Rc Circuit Calculator - Tau, Cutoff Frequency, and V(t)

A RC circuit calculator solves tau = R C, cutoff frequency fc = 1/(2 pi R C), and the V(t) charging and discharging exponentials from a resistor, capacitor, and elapsed time.

• • Time-constant homework and lab checks: Convert R and C into tau, then compare a measured capacitor voltage against the theoretical curve.
• • RC filter design: Convert the same R and C into fc so the -3 dB point is known before the circuit is built.
• • Power-on reset and timing: Read V(t) to predict the voltage on a reset capacitor, 555 timer node, or debounce network.
• • Battery and supply rail monitoring: Compare V_charge(t) and V_discharge(t) to size hold-up time on a battery-backed rail.

The calculator assumes an ideal resistor in series with an ideal capacitor and a DC supply. Real capacitors add ESR and leakage; real resistors add parasitic inductance at high frequency. Check a datasheet for power or precision work.

When the design goal is the finite time to a chosen voltage threshold, the Capacitor Charge Time Calculator pairs the same R and C with a target voltage and supply voltage.

The calculator takes the resistance R and the capacitance C and turns them into tau = R C, then takes 1 / (2 pi tau) and turns it into fc, and evaluates V(t) = Vs (1 - e^(-t/tau)) and V(t) = Vi e^(-t/tau).

• R: Resistance in ohms in series with the capacitor. Calculator accepts ohm, kohm, and Mohm prefixes.
• C: Capacitance of the capacitor in farads. Calculator accepts F, mF, uF, nF, and pF prefixes.
• t: Elapsed time at which the capacitor voltage is evaluated, in seconds. Calculator accepts us, ms, and s prefixes.
• Vs: Supply voltage that the charging curve approaches as t goes to infinity.
• Vi: Initial voltage on the capacitor at t = 0 for the discharging curve.
• tau: Time constant in seconds, equal to R times C. Auto-prefixed to us, ms, or s so the printed value stays readable across filter, audio, and timing applications.
• fc: Cutoff frequency in hertz, equal to 1 / (2 pi R C). Auto-prefixed to Hz, kHz, or MHz so the printed value stays readable from sub-audio to RF.

The same tau controls both curves, so the time it takes a capacitor to reach a chosen fraction of the supply equals the time it takes a charged capacitor to fall to the same fraction of its initial voltage. The cutoff frequency is the -3 dB point of a low-pass filter and the corner of a high-pass filter.

According to Wikipedia (RC circuit), tau = R C, V(t) = Vs (1 - e^(-t/tau)) for charging, and V(t) = Vi e^(-t/tau) for discharging.

Once tau is known, the AC behavior of the same capacitor is Xc = 1 / (2 pi f C), and the Capacitive Reactance converts any C and f into that reactance in ohms.

Four ideas make the result panel easier to read: the role of R and C in tau, the exponential approach to the boundary voltage, the 3 dB cutoff, and the symmetry between charge and discharge.

The charging progress and discharge remaining columns come straight from the exponentials above, so reading both side by side is a quick way to see how much headroom the circuit has at a given elapsed time.

If the capacitance is not yet known, the Capacitance Calculator takes the parallel-plate geometry and dielectric material of the capacitor and returns C in farads.

Type a resistance, a capacitance, a time, and the two boundary voltages, then read tau, fc, and V(t) for charge and discharge in the result panel.

1. 1 Enter the resistance: Type the resistor value and pick ohm, kohm, or Mohm. The calculator converts to ohms before tau = R C runs.
2. 2 Enter the capacitance: Type the capacitor value and pick F, mF, uF, nF, or pF. The calculator converts to farads.
3. 3 Enter the elapsed time: Type the time at which you want V(t) and pick us, ms, or s.
4. 4 Enter Vs and Vi: Type Vs in volts for the charging curve and Vi in volts for the discharging curve.
5. 5 Read tau and fc: Read tau in the auto-prefixed seconds value (us, ms, or s) and fc in the auto-prefixed hertz value (Hz, kHz, or MHz).
6. 6 Read V(t) and progress: Read V_charge(t) and V_discharge(t) in volts and the progress percentages.

To find the cutoff frequency of a 10 kohm / 1 uF low-pass filter for a 1 kHz audio signal, pick 10 kohm and 1 uF. The calculator returns tau = 10 ms and fc approximately 15.92 Hz, well below the audio band, so the pair will pass audio cleanly while filtering out sub-audio DC drift.

When the design needs the steady-state current or power dissipation across R on the same node, the Ohm's Law & Basic Circuit Calculator handles V = I R for any combination.

The calculator replaces three separate lookups (tau, fc, V(t)) with one result panel that updates as any input changes.

• • Time constant and cutoff from one pair of inputs: Reads tau and fc from the same R and C without entering the formulas twice or switching units by hand.
• • Resistance prefix library: Covers ohm, kohm, and Mohm so values from a resistor drawer or multimeter drop in without manual conversion to ohms.
• • Capacitance prefix library: Covers F, mF, uF, nF, and pF so values from a datasheet or capacitor code drop in without manual conversion.
• • Time prefix library: Covers us, ms, and s so the same form handles a reset at microseconds, a debounce at milliseconds, and a hold-up at seconds.
• • Charging and discharging curves side by side: Reports V_charge(t) and V_discharge(t) with matching progress percentages so the same panel answers both time-to-voltage and voltage-at-time.
• • Auto-prefixed tau and fc: Picks us, ms, or s for tau and Hz, kHz, or MHz for fc so the printed values stay in a readable range from a 1 pF / 1 ohm RF pair to a 1 mF / 10 Mohm long-period pair.

When the goal is the stored charge Q = C V or the stored energy E = 1/2 C V^2 at the chosen boundary voltage, the Capacitor Charge Calculator takes the same C and returns the coulombs, joules, and watt-hours.

Three inputs drive the headline numbers: R, C, and the elapsed time t. The boundary voltages Vs and Vi drive only the voltage columns.

The textbook model assumes an ideal resistor in series with an ideal capacitor and a DC supply. At high frequency self-resonant frequency and parasitic inductance dominate.

The exponentials assume Vs and Vi stay constant. If the source has internal resistance or the capacitor leaks, the effective time constant is shorter than R * C.

Zero or negative resistance and capacitance are rejected because tau = R C and fc = 1 / (2 pi R C) both require non-zero inputs.

According to Wikipedia (Capacitor), the stored charge is Q = C V, which is why Vs and Vi are the supply voltage and the starting voltage on the same C.

According to Wikipedia (Time constant), the time constant of an RC circuit is tau = R C, the bandwidth of the resulting RC filter is f = 1 / (2 pi tau), and after one tau a charging capacitor reaches about 63.2 percent of the supply voltage and a discharging capacitor falls to about 36.8 percent of its initial voltage.

When the resistor is paired with several capacitors in series or parallel, the Capacitor Calculator returns the equivalent C for the combined network.