RC Charge from 0

Calculates the time required for an RC charging node, starting at 0 V, to reach a specified threshold voltage after a step input is applied. Assumes an ideal step source to a constant input voltage, fixed resistance and capacitance, zero initial capacitor voltage, and no loading on the node. Valid only when the threshold is less than the input voltage; as the threshold approaches the input level, the time increases rapidly and becomes numerically sensitive.

\(t = -R* C \ln\left(1 - \frac{V_{th}}{V_{in}}\right)\)

Instructions: Select the variable you want to solve for, and fill in the others.

Solve	Symbol	Input Value	Unit	Description
	\(t\)		\(s\)
	\(R\)		\(\Omega\)
	\(C\)		\(F\)
	\(V_{th}\)		\(V\)
	\(V_{in}\)		\(V\)

References

EEVblog forum discussion directly presents the equation t = RC * ln(1 - Vc/Vs) for calculating the time in an RC circuit to reach a specific capacitor voltage Vc from an initial state, with an example using supply voltage Vs=5V from 1V to 4V. ↗
Electronics Tutorials explains the RC time constant and provides the charging voltage equation VC(t) = V(1 - e^{-t/RC}), from which the given equation t = -RC ln(1 - V_target/V_step) is directly derived by solving for time t when VC(t) = V_target starting from 0V. ↗