Pole-zero plot online
This free online pole-zero tool plots the poles (roots of the denominator) and zeros (roots of the numerator) of a transfer function H(s) in the s-plane. Poles are drawn as ✕ and zeros as ○.
What the pole-zero map tells you
The pole locations set stability and speed: a system is stable when every pole lies in the left half-plane. Poles near the imaginary axis are slow and lightly damped; complex poles cause oscillation. Zeros shape the response but do not affect stability.
Frequently asked questions
- What is a pole-zero plot?
- A pole-zero plot marks the poles (roots of the denominator, drawn ✕) and zeros (roots of the numerator, drawn ○) of a transfer function in the complex s-plane. Their positions determine the system's stability and its transient response.
- How do poles and zeros affect stability?
- A continuous-time system is stable only if every pole lies in the left half of the s-plane (negative real part). A pole on the imaginary axis is marginally stable, and any pole in the right half-plane makes the system unstable. Zeros do not affect stability but shape the response.
- How do you find the poles and zeros of a transfer function?
- Factor the numerator and denominator of H(s) = N(s)/D(s). The roots of N(s) are the zeros and the roots of D(s) are the poles. This tool finds them numerically and plots them for you.
- Is this pole-zero plotter free?
- Yes, it runs entirely in your browser with no signup or cost.