ONE FORMULA, ONE ANSWER
First Order Settling Time Calculator
Check waiting time for a stable first-order process or sensor response. Choose input units and calculate one value within the stated conditions.
Inputs
Calculations run in this browser. Scientific notation such as 1.2e-3 is supported. Do not group thousands.
Result
First-order settling time t_s
Enter values and select Calculate.
t_s = −τ ln(ε)
Assumptions
Use τ>0 and 0<ε<1. This is the exact stable first-order unit-step response with no pure delay or overshoot. Entering 2% means ε=0.02. Do not apply a blanket 4τ rule to systems with multiple poles.
Displayed values are floating-point approximations. Measurement uncertainty and design safety factors are not calculated.
Formula references and credits
NaNa Lab created the code, descriptions, icons and preview images. Text, figures and code from the linked references have not been reproduced.
Physical constants: NIST / CODATA 2022. The values of μ₀ and ε₀ are measured recommendations, not exact defining constants. Values and precision notes are in the source record.
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