RC Time Constant Calculator

An RC time constant describes how fast a capacitor charges toward, or discharges away from, a voltage through a series resistance. In field and design work, this number sets the delay in timing and debounce circuits, the discharge time of a capacitor bank through its bleed resistor, and the response time of snubber and filter networks used across contactor coils, motor drives, and power-supply capacitors. The calculator returns three values from four inputs: time constant, target time, and target fraction.

Inputs and What They Represent

• Resistance — series resistance in the RC path, entered in ohms (Ω). In this example, 10,000 Ω.
• Capacitance — capacitor value in microfarads (µF). In this example, 10 µF.
• Transition mode — selects Charge or Discharge. Charge models a capacitor rising toward a source voltage through R; discharge models a charged capacitor bleeding down through R.
• Target percentage — for charge mode, the final charged percentage of the applied voltage reached; for discharge mode, the percentage of the initial voltage still remaining on the capacitor.

These four fields map directly onto a real RC network: a resistor and capacitor in series, with the capacitor being charged or discharged through that resistor.

Time Constant Formula

The RC time constant is:

\(\tau = R \times C\)

With resistance in ohms and capacitance in farads, τ is in seconds. This is the time required for the capacitor voltage to move through 63.2% of the remaining difference between its current voltage and the target voltage — the defining property of a first-order exponential response, independent of the target percentage entered.

For the given inputs:

\(\tau = 10{,}000\ \Omega \times (10\ \mu F = 10\times10^{-6}\ F) = 0.1\ \text{s}\)

Time constant: 0.1 s.

Charge vs. Discharge: Target Time Formula

The target time is the point at which the capacitor reaches the entered target percentage, derived from the exponential charge/discharge equations.

For charge mode, capacitor voltage rises as:

\(V(t) = V_{final}\left(1 - e^{-t/\tau}\right)\)

Solving for t at a target fraction (p) (target percentage ÷ 100):

\(t = -\tau \ln(1 - p)\)

For discharge mode, capacitor voltage decays as:

\(V(t) = V_{initial}, e^{-t/\tau}\)

Solving for t at a target fraction (p) (percentage remaining):

\(t = -\tau \ln(p)\)

The target fraction output is simply the target percentage expressed as a decimal (target percentage ÷ 100), used internally in both equations above.

Calculation Example

With τ = 0.1 s, mode = Charge, target percentage = 50%:

1. Target fraction: p = 50 / 100 = 0.5

2. Apply the charge formula: t = −τ · ln(1 − p) = −0.1 · ln(0.5) = −0.1 × (−0.693) = 0.0693 s

Target time: 0.0693 s — the capacitor reaches 50% of the applied voltage 69.3 milliseconds after the charge path is energized, given a 10,000 Ω series resistor and a 10 µF capacitor.

Field Application: Discharge Time and Bleed Resistors

When the calculator is run in Discharge mode, the target time gives the interval for a capacitor to fall to a specified percentage of its stored voltage through a known bleed or discharge resistor. This value is used when sizing a discharge resistor for a capacitor bank, power-factor correction capacitor, or motor-run/start capacitor so that residual voltage drops to a safe touch level within a required interval. NEC 460.28 requires capacitors rated over 600 V, and capacitors on general-purpose circuits under specific conditions, to discharge to 50 V or less within 1 minute of de-energization; the arithmetic here produces the time-to-percentage figure that must then be checked against the applicable discharge-time requirement and against the capacitor’s actual rated voltage, not derived by the calculator itself.

In Charge mode, the same formula sets delay timing for RC-based timing networks, debounce circuits on contactor and relay control inputs, and snubber networks across coil contacts, where the target time defines how long the circuit takes to reach a switching threshold after voltage is applied.

Field and Circuit Limits

The calculator models an ideal first-order RC network — a single resistor in series with a single capacitor, with no parasitic inductance, no leakage current across the capacitor dielectric, and no additional load drawing current from the RC node. Actual capacitors have equivalent series resistance (ESR) and leakage that shift real charge/discharge curves away from the ideal exponential, particularly for electrolytic types at low percentages or long time constants. Series resistance from wiring, connectors, or a parallel load path is not included and must be added to the entered resistance value if it is significant relative to R.

For discharge-resistor sizing tied to a code-mandated discharge interval, verify the applied voltage rating, resistor power dissipation \(P = V^2/R\) at initial voltage, and the specific NEC section governing the capacitor installation with the authority having jurisdiction before finalizing resistor selection — the calculator returns only the time-to-percentage arithmetic, not a compliance determination.