Many readers ask the origin of the 63%.

The answer is found in examining the equation for the exponential charging process.  Assume that initially the membrane potential (V_m) is uncharged and then in response to some step stimulus, the membrane potential charges over time to a final value of 100% charged from its initial value of 0% charged.

This process can be described by the equation

Where t is time and τ is the time constant.

To illustrate the behavior of the equation, take some extreme cases. Assume time = 0. Then

V_m   =    0%

Now assume t = ∞. Then

V_m   =    100%

Now take the interesting case where the time equals the value of τ (i.e., t = τ)

V_m   =    63%

Mathematically, τ can be considered a constant that stretches or shrinks the exponential response in the temporal domain. As an exercise, try solving the equation with different values of τ.