes and breakaway points?
- Asymptotes are the straight-line directions branches follow toward infinity; breakaway/break-in points are where branches meet on the real axis and split apart. Both are computed and marked, along with the imaginary-axis crossings.
- Is this root locus tool free?
- Yes, it is free and runs entirely in your browser.