Time Constant Calculator

Input

Voltage (V)

Capacitance (C)

Load Resistance (R)

Output

Time Constant (τ)

Energy (E)

E = V² × C 2

τ = R C

Enter voltage, capacitance and resistance to view the RC charging / discharging curves.

Understanding time constants in RC and RL circuits

The time constant is a fundamental parameter describing how quickly a circuit responds to changes in voltage or current. In both RC (resistor–capacitor) and RL (resistor–inductor) networks, the time constant determines the speed of charging, discharging or current rise and decay.

This calculator computes τ (tau), the circuit’s time constant, and shows how the voltage or current evolves over time using standard exponential response curves.

Time constant formulas

RC circuit

For a resistor R in series with a capacitor C:

τ = R × C

where:

R = resistance (Ω)
C = capacitance (F)

RL circuit

For a resistor R in series with an inductor L:

τ = L / R

where:

L = inductance (H)
R = resistance (Ω)

Exponential response behavior

RC charging

The capacitor voltage follows:

V(t) = V_in (1 − e^−t/τ)

RC discharging

V(t) = V₀ e^−t/τ

RL current rise

I(t) = I_max (1 − e^−t/τ)

RL current decay

I(t) = I₀ e^−t/τ

Key time markers

Time constant τ indicates how fast the circuit approaches its final value:

Time	RC Charging	RC Discharge	RL Rise/Decay
1 τ	63.2% of final value	36.8% remaining	63.2% of final
3 τ	95% of final	5% remaining	95% of final
5 τ	99.3% of final	0.7% remaining	99.3% of final

How to use the Time Constant Calculator

Select circuit type: Choose RC or RL.
Enter component values: Input R and C for RC circuits or R and L for RL circuits.
Review τ (time constant): The calculator outputs the time constant in seconds, milliseconds or microseconds depending on values.
View transient curve: A plotted waveform shows charging, discharging or current rise/decay over multiple time constants.

Applications of time constant analysis

Signal filtering (cutoff frequency directly related to RC/RL time constant)
Debouncing switches using RC networks
Timing circuits in analog/digital electronics
Soft-start and ramp control using RC charging
Transient response in motor drives and inductive loads
Pulse shaping and smoothing in communication systems

The time constant calculator provides a clear visualization of exponential behavior, helping designers understand dynamic circuit response and select optimal component values for timing, filtering and control applications.

FAQ about Time Constant Calculator

Why is the time constant important in filtering?

Yes.

If the capacitor or inductor interacts with additional resistances or impedances, the effective R in the circuit changes.

This modifies τ, especially in:

voltage dividers feeding RC networks
RL circuits with parasitic resistance
sensor interfaces

Why does 5τ represent “fully charged” even though it’s not 100%?

Exponential curves never mathematically reach the final value.

At 5τ, the output reaches 99.3% of final—close enough that engineers treat it as fully settled for practical purposes.

Is τ affected by load or external circuitry?

RC and RL filters derive their cutoff frequency from τ:

<code>f<sub>c</sub> = 1 / (2π τ)</code>

A larger τ = slower response = lower cutoff.

Time constant directly shapes how signals are attenuated or smoothed.