RC Time Constant Calculator
This RC Time Constant Calculator determines how quickly a capacitor charges or discharges through a resistor. Enter resistance, capacitance, and voltage to calculate τ and the 1τ, 3τ, and 5τ timing references.
The results include ideal charging and discharging voltages for each reference time. They are useful when designing reset delays, switch debouncing, timing networks, simple filters, sensor interfaces, and capacitor discharge paths.
Calculations use base SI units internally and model an ideal first-order RC circuit. Practical component tolerance, source impedance, loading, leakage, and ESR should be evaluated separately.
RC Time Constant Calculator
Calculate the RC time constant and capacitor charging or discharging reference values from resistance, capacitance, and voltage.
Total resistance in the capacitor charge or discharge path.
Effective capacitance connected in the RC network.
Final charging voltage or starting discharge voltage.
RC time constant (τ)
1 ms
τ = R × C
- 1τ reference time
- 1ms
- 3τ reference time
- 3ms
- 5τ reference time
- 5ms
Charging and Discharging Reference
Ideal capacitor voltage at each time reference using the entered supply or initial voltage.
| Reference | Time | Charging level | Charging voltage | Discharging voltage |
|---|---|---|---|---|
| 1τ | 1 ms | 63.2% | 3.161 V | 1.839 V (36.8%) |
| 3τ | 3 ms | 95% | 4.751 V | 248.935 mV (5%) |
| 5τ | 5 ms | 99.3% | 4.966 V | 33.69 mV (0.7%) |
RC Circuit Diagram
A resistor limits current into the capacitor. The capacitor voltage at Vc changes exponentially when the switch connects the network to the supply or a discharge path.
RC Time Constant Formulas
Charging rises toward the supply voltage, while discharging falls toward zero. Both curves are governed by the same product of R and C.
Time constant: τ = R × CCharging: Vc(t) = Vs × (1 - e^(-t / RC))Discharging: Vc(t) = V0 × e^(-t / RC)- τ = RC time constant in seconds (s)
- R = Resistance in ohms (Ω)
- C = Capacitance in farads (F)
- Vs = Final supply voltage during charging
- V0 = Initial capacitor voltage during discharging
- t = Elapsed time in seconds (s)
How to Use This Calculator
- Enter the resistance in the capacitor current path and select Ω, kΩ, or MΩ.
- Enter the effective capacitance and select pF, nF, µF, mF, or F.
- Enter the charging supply voltage or the initial capacitor voltage used for discharge calculations.
- Select Calculate to view τ, 1τ, 3τ, 5τ, and the corresponding ideal charge and discharge voltages.
Input Parameters
Resistance
Use the total Thevenin resistance seen by the capacitor, including intended resistors and relevant source resistance.
Capacitance
Use the effective capacitance under the expected voltage, temperature, frequency, and dielectric conditions.
Voltage
For charging, enter the final supply voltage. For discharging, enter the capacitor voltage at the start of the decay.
Worked Example
10 kΩ and 100 nF RC Network
R = 10 kΩ = 10,000 Ω
C = 100 nF = 0.0000001 F
Vs = 5 V
τ = R × C = 10,000 × 0.0000001 = 0.001 s
τ = 1 ms
3τ = 3 ms and 5τ = 5 ms.
Charging at 1τ: 5 V × (1 - e⁻¹) ≈ 3.16 V. Charging at 5τ: 5 V × (1 - e⁻⁵) ≈ 4.97 V.
Engineering Notes
One time constant is 63.2%
After 1τ, an ideal charging capacitor reaches about 63.2% of its final voltage, while a discharging capacitor retains about 36.8%.
Five time constants approximate completion
At 5τ, charging reaches about 99.3% and discharging falls to about 0.7%. This is commonly treated as a practical full transition.
Real capacitors are non-ideal
Tolerance, leakage current, ESR, dielectric absorption, aging, and ceramic capacitor DC bias can shift the measured timing response.
Source and load impedance matter
Driver resistance and connected loads alter the effective resistance seen by the capacitor and can change both the final voltage and time constant.
RC networks support many functions
Common uses include low-pass filters, startup delays, switch debouncing, pulse shaping, sensor smoothing, and simple timing circuits.
Common Mistakes
- Mixing kΩ, MΩ, nF, and µF without converting to SI units.
- Using only the labeled resistor instead of total source resistance.
- Assuming the capacitor reaches exactly 100% after five time constants.
- Ignoring input thresholds when using an RC network as a logic delay.
- Using nominal capacitance without checking tolerance and DC bias.
FAQ
What is an RC time constant?
The RC time constant, represented by τ, describes how quickly a capacitor charges or discharges through a resistance. One time constant equals resistance in ohms multiplied by capacitance in farads.
How do you calculate RC time constant?
Multiply resistance by capacitance using base SI units: τ = R × C. For example, 10 kΩ multiplied by 100 nF equals 0.001 seconds, or 1 ms.
What voltage does a capacitor reach after one time constant?
During ideal charging, the capacitor reaches approximately 63.2% of the supply voltage after one time constant. During discharge, approximately 36.8% of the initial voltage remains.
How long does it take a capacitor to fully charge?
An ideal capacitor approaches the final voltage asymptotically and never reaches it mathematically. Engineers commonly use five time constants, where the capacitor reaches about 99.3%, as an approximate full-charge time.
What is the difference between charging and discharging in an RC circuit?
Charging voltage rises exponentially toward the supply voltage, while discharging voltage falls exponentially from its initial value toward zero. Both processes use the same RC time constant.
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Browse the Capacitors calculator category or review component selection information in the Engineering Reference Center.
This calculator provides ideal first-order RC results for engineering reference. Verify component tolerance, dielectric behavior, leakage, ESR, source and load impedance, voltage thresholds, temperature, and measured circuit timing before using the result in production hardware.