Transfer Function Helper
Enter numerator and denominator polynomial coefficients to instantly compute DC gain, poles, natural frequency, damping ratio, and step response metrics.
Transfer Function G(s)
Enter polynomial coefficients in descending power of s (space-separated).
N(s)
G(s) = ─────
D(s)
Example: 1 3 represents s + 3
Example: 1 5 6 represents s² + 5s + 6
Enter coefficients and click Analyze to see results.
System Classification
Core Parameters
Poles & Zeros
Poles (roots of D(s))
Zeros (roots of N(s))
Step Response Characteristics
Summary
Enter numerator and denominator polynomial coefficients to instantly compute DC gain, poles, natural frequency, damping ratio, and step response metrics.
How it works
- Enter the numerator coefficients (e.g. "5" for a gain of 5, or "1 2" for s+2).
- Enter the denominator coefficients (e.g. "1 3 2" for s²+3s+2).
- The tool detects whether the system is first-order or second-order automatically.
- Key parameters are computed: DC gain, pole locations, natural frequency, and damping ratio.
- Step response characteristics including percent overshoot, settling time, and peak time are displayed.
Use cases
- Verify hand-calculated transfer function parameters in control systems coursework.
- Quickly check stability margins by inspecting real pole locations.
- Determine if a second-order system is underdamped, critically damped, or overdamped.
- Compute percent overshoot and settling time for PID controller design.
- Analyze DC gain (steady-state output) for a unit step input.
- Check pole-zero locations before root locus or Bode plot analysis.
- Validate system parameters derived from state-space models.
- Estimate time constant and bandwidth for first-order plants.
Frequently Asked Questions
Last updated: 2026-06-10 ·
Reviewed by Nham Vu