RC time constant:
τ = R × C

What the RC time constant is

The RC time constant is the resistance multiplied by the capacitance, giving a time in seconds. A 10 kΩ resistor with a 10 µF capacitor has a time constant of 0.1 seconds. It tells you how quickly the capacitor charges or discharges through that resistor.

The symbol is the Greek letter tau, τ. After one time constant a charging capacitor has reached about 63.2% of its final voltage, and a discharging one has fallen to about 36.8% of its starting voltage. Those percentages come from the exponential curve of the circuit.

The formula and a worked example

Choosing R and C for a target delay

Designers often work backwards. To get a time constant of about 0.47 s with a 10 µF capacitor, rearrange the formula to R = τ ÷ C. That gives 0.47 ÷ 0.00001 = 47,000 Ω, or 47 kΩ, which is a standard resistor value.

Typical uses include a button debounce that waits a few milliseconds, a slow fade for an LED, and a reset delay that holds a chip off for a moment after power-up. Each one is a choice of R and C whose product gives the delay you want.

Units and the link to cut-off frequency

Kilohms times microfarads gives milliseconds, because 1,000 × 0.000001 = 0.001. That shortcut is quick for hand checks, but the Calcylator form wants plain ohms and farads, so convert before you type.

The same product sets the cut-off frequency of a simple RC filter: fc = 1 ÷ (2π × R × C). For 1 kΩ and 1 µF, that is about 159.15 Hz. Slower circuits, with larger τ, have a lower cut-off.

As a rule of thumb, a capacitor is considered almost fully charged after about five time constants, at which point it has reached more than 99% of its final value. For the 0.1 s example that is roughly half a second.

Where RC time constants show up

Camera flash circuits, timer chips, touch sensors and the smoothing capacitor in a power supply all rely on an RC time. A technician checking a faulty board often measures how long a voltage takes to rise, then compares it with the product of the two component values to spot a part that has drifted.

The same maths describes discharge. A capacitor left connected across a resistor loses its charge following the same curve, which is why large capacitors in a power supply are paired with a bleeder resistor that drains them over time.

Common RC time constant mistakes

• Entering microfarads as farads, which makes τ a million times too large.
• Mixing kilohms and ohms in the same calculation.
• Expecting the capacitor to be full after exactly one time constant.
• Forgetting the tolerance. Capacitors are often wide-tolerance parts, so real delays vary.
• Ignoring the source resistance, which adds to R.