RC Circuit Time Constant: Formula and Calculation

Calculate an RC circuit’s time constant by multiplying its resistance by its capacitance: τ = R × C. Enter resistance in ohms and capacitance in farads to get τ in seconds; this calculator also shows the time to reach about 63.2% of a final voltage and the approximate five-time-constant settling time.

Formula

The time constant of a simple first-order RC circuit is τ = R × C. In this calculator, capacitance is entered in microfarads, so the conversion is τ (seconds) = R (ohms) × C (microfarads) × 0.000001. One microfarad is 10⁻⁶ farad. If capacitance is already in farads, use τ = R × C directly.

• τ (tau) is the time constant, in seconds (s).
• R is the effective resistance seen by the capacitor, in ohms (Ω).
• C is the effective capacitance, in farads (F), or in microfarads (µF) when using the calculator.
• t63 is one time constant: the time at which a charging capacitor reaches about 63.2% of its final voltage.
• tsettle is five time constants, a useful approximation for reaching within about 1% of the final value.

Worked Example

Using the calculator’s default values, R = 10,000 Ω and C = 100 µF:

1. Convert capacitance to farads: 100 µF × 0.000001 = 0.0001 F.
2. Multiply resistance by capacitance: τ = 10,000 Ω × 0.0001 F = 1 second.
3. After one time constant, the charging voltage has reached about 63.2% of its final value: t63 = 1 second.
4. Five time constants are 5 × 1 = 5 seconds, so the approximate 1% settling time is 5 seconds.

The calculator displays each result to three decimal places: τ = 1.000 s, t63 = 1.000 s, and tsettle = 5.000 s.

How the Time Constant Describes Circuit Behavior

A time constant is a measure of how quickly a capacitor’s voltage changes through a resistance. It is not the time needed to finish charging or discharging exactly. In an ideal RC circuit, the voltage approaches its final level exponentially, getting closer without reaching it at any finite time.

For a capacitor charging toward a steady supply voltage, the voltage after time t is V_C(t) = V_final[1 − e^−t/τ], assuming it starts at zero. For discharging from an initial voltage, it is V_C(t) = V_initiale^−t/τ. Here, e is the base of natural logarithms, and t and τ must use the same time unit.

• After 1τ, charging is about 63.2% complete; during discharge, about 36.8% of the initial voltage remains.
• After 2τ, charging is about 86.5% complete; about 13.5% remains during discharge.
• After 3τ, charging is about 95.0% complete; about 5.0% remains during discharge.
• After 5τ, charging is about 99.3% complete; about 0.7% remains during discharge.

These percentages describe voltage relative to its starting and final values, not necessarily the supply voltage itself. For example, if a capacitor charges from 0 V toward 10 V, it reaches about 6.32 V after one time constant.

Finding the Effective Resistance

Use the resistance that the capacitor “sees” in the circuit, not automatically the value of a nearby resistor. To find it in a linear resistor network, remove the capacitor and determine the equivalent resistance looking into its two terminals. For independent ideal voltage sources, set them to zero while finding resistance: replace voltage sources with shorts and current sources with open circuits. Dependent sources remain active, so more careful circuit analysis may be needed.

If a capacitor charges through a single resistor from an ideal voltage source, the effective resistance is often just that resistor. If several resistors or a source’s output resistance are involved, their network may change the result. A practical way to analyze a more complex circuit is to find the Thevenin equivalent seen by the capacitor; its resistance and the capacitor’s capacitance determine τ.

Units, Components, and Practical Limits

Resistance may be listed in ohms, kilohms (kΩ), or megohms (MΩ); capacitance may be in farads, millifarads (mF), microfarads (µF), nanofarads (nF), or picofarads (pF). Convert to base units before multiplying. For instance, 4.7 kΩ is 4,700 Ω and 22 nF is 0.000000022 F, giving τ = 0.0001034 s, or about 103 µs. This formula is metric and electrical-unit based; US customary units such as inches or feet are not used for R, C, or τ.

Real components have tolerances, and capacitance can vary with temperature, applied voltage, frequency, or age depending on the component type. The calculated value is therefore a nominal estimate when it uses nominal component values. Leakage, source resistance, load resistance, and measurement equipment can also affect a real circuit’s response. At sufficiently high frequencies or with distributed wiring and components, a single lumped RC time constant may not describe the behavior adequately.

Common Calculation Mistakes

• Mixing prefixes: multiplying ohms by a number in µF as though it were farads gives a result one million times too large. Apply the conversion factor.
• Using the wrong resistance: calculate the equivalent resistance seen by the capacitor, including relevant source and load effects.
• Calling 5τ an exact finish: five time constants means roughly 99.3% charged, not 100%. The required settling tolerance depends on the application.
• Confusing voltage percentages: 63.2% is the charging voltage after one τ, while 36.8% is the fraction remaining during discharge.
• Rounding too early: keep extra digits during unit conversion and multiplication, then round the displayed result to a useful precision.

Frequently Asked Questions

What is the formula for an RC time constant?
For a first-order RC circuit, τ = R × C, where R is the effective resistance in ohms and C is the capacitance in farads. The result is in seconds.

How do I calculate the time constant with capacitance in microfarads?
Multiply resistance in ohms by capacitance in microfarads, then multiply by 0.000001. For example, 10 kΩ and 100 µF give 10,000 × 100 × 0.000001 = 1 second.

How many time constants does a capacitor take to charge?
There is no exact finite time to reach 100% in the ideal exponential model. One time constant reaches about 63.2%; five reach about 99.3%, often treated as practically settled when that accuracy is sufficient.

Does the time constant change during discharge?
For a linear circuit with the same effective resistance and capacitance, the time constant is the same for charging and discharging. The initial and final voltages differ, but the exponential rate is governed by RC.

What if the circuit has more than one resistor?
Find the equivalent resistance looking into the capacitor’s terminals, with independent sources set to zero for the resistance calculation. In a linear circuit, using the Thevenin equivalent is a standard way to reduce the rest of the network to one effective source and resistance.

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in r | Resistance | ohm | 10000 | 0
in c | Capacitance | uF | 100 | 0
out tau | Time constant | s | r * c * 0.000001 | 3
out t63 | Time to 63.2% | s | tau | 3
out tsettle | Approx. settling time (5τ) | s | 5 * tau | 3