RC Circuit Calculator
Enter your capacitance, resistance, and supply voltage to calculate the time constant, charge/discharge times, energy stored, and view the voltage curve.
Charging Milestones
| Time Constants | Time | Voltage | % Charged |
|---|
Voltage at a Specific Time
Charging Curve
Common Capacitor Values Reference
| Capacitance | Typical Use | Type |
|---|---|---|
| 10 pF -- 100 pF | RF tuning, oscillator circuits | Ceramic (C0G/NP0) |
| 100 pF -- 10 nF | Decoupling, filtering high-freq noise | Ceramic (X7R) |
| 10 nF -- 100 nF | Bypass capacitors, timing circuits | Ceramic, Film |
| 100 nF -- 1 uF | Power supply decoupling, signal coupling | Ceramic (MLCC), Film |
| 1 uF -- 100 uF | Power filtering, audio coupling | Ceramic, Electrolytic |
| 100 uF -- 10 mF | Bulk power filtering, energy storage | Electrolytic, Tantalum |
| 1 F -- 100 F | Energy backup, hold-up power | Supercapacitor (EDLC) |
RC Circuit Formulas
Time Constant
tau = R x C
Where R is resistance in ohms and C is capacitance in farads. The time constant tau (tau) is measured in seconds.
Charging Voltage
V(t) = Vs x (1 - e^(-t / RC))
Vs is the supply voltage. The capacitor charges toward Vs, reaching 63.2% after one time constant.
Discharging Voltage
V(t) = V0 x e^(-t / RC)
V0 is the initial voltage. The capacitor discharges toward 0 V, retaining 36.8% after one time constant.
Energy Stored
E = 0.5 x C x V^2
E is energy in joules, C is capacitance in farads, and V is voltage across the capacitor.
Time to Reach a Target Voltage (Charging)
t = -RC x ln(1 - Vt / Vs)
Vt is the target voltage. This formula gives the time required to charge from 0 V to Vt.
Time to Reach a Target Voltage (Discharging)
t = -RC x ln(Vt / V0)
Vt is the target voltage. This formula gives the time to discharge from V0 to Vt.
Examples
Example 1 -- 555 Timer Circuit
Input: C = 10 uF, R = 100 k-ohm, Vs = 9 V
- tau = 100,000 x 0.00001 = 1.0 second
- Time to 63.2%: 1.0 s (voltage = 5.69 V)
- Time to 99%: 4.6 s (voltage = 8.91 V)
- Energy at full charge: 0.5 x 10e-6 x 81 = 0.000405 J (405 uJ)
Example 2 -- Decoupling Capacitor
Input: C = 100 nF, R = 50 ohm, Vs = 3.3 V
- tau = 50 x 0.0000001 = 5 us (microseconds)
- Time to 99%: 23 us
- Energy at full charge: 0.5 x 100e-9 x 10.89 = 0.54 uJ
Example 3 -- Supercapacitor Backup
Input: C = 1 F, R = 10 ohm, Vs = 5 V
- tau = 10 x 1 = 10 seconds
- Time to 99%: 46.1 s
- Energy at full charge: 0.5 x 1 x 25 = 12.5 J
Frequently Asked Questions
What is an RC time constant?
The RC time constant (tau, or tau) equals R multiplied by C. It represents the time for a charging capacitor to reach 63.2% of the supply voltage, or for a discharging capacitor to fall to 36.8% of its initial voltage. For example, a 10 k-ohm resistor with a 100 uF capacitor gives tau = 1 second.
How long does it take to fully charge a capacitor?
A capacitor in an RC circuit never reaches exactly 100% charge because the charging curve is exponential and asymptotic. In practice, engineers consider it fully charged after 5 time constants (5 tau), when it has reached 99.3% of the supply voltage. After 3 tau it is at 95%, and after 4 tau it is at 98.2%.
What happens during capacitor discharge?
When a charged capacitor is connected through a resistor (with the supply removed), the voltage decays exponentially. After 1 tau, voltage drops to 36.8% of the initial value. After 5 tau, it has fallen to less than 1% (0.67%) and is considered fully discharged.
How does resistance affect charge time?
Higher resistance slows down charging and discharging because it limits the current flowing into or out of the capacitor. Doubling the resistance doubles the time constant and therefore doubles the time to reach any given percentage of charge.
What is the energy stored in a capacitor?
The energy stored is E = 0.5 x C x V^2. For a 1000 uF capacitor charged to 12 V, that is 0.5 x 0.001 x 144 = 0.072 joules (72 mJ). This energy is released during discharge and can power circuits briefly or produce a spark.
Can I use this calculator for AC circuits?
This calculator is designed for DC RC circuits (charging and discharging a capacitor through a resistor from a DC supply). For AC circuits involving capacitors, you would need an impedance calculator that accounts for capacitive reactance (Xc = 1 / (2 x pi x f x C)).
Does this calculator store my data?
No. All calculations run entirely in your browser. No data is sent to any server, and nothing is stored.
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Privacy & Limitations
- All calculations run entirely in your browser -- nothing is sent to any server.
- Results are computed using standard formulas and should be verified for critical applications.
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Capacitor Charge Calculator FAQ
What is an RC time constant?
The RC time constant (tau) is the product of resistance (R) and capacitance (C) in an RC circuit. It represents the time it takes for a capacitor to charge to approximately 63.2% of the supply voltage, or discharge to about 36.8% of its initial voltage. The unit is seconds.
How long does it take to fully charge a capacitor?
Theoretically, a capacitor never fully charges in an RC circuit because the charging curve is exponential and approaches the supply voltage asymptotically. In practice, a capacitor is considered fully charged after 5 time constants (5 tau), at which point it has reached 99.3% of the supply voltage.
What is the formula for capacitor charging voltage?
The voltage across a charging capacitor at time t is V(t) = Vs * (1 - e^(-t/RC)), where Vs is the supply voltage, R is the resistance in ohms, C is the capacitance in farads, and e is Euler's number (approximately 2.71828).
What is the formula for capacitor discharging voltage?
The voltage across a discharging capacitor at time t is V(t) = V0 * e^(-t/RC), where V0 is the initial voltage, R is the resistance in ohms, and C is the capacitance in farads.
How do you calculate energy stored in a capacitor?
The energy stored in a capacitor is calculated using E = 0.5 * C * V^2, where C is the capacitance in farads and V is the voltage across the capacitor. The result is in joules.
Does this calculator store my data?
No. All calculations run entirely in your browser. No data is sent to any server, and nothing is stored.