time constant [′tīm ‚kän·stənt]
Time constant
When time t is zero, f(t) in Eq. (1) has the magnitude 1, and when t equals T the magnirude is 1/e. Here e is the transcendental number whose value is approximately 2.71828, and the change in magnitude is 1 - (1/e) = 0.63212. The function has moved 63.2% of the way to its final value. The same factor also holds for Eq. (2).
(physics)
The time required for a physical quantity to rise from zero to 1-1/e(that is, 63.2%) of its final steady value when it varies with timetas 1 -e-kt.
The time required for a physical quantity to fall to 1/e(that is, 36.8%) of its initial value when it varies with timetase-kt.
Generally, the time required for an instrument to indicate a given percentage of the final reading resulting from an input signal. Also known as lag coefficient.
Time constant
A characteristic time that governs the approach of an exponential function to a steady-state value. When a physical quantity is varying as a decreasing exponential function of time as in Eq. (1), or as an increasing exponential function as in Eq. (2), the approach to the steady-state value achieved after a long time is governed by a characteristic time T as given in Eq. (3). This time T is called the time constant. (1) 
(2) 
(3) When time t is zero, f(t) in Eq. (1) has the magnitude 1, and when t equals T the magnirude is 1/e. Here e is the transcendental number whose value is approximately 2.71828, and the change in magnitude is 1 - (1/e) = 0.63212. The function has moved 63.2% of the way to its final value. The same factor also holds for Eq. (2). The initial rate of change of both the increasing and decreasing functions is equal to the maximum amplitude of the function divided by the time constant.
The concept of time constant is useful when evaluating the presence of transient phenomena.
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