Time constant
τ = RC
The product of resistance and capacitance sets the first-order time scale.
RC Time Constant Calculator
Calculate an ideal first-order RC charging or discharging transient at a selected time.
Access: Free to use, no installation, and No account required.
Inputs
For discharge mode, the engine targets 0 V. The source-voltage field is therefore ignored by the transient equation.
Results
RC time constant
The time constant is τ = RC. After one time constant a charging capacitor has traversed about 63.2% of the difference to its final value; after about five time constants it is effectively settled for many engineering purposes.
Ideal-model limitations
ESR, leakage, dielectric absorption, source resistance, current limiting, tolerance, temperature, and nonlinear components are not modeled here.
Engineering reference
RC Time Constant Calculator: background and worked detail
Use the RC Time Constant Calculator to calculate τ = RC and the ideal charging or discharging capacitor voltage, current, charge, and stored energy at a selected time.
Charging, discharging, and τ
Charging voltage
V_C(t) = V_s + (V_0−V_s)e^(−t/RC)
The capacitor voltage exponentially approaches the source voltage.
Discharge voltage
V_C(t) = V_0e^(−t/RC)
With a zero-volt target, the stored voltage decays exponentially.
1 kΩ and 100 µF charging from 0 V to 5 V
Set R = 1,000 Ω, C = 100 µF, source = 5 V, initial voltage = 0 V, and time = 100 ms.
- τ = 1,000 × 100 µF = 0.100 s.
- At t = τ, V_C = 5(1−e⁻¹) ≈ 3.16 V.
- Current at one time constant is about 1.84 mA.
Result: The example demonstrates the 63.2% one-time-constant charging rule.
Reading exponential settling
A first-order RC network changes exponentially toward its final value. One time constant corresponds to 63.2% of the total charging transition, or 36.8% of the initial voltage remaining during ideal discharge.
The model treats R and C as ideal lumped components. Source impedance, capacitor ESR and leakage, dielectric absorption, component tolerance, temperature, current limiting, and nonlinear connected circuitry can alter the actual waveform.
Assumptions and model boundaries
Assumptions
- Ideal linear resistor and capacitor.
- A constant source voltage is used in charge mode.
- The network is represented by a single first-order RC state.
Limitations
- Does not model capacitor tolerance, ESR, leakage, dielectric absorption, voltage coefficient, or source current limiting.
- Complex RC networks and active circuits require circuit-level analysis.
RC Time Constant Calculator FAQ
Why is five time constants considered settled?
After 5τ, an ideal first-order charging response has completed about 99.3% of its transition.
Does capacitor voltage change instantly?
No in the ideal model. A capacitor's voltage is continuous unless an impulse current is allowed.
Should source resistance be included?
Yes. Any meaningful source resistance in series with the capacitor should be included in the effective R used for the time constant.
Validation checks
One time constant
Case: Evaluate a 0 V to Vs charge at t = RC.
Expected: Capacitor voltage should be approximately 0.632 Vs.
Five time constants
Case: Evaluate the same charge at t = 5RC.
Expected: Capacitor voltage should be approximately 0.993 Vs.
Where this calculation comes from
Shared with the Introductory Circuits Workbench, which also covers the transient response of RL and RLC networks.
Open the source workbench →Read calculation and source methodology →