Second-Order System Calculator (Step Response)
Poles, overshoot, rise time, settling time and bandwidth of a standard second-order system G(s) = Kωₙ²/(s² + 2ζωₙs + ωₙ²).
How to use the Second-Order System Calculator
- Enter or select: Natural frequency ωₙ, Damping ratio ζ, DC gain K.
- The results (Poles, Type, Percent overshoot, Peak time, Rise time (10–90 %), Settling time (2 %), −3 dB bandwidth, Resonant peak) are calculated instantly as you type.
- Use “Copy link” to share the calculation with the same input values.
Formula
- Overshoot = 100·e^(−πζ/√(1−ζ²))
- t_p = π/ω_d
- t_s ≈ 4/(ζωₙ)
- t_r ≈ (1 + 1.1ζ + 1.4ζ²)/ωₙ