RC Time Constant
τ = R × C
Quick answer
This calculator solves τ = R × C for Time Constant. With Resistance 10 kΩ, Capacitance 100 µF, the result is 1 s. It solves in 3 directions, so you can enter the values you have and get the one you need.
Calculator
Formula
Description
The RC time constant defines how quickly a capacitor charges or discharges through a resistor. After one time constant (1τ), the capacitor reaches approximately 63.2% of its final voltage when charging, or drops to 36.8% when discharging. After 5τ the capacitor is considered fully charged or discharged (99.3%). The exponential charging curve follows V(t) = Vfinal × (1 - e^(-t/τ)), making the time constant the key parameter for timing circuits, filters, debounce circuits, and power supply soft-start designs.
Variables
- τ — Time constant in seconds (s)
- R — Resistance in ohms (Ω)
- C — Capacitance in farads (F)
Practical Notes
The RC time constant also defines the -3dB cutoff frequency of a simple RC low-pass or high-pass filter: f_cutoff = 1/(2πRC) = 1/(2πτ). For debouncing mechanical switches, a typical RC of 10-50ms works well.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| tau | Time Constant | ms | ps, ns, µs, ms, s, min, h |
| R | Resistance | kΩ | mΩ, Ω, kΩ, MΩ |
| C | Capacitance | µF | pF, nF, µF, mF, F |
Step by step
- 1. What you know: Resistance 10 kΩ, Capacitance 100 µF
- 2. The relation: τ = R × C
- 3. Substitute: R = 10 kΩ, C = 100 µF
- 4. Result: Time Constant = 1 s
Worked examples
Minimum range
Given: Resistance 100 Ω, Capacitance 100 nF
Result: Time Constant = 10 µs
Low range
Given: Resistance 1 kΩ, Capacitance 1 µF
Result: Time Constant = 1 ms
Typical
Given: Resistance 10 kΩ, Capacitance 100 µF
Result: Time Constant = 1 s
High range
Given: Resistance 100 kΩ, Capacitance 1 mF
Result: Time Constant = 1.667 min
Maximum range
Given: Resistance 1 MΩ, Capacitance 10 mF
Result: Time Constant = 2.778 h
Solving for each variable
Solve for Time Constant
Resistance 100 Ω, Capacitance 100 nF → 10 µs
Solve for Resistance
Time Constant 100 µs, Capacitance 100 nF → 1 kΩ
Solve for Capacitance
Time Constant 100 µs, Resistance 100 Ω → 1 µF
How Time Constant changes with Resistance
| Resistance (input) | Time Constant (result) |
|---|---|
| 1 kΩ | 100 ms |
| 2.5 kΩ | 0.25 s |
| 5 kΩ | 0.5 s |
| 7.5 kΩ | 0.75 s |
| 10 kΩ | 1 s |
| 15 kΩ | 1.5 s |
| 20 kΩ | 2 s |
| 40 kΩ | 4 s |
| 70 kΩ | 7 s |
| 100 kΩ | 10 s |
The same result in other units
| Unit | Value |
|---|---|
| µs | 1000000 |
| ms | 1000 |
| s | 1 |
| min | 0.01667 |
| h | 0.0002778 |
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<p><a href="https://vbatpower.com/formulas/rc-time-constant/">RC Time Constant</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate RC Time Constant?
Use τ = R × C. With Resistance 10 kΩ, Capacitance 100 µF, Time Constant works out to 1 s.
What is the formula for RC Time Constant?
The formula is τ = R × C. The RC time constant defines how quickly a capacitor charges or discharges through a resistor.
How do you find Resistance when you know the other values?
Rearrange for Resistance: with Time Constant 100 µs, Capacitance 100 nF, Resistance is 1 kΩ.
How do you find Capacitance when you know the other values?
Rearrange for Capacitance: with Time Constant 100 µs, Resistance 100 Ω, Capacitance is 1 µF.
What units does RC Time Constant use?
Time Constant is shown in µs, ms, s, min, h. Values are held in SI base units internally, so you can mix prefixes without converting by hand.
Related Concepts
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