Enter the resistance and capacitance (with units) and the desired charge percentage into the calculator to estimate the time for an ideal RC circuit to reach that percentage of its final voltage.
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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.
