Rule of thumb · Control SystemsNº 50 / 96

One τ is 63%; five is settled

A first-order system covers 63% of a step in one time constant and is effectively settled after 4–5.

Why it works

Follows directly from the exponential 1 − e^(−t/τ). Knowing τ tells you the whole response timeline.

Do it exactly

Estimate with the rule, then check it against the calculator that models it properly.

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