Free Step Response Time Calculator
Calculate rise time and time constant for a first-order system step response.
s
Rise Time (10% to 90%)
2.197 s
Time to 63.2% of Final Value1.000 s
Time to 95% of Final Value3.000 s
Time to 99% of Final Value4.605 s
Steady-State Output5.000
Rise Time (10% to 90%) vs Time Constant (tau)
First-Order Step Response
A first-order system responds to a step input as an exponential approach to the final value. The speed of response is governed by the time constant tau.
Key Relationships
y(t) = K × u × (1 - e^(-t/tau))
First-order systems have no overshoot; the output monotonically approaches the steady state.
Example Calculation
A temperature control system with tau = 1 s, gain = 5, step input = 1.
- 01Final value = 5 × 1 = 5
- 02Rise time = 2.197 × 1 = 2.197 s
- 03Time to 63.2% = 1 s (output = 3.16)
- 04Time to 95% = 3 s (output = 4.75)
- 05Time to 99% = 4.605 s (output = 4.95)
Frequently Asked Questions
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