RC Time Constant Calculator

Calculator

Provide any two of \( R \), \( C \), \( \tau \) — the third is solved. Optionally provide a time \( t \) and an initial or supply voltage to calculate the charging or discharging voltage at that time.

• Resistance (R):
• Ω kΩ MΩ

• Capacitance (C):
• F mF µF nF pF

• Time constant (τ):
• s ms µs min

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• Time (t) — optional:
• s ms µs min

• Supply voltage V_s (charging) — optional:
• V mV kV

• Initial voltage V₀ (discharging) — optional:
• V mV kV

Provide any two of R, C, τ to calculate.

Calculate

RC Time Constant — Explanation

The RC time constant \( \tau \) characterises how quickly a capacitor charges or discharges through a resistor: \[ \tau = R \cdot C \] Where \( R \) is in Ohms and \( C \) is in Farads, giving \( \tau \) in seconds. It is the single most important parameter of any RC circuit — it sets the speed of every transition.

Charging

When a discharged capacitor is connected to a supply voltage \( V_s \) through a resistor, the voltage across the capacitor rises exponentially: \[ V(t) = V_s \cdot \left(1 - e^{-t/\tau}\right) \] After one time constant the capacitor has charged to \( 1 - 1/e \approx 63.2\% \) of \( V_s \). After five time constants it is considered fully charged: \[ \begin{align} t = 1\tau &\Rightarrow V = 63.2\%\ V_s \\ t = 2\tau &\Rightarrow V = 86.5\%\ V_s \\ t = 3\tau &\Rightarrow V = 95.0\%\ V_s \\ t = 4\tau &\Rightarrow V = 98.2\%\ V_s \\ t = 5\tau &\Rightarrow V = 99.3\%\ V_s \end{align} \]

Discharging

When a fully charged capacitor discharges through a resistor, the voltage decays exponentially: \[ V(t) = V_0 \cdot e^{-t/\tau} \] After one time constant the voltage has dropped to \( 1/e \approx 36.8\% \) of \( V_0 \). The decay is the mirror image of the charging curve. To compute the exact voltage, current, and charge at a specific time, use the capacitor discharge calculator.

Purpose of the Calculator

Given any two of \( R \), \( C \), \( \tau \), the calculator solves for the third:

• To solve for \( \tau \): \[ \tau = R \cdot C \]
• To solve for \( R \): \[ R = \frac{\tau}{C} \]
• To solve for \( C \): \[ C = \frac{\tau}{R} \]

Optionally, providing \( t \) and \( V_s \) or \( V_0 \) calculates the charging or discharging voltage at that time. Both can be provided simultaneously to compare charging and discharging in the same circuit. If C is a combination of capacitors, compute the equivalent value first with the capacitors in series or capacitors in parallel calculator.

Related Tools

• Capacitor Discharge Calculator — compute voltage, current, and charge over time for an RC discharge.
• Capacitor Impedance Calculator — frequency-domain view of the same RC circuit.
• Capacitors in Series / Capacitors in Parallel — if C is a network, compute the equivalent capacitance first.
• RL Time Constant Calculator — the inductive equivalent: \( \tau = L/R \), current as the state variable.

More calculators: blog.hirnschall.net/tools/.