RC Time Constant Calculator

About RC Time Constant Calculator

RC time constant: time to charge to 63.2%. After 5τ, the capacitor is ~99.3% charged.

How to use this calculator

1. Enter the resistance \(R\) in ohms and the capacitance \(C\) in farads.
2. Use the calculator to find the time constant \(\tau = RC\).
3. If you want charging behavior, compare time to \(\tau\) to see how far the capacitor has charged.
4. Use the result to estimate circuit response speed or to check a design target.

The formula explained

The formula \(\tau = RC\) computes the RC time constant, which is the characteristic time for a capacitor to charge or discharge through a resistor. It is the time for the voltage to reach about \(63.2\%\) of its final value during charging, or drop to about \(36.8\%\) of its initial value during discharging.

• \(\tau\) = the time constant, in seconds
• \(R\) = resistance, in ohms
• \(C\) = capacitance, in farads

Step by step method

1. Write down the resistance \(R\) and capacitance \(C\) for the circuit.
2. Multiply them using \(\tau = RC\) to get the time constant in seconds.
3. For charging, remember that after one \(\tau\), the capacitor has reached about \(63.2\%\) of its final voltage.
4. For discharging, remember that after one \(\tau\), the capacitor has fallen to about \(36.8\%\) of its starting voltage.

Worked example

Problem. Find the RC time constant for a circuit with \(R = 4{,}700\) \(\Omega\) and \(C = 220\) \(\mu\text{F}\).

1. Convert the capacitance: \(220\) \(\mu\text{F} = 220 \times 10^{-6}\) \(\text{F}\).
2. Use \(\tau = RC\): \(\tau = 4{,}700 \times 220 \times 10^{-6}\).
3. Calculate \(\tau = 1.034\) \(\text{s}\), so the time constant is about \(1.03\) seconds.

Tips and common mistakes

• Make sure capacitance is in farads before multiplying, because microfarads and nanofarads must be converted first.
• A larger \(R\) or \(C\) always makes \(\tau\) larger, so the circuit responds more slowly.

Frequently asked questions