RC Time Constant Calculator
Calculate how long a capacitor takes to charge or discharge through a resistor.
Charging:
t = -RC ln(1 - Vt/Vs)
Discharging:
t = -RC ln(Vt/V0)
What is an RC time constant?
In an RC circuit, the resistor (R) and capacitor (C) together control how quickly voltage changes over time. The key value is the time constant, written as τ = R × C. It is measured in seconds and gives you a fast way to estimate circuit behavior.
- After 1τ: capacitor reaches about 63.2% of final value when charging.
- After 2τ: about 86.5%.
- After 3τ: about 95.0%.
- After 5τ: practically complete (~99.3%).
How this RC time calculator works
Charging mode
Choose Charging when the capacitor starts near 0 V and moves toward the supply voltage. Enter resistance, capacitance, supply voltage, and your target voltage. The calculator solves for time using the exponential charging equation.
Discharging mode
Choose Discharging when the capacitor starts charged and decays toward 0 V through a resistor. Enter the initial voltage as the start voltage, plus your target voltage. The tool then calculates the decay time.
Practical uses
- Delay circuits: power-on reset timing and startup delays.
- Low-pass filters: smoothing noisy sensor or PWM signals.
- Debouncing: switch input conditioning in embedded systems.
- Pulse shaping: setting timing windows in analog/digital interface circuits.
Design tips
1) Use realistic component tolerance
Real resistors and capacitors are not exact. A 5% resistor and 10% capacitor can shift timing noticeably. For precision timing, consider tighter tolerance parts or calibrate in firmware.
2) Watch leakage and loading
Input impedance of your next stage can load the RC node, changing effective R and C. For long time constants, capacitor leakage can become significant.
3) Choose target level carefully
Time to 50%, 63.2%, 90%, and 99% are very different. Make sure your target voltage matches the actual threshold of your comparator, ADC, logic input, or transistor stage.
Quick reference
For charging from 0 V toward a final value:
- 50% occurs at about 0.693τ
- 90% occurs at about 2.303τ
- 95% occurs at about 2.996τ
- 99% occurs at about 4.605τ
Example
If R = 10 kΩ and C = 100 µF, then τ = 10,000 × 0.0001 = 1 second. Reaching 90% in charging mode takes about 2.3 seconds.
Final thoughts
RC timing is one of the most useful ideas in electronics. With a single resistor and capacitor, you can shape signals, add delays, and smooth noise. Use this calculator to move quickly from concept to practical values.