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Calculate the energy stored in a capacitor and the RC time constant. Enter the voltage across the capacitor, capacitance, and load resistance to obtain the energy (E) and time constant (T).
Enter your parameters below to calculate results.
The Time Constant Calculator determines the RC time constant of a resistor-capacitor circuit and the energy stored in a charged capacitor. Enter the resistance, capacitance, and voltage to calculate the response time in seconds and stored energy in joules.
The time constant does not represent the exact time required for a capacitor to become completely charged or discharged. Instead, it describes the speed of the exponential response. After one time constant, a charging capacitor has completed about 63.2% of the voltage change, while a discharging capacitor retains about 36.8% of its initial voltage. An interval of five time constants corresponds to about 99.3% of the total change and is commonly used as a practical settling estimate.
This calculator is useful for RC delay circuits, reset networks, sensor filtering, power-supply startup, capacitor discharge planning, pulse circuits, debounce networks, and first-order low-pass or high-pass filters.
| Input | Meaning | Common Units |
|---|---|---|
| Voltage, V | The voltage across the capacitor used in the stored-energy calculation. | V |
| Capacitance, C | The capacitance of the capacitor. | F, mF, µF, nF, pF |
| Resistance, R | The effective resistance through which the capacitor charges or discharges. | Ω, kΩ, MΩ |
| Output | Meaning | SI Unit |
|---|---|---|
| Time constant, τ | The characteristic time for the RC voltage and current response. | s |
| Stored energy, E | The ideal electrical energy stored in the capacitor at the entered voltage. | J |
The ideal energy stored in a capacitor is:
E = 0.5 × C × V2
Where:
The voltage is squared, so stored energy rises quickly as voltage increases. Doubling the voltage stores four times as much energy when capacitance remains unchanged.
Consider a 1000 µF capacitor charged to 10 V. First convert the capacitance to farads:
1000 µF = 0.001 F
Then calculate the stored energy:
E = 0.5 × 0.001 × 102 = 0.05 J
The ideal stored energy is 0.05 joule. Resistance affects how quickly this energy is transferred, but it does not change the ideal energy stored at a specified capacitance and voltage.
For a simple RC circuit, the time constant is:
τ = R × C
Where:
When additional components are connected to the capacitor, use the effective resistance seen from the capacitor terminals rather than automatically using the value of a single labeled resistor. Independent voltage sources are set to zero when determining this resistance for a linear RC network.
Consider a 2000 µF capacitor charging or discharging through a 10 kΩ resistor:
τ = 10000 × 0.002 = 20 s
After 20 seconds, the capacitor has completed about 63.2% of a charging transition or retains about 36.8% of its initial voltage during discharge. A practical five-time-constant estimate is 100 seconds.
For a capacitor that starts at 0 V and charges through a resistor toward a constant supply voltage, the capacitor voltage is:
VC(t) = VS × (1 - e-t/RC)
For a capacitor with an initial voltage that is not zero, the more general equation is:
VC(t) = VF + (V0 - VF) × e-t/RC
Where V0 is the initial capacitor voltage and VF is the final steady-state voltage. The capacitor voltage changes rapidly at first, then approaches the final value more slowly.
For a capacitor discharging through a resistor toward 0 V:
VC(t) = V0 × e-t/RC
The ideal discharge current has the same exponential decay. Its initial magnitude is approximately V0 divided by R; it then decreases as the capacitor voltage falls.
| Elapsed Time | Charging Voltage | Discharging Voltage Remaining |
|---|---|---|
| 0.5τ | 39.3% of final voltage | 60.7% of initial voltage |
| 1τ | 63.2% of final voltage | 36.8% of initial voltage |
| 2τ | 86.5% of final voltage | 13.5% of initial voltage |
| 3τ | 95.0% of final voltage | 5.0% of initial voltage |
| 4τ | 98.2% of final voltage | 1.8% of initial voltage |
| 5τ | 99.3% of final voltage | 0.7% of initial voltage |
A capacitor never reaches its final value in a mathematically exact sense because the response is exponential. In practical circuit work, a response is often considered fully settled after five time constants when an error of about 0.7% is acceptable. Precision systems may require a longer settling interval.
One time constant is only a reference point. When a circuit must reach a specific threshold, calculate the required time directly.
t = -R × C × ln(1 - VT / VS)
VT is the target capacitor voltage and VS is the charging supply voltage. The target must be lower than the supply voltage for this ideal equation.
t = R × C × ln(V0 / VT)
V0 is the initial voltage and VT is the desired lower voltage. These equations are useful for reset thresholds, logic input thresholds, delay circuits, and capacitor safety-discharge calculations.
The formula τ = RC gives seconds when resistance is in ohms and capacitance is in farads. The following combinations can reduce conversion mistakes:
| Resistance Unit | Capacitance Unit | Resulting Time Unit |
|---|---|---|
| Ω | F | s |
| Ω | µF | µs |
| kΩ | µF | ms |
| MΩ | µF | s |
| kΩ | nF | µs |
| MΩ | nF | ms |
| Value | Equivalent SI Value |
|---|---|
| 1 mF | 0.001 F |
| 1 µF | 0.000001 F |
| 1 nF | 0.000000001 F |
| 1 pF | 0.000000000001 F |
| 1 kΩ | 1000 Ω |
| 1 MΩ | 1000000 Ω |
A 47 µF capacitor charges from 0 V toward 5 V through a 100 kΩ resistor.
τ = 100000 × 0.000047 = 4.7 s
| Elapsed Time | Approximate Capacitor Voltage |
|---|---|
| 4.7 s | 3.16 V |
| 9.4 s | 4.32 V |
| 14.1 s | 4.75 V |
| 23.5 s | 4.97 V |
If a logic input changes state at 3.0 V, the switching delay is not exactly one time constant. Using the target-voltage equation gives approximately 4.31 seconds for an ideal circuit.
For a first-order RC filter, the time constant is related to the cutoff frequency:
fC = 1 / (2 × π × R × C) = 1 / (2 × π × τ)
A larger time constant produces a lower cutoff frequency and a slower transient response. This relationship applies to ideal first-order RC networks; source and load impedances must be included when they affect the resistance seen by the capacitor.
The RC time constant is the product of effective resistance and capacitance. It describes how quickly capacitor voltage and circuit current respond to a step change.
Ideal capacitor charging follows 1 - e-t/RC. At t = RC, this becomes 1 - e-1, which is approximately 0.632.
An ideal capacitor approaches its final voltage exponentially and never reaches it exactly. After five time constants, the voltage reaches about 99.3% of its final value, which is often close enough for practical estimates. Precision applications may need a stricter settling requirement.
For an ideal capacitor at a fixed final voltage, stored energy depends on capacitance and voltage. Resistance changes charging and discharging speed and controls current, but not the ideal final energy.
Yes, but the numerical result is in milliseconds. For example, 10 kΩ × 100 µF = 1000 ms, which equals 1 second.
Use the effective resistance seen by the capacitor. This may include a timing resistor, source resistance, load resistance, switch resistance, and other paths connected to the capacitor.
No. After five time constants, about 0.7% of the transition remains. Systems with tighter accuracy requirements need more settling time, while threshold circuits may require less.
Yes. Large-capacitance or high-voltage capacitors can store hazardous energy. Use a suitable discharge path and verify the voltage before touching or servicing the circuit.