What Is an RC Time Constant?

The time constant τ (tau) of an RC circuit equals the product of resistance and capacitance: τ = R × C. This single value determines how quickly the capacitor charges or discharges. A larger time constant means slower voltage changes, while a smaller time constant means faster changes. The units work out because Ω × F = seconds.

RC Charging: Exponential Approach to Supply Voltage

When charging a capacitor from 0V toward a supply voltage V_s, the capacitor voltage follows V_c(t) = V_s × (1 - e^(-t/τ)). The voltage rises quickly at first when the current is highest, then slows as it approaches V_s. Key milestones: at 1τ the capacitor reaches ~63.2% of V_s, at 2τ about 86.5%, at 3τ about 95%, and at 5τ about 99.3%.

RC Discharging: Exponential Decay

When discharging a capacitor from initial voltage V_0 toward 0V, the voltage follows V_c(t) = V_0 × e^(-t/τ). The voltage drops quickly at first when current is highest, then slows as it approaches zero. At 1τ the voltage has dropped to ~36.8% of V_0, at 2τ to ~13.5%, and at 5τ to less than 1%.

Voltage, Current, and Time

Why the Exponential Shape?

The exponential behavior arises because the charging/discharging current depends on the voltage difference across the resistor. As the capacitor charges, this difference decreases, which reduces the current, which slows the rate of voltage change. This feedback creates the characteristic exponential curve.

How This Calculator Helps

Use this calculator to explore how different R and C values affect the time constant and charging behavior. Compare multiple scenarios to see how doubling resistance or capacitance doubles τ. Calculate how long it takes to reach specific voltage thresholds—useful for understanding timing circuits, filters, and sensor signal conditioning.

Limitations & Assumptions

This calculator models ideal RC circuits. Real components have additional characteristics: capacitors have equivalent series resistance (ESR) and leakage current; resistors have temperature coefficients; power supplies have internal resistance. For precision timing or high-frequency applications, these factors become significant. Always verify designs with proper simulation tools and real measurements.