Calculate capacitor charge time from resistance, capacitance, and desired voltage percentage, with output in seconds, minutes, or hours.
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Capacitor Charge Time Formula
The following formula can be used to calculate the time for a capacitor in an ideal RC circuit to charge to a specified percentage of its final voltage.
t = -R \cdot C \cdot \ln(1 - f)
- Where t is the time (seconds)
- R is the effective resistance in the charging path (ohms)
- C is the capacitance (farads)
- f is the desired fraction of the final voltage (for example, 0.99 for 99%), where f = V(t)/V₀
To calculate the capacitor charge time, multiply R by C, then multiply by −ln(1 − f). As a common rule of thumb, many engineers use t ≈ 5RC to mean “essentially charged,” which corresponds to about 99.33% (not exactly 99%). For exactly 99% charge, t ≈ 4.605RC.
Capacitor Charge Time Definition
Capacitor charge time is the time it takes a capacitor in an RC circuit to reach a specified percentage of its final voltage after a step change in the supply. It is commonly expressed in terms of the time constant τ = RC. For example, 99% charge occurs at about 4.605τ, while 5τ corresponds to about 99.33%.
Capacitor Charge Time Example
How to calculate capacitor charge time?
- First, determine the resistance.
Determine the effective resistance in the capacitor’s charging path (for example, the series resistor plus any significant source/internal resistance).
- Next, determine the capacitance.
Find the capacitance value (from measurement or the component’s rated value).
- Finally, calculate the charge time.
Choose the desired charge percentage and calculate the time using t = -RC ln(1 – f) (or use the 5RC rule-of-thumb for ~99.3%).
FAQ
In an ideal RC circuit, a capacitor reaches 63.2% of its final voltage after 1 time constant (τ = RC). After 5 time constants it reaches about 99.33%. For exactly 99% charge, the time is about 4.605τ. Typically, 4–5 time constants is considered “fully charged” for practical purposes (it will never reach 100% in the ideal exponential model).
In an ideal RC discharge, after 1 time constant (τ = RC) the capacitor’s voltage (and stored charge) remaining is 36.8% of the initial value, meaning 63.2% has discharged. After 5 time constants, about 0.67% remains (about 99.33% discharged). For exactly 99% discharged, the time is about 4.605τ.
