RC Time Constant Calculator
Calculate the RC time constant and the charge or discharge curve it produces.
About RC Time Constant Calculator
The capacitor charges exponentially, reaching 63.2 per cent of supply in one time constant and about 99 per cent in five. The corner frequency of the equivalent filter is the reciprocal of 2πτ. Five time constants is the standard settling allowance in timing and sampling circuits, because the remaining error is below one per cent.
Formula
RC Time Constant
τ = R C; V(t) = V_supply (1 − e^(−t/τ))
- τ
- Time constant, the time to reach 63.2% of the final value
- 5τ
- Conventionally taken as fully charged, at 99.3%
Worked example
With the default values below, RC Time Constant Calculator returns Time Constant of 0.100000. Change any input above and every figure here is recalculated in your browser.
Inputs used
- Resistanceminimum 0.01 ohm
- 10,000 ohm
- Capacitanceminimum 0 F
- 0.00001 F
- Supply voltageminimum 0 V
- 5 V
- Time elapsedminimum 0 s
- 0.1 s
Results
- Time Constant
- 0.100000 s
- Capacitor Voltage at That Time
- 3.16060 V
- Time to Reach 63.2%
- 0.100000 s
- Time to Reach 99% (5 Time Constants)
- 0.500000 s
- Corner Frequency
- 1.5915 Hz
Step by step
- 1Values used
- 2RC Time Constant
- 3Time Constant= 0.100000 s
- 4Capacitor Voltage at That Time= 3.16060 V
- 5Time to Reach 63.2%= 0.100000 s
- 6Time to Reach 99% (5 Time Constants)= 0.500000 s
- 7Corner Frequency= 1.5915 Hz
Assumptions and limits
- The result is derived only from the 4 inputs listed above. Anything not among them is not part of the calculation.
- In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
- Figures are rounded for display to 6 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.
Frequently Asked Questions
How is RC Time Constant calculated?
τ = R C; V(t) = V_supply (1 − e^(−t/τ)) The capacitor charges exponentially, reaching 63.2 per cent of supply in one time constant and about 99 per cent in five. The corner frequency of the equivalent filter is the reciprocal of 2πτ.
Why does RC Time Constant matter?
Five time constants is the standard settling allowance in timing and sampling circuits, because the remaining error is below one per cent.
What values do I need to enter?
This calculator takes 4 inputs: Resistance, Capacitance, Supply voltage, Time elapsed. The pre-filled defaults are a realistic starting point — replace them with figures from your own environment for a result you can act on.