RC Circuit Calculator
Calculate RC time constant, charging or discharging capacitor voltage, charge, current, and low-pass cutoff frequency. Every answer includes formula substitution, solution steps, and a live value-labelled circuit diagram.
RC Circuit Diagram and Live Values
The blue capacitor fill and labels show exactly how far the circuit has charged or discharged.
Step-by-Step Solution
Here's exactly how this answer was calculated, one step at a time.
Given: R = 1,000 Ω, C = 100 µF, V = 12 V, t = 0.1 s
Step 1: Convert capacitance to farads
RC formulas use capacitance in farads.
C = 100 µF = 0.0001 FStep 2: Find the RC time constant
τ = R × C = 1,000 Ω × 0.0001 F = 0.1 sStep 3: Use the charging-voltage formula
Vc = Vs(1 − e^(−t/RC))Step 4: Substitute the values
Vc = 12(1 − e^(−0.1/0.1))Step 5: Calculate capacitor voltage
Vc = 7.585447 V
The capacitor voltage is:
7.585447 V
Free RC Circuit Calculator
This RC Circuit Calculator finds the time constant of a resistor-capacitor circuit and its capacitor voltage at any chosen time. Select charging or discharging, enter resistance in ohms and capacitance in microfarads, then see the exact formula, substitutions, capacitor charge, current, and cutoff frequency. The labelled circuit image updates with the same values, so the calculation is visible rather than just a final number.
It is useful for physics homework, electronics revision, timer design, low-pass filters, switch debouncing, and checking a basic capacitor timing circuit. The result uses ideal-component DC equations. Real capacitors have tolerance, leakage and equivalent series resistance, so treat the calculation as a strong starting point and confirm a finished design by measurement.
What Is an RC Circuit?
An RC circuit contains a resistor (R) and capacitor (C). The resistor limits the current while the capacitor stores charge. Because the current is limited, the capacitor voltage changes smoothly over time instead of jumping instantly. This gradual response is why RC circuits make useful delays, filters and waveform-shaping networks.
At the first instant of charging, an uncharged capacitor behaves approximately like a short circuit and current is highest. As its voltage rises, the voltage across the resistor falls and current tapers away. During discharge, stored capacitor energy drives current through the resistor and the voltage falls exponentially.
RC Time Constant Formula
The central RC circuit formula is τ = R × C. Tau (τ) is the time constant in seconds, R is resistance in ohms, and C is capacitance in farads. Convert microfarads before multiplying: 100 µF is 0.000100 F. For 1,000 Ω and 100 µF, τ = 1000 × 0.000100 = 0.1 seconds.
After one time constant, a charging capacitor reaches about 63.2% of its final voltage. After two tau it reaches 86.5%, after three it reaches 95%, and after five tau it is about 99.3% charged. A discharging capacitor has 36.8% of its starting voltage after one tau and about 0.7% after five tau.
Capacitor Charging Formula and Worked Steps
Use Vc = Vs(1 − e^(−t/RC)) for a capacitor charging from a DC source. Vc is capacitor voltage, Vs is supply voltage, t is elapsed time and e is Euler's number. First calculate τ, divide elapsed time by τ, then use the exponential term.
Example: a 12 V supply, 1 kΩ resistor and 100 µF capacitor give τ = 0.1 s. At t = 0.1 s, Vc = 12(1 − e^(−1)) = 12(0.632) = 7.59 V. The diagram marks that 63.2% charge level. The remaining resistor voltage is 4.41 V, so current is 4.41 V / 1000 Ω = 4.41 mA.
Capacitor Discharge Formula
Use Vc = V0e^(−t/RC) when a capacitor discharges through a resistor. V0 is its starting voltage. With the same 1 kΩ and 100 µF circuit, a 12 V capacitor has Vc = 12e^(−1) = 4.41 V after 0.1 s. The polarity and current direction depend on circuit wiring, while this calculator reports the current sign to identify discharge direction.
Capacitors retain energy after a supply is removed. Disconnect power and use an appropriate resistor-based discharge method before handling a real circuit. High-voltage or large-energy equipment needs qualified procedures; do not rely on an online calculation as a safety assessment.
RC Cutoff Frequency
An RC low-pass filter has cutoff frequency fc = 1 / (2πRC). At this frequency, output magnitude is about 70.7% of the low-frequency value. The same R and C that give a larger timing delay produce a lower cutoff frequency. This relationship makes an RC network useful for smoothing signals and reducing high-frequency noise.
For τ = 0.1 seconds, fc = 1/(2π × 0.1) = 1.59 Hz. Choose components with realistic tolerances: a 5% resistor and 20% capacitor can make the actual time or cutoff noticeably different. Film capacitors are often more stable than electrolytics for precision timing.
RC Circuit Design Tips
Keep units consistent, especially kilohms, microfarads and milliseconds. A 10 kΩ resistor is 10,000 Ω; 47 µF is 0.000047 F; 250 ms is 0.25 s. Verify capacitor voltage rating, polarity for electrolytics, resistor power rating, leakage and the load connected to the capacitor node.
An input or output load changes effective resistance and may alter the expected timing. In sensitive timing circuits, use a buffer. For high current, rapid pulses or resonant behaviour, consider additional effects such as ESR and inductance. These equations describe the standard first-order RC circuit.
Frequently Asked Questions
What is the RC time constant formula?
τ = R × C, using resistance in ohms and capacitance in farads. The result is seconds.
How charged is a capacitor after one time constant?
A charging capacitor reaches approximately 63.2% of its final voltage after one τ; after five τ it is about 99.3% charged.
What is the capacitor discharge formula?
Vc = V0e^(−t/RC), where V0 is initial voltage and t is elapsed time.
How do I find RC cutoff frequency?
Use fc = 1/(2πRC). Larger resistance or capacitance gives a lower cutoff frequency.