RC Circuit Time Constant Calculator
About RC Time Constant
The time constant (τ) is the time it takes for the capacitor to charge to 63% of the supply voltage.
Formula: τ = R × C
About This Calculator
RC Circuit Time Constant Calculator is designed to reduce manual errors and give repeatable outputs when you need quick, reliable answers.
Calculate the time constant (τ) of an RC circuit from resistance and capacitance values. Essential for designing filters, timing circuits, signal smoothing, and understanding charge/discharge behavior in electronics.
If your workflow expands, pair this calculator with Ohm's Law Calculator and Resistor Color Code Calculator to cross-check assumptions and build a stronger analysis chain.
Formula
τ = R × C, where τ is the time constant in seconds, R is resistance in ohms (Ω), and C is capacitance in farads (F). The capacitor reaches 63.2% charge in 1τ and 99.3% in 5τ.
Example Calculation
The worked example below demonstrates how the input fields translate into the final output. Use it as a quick validation pass before entering your own numbers.
- resistance (Ω): 10000
- capacitance (F): 0.0001
Explanation of Results
Result Interpretation
τ = 10,000 Ω × 0.0001 F = 1 second. This means the capacitor charges to 63.2% of supply voltage in 1 second and is effectively fully charged (99.3%) after 5 seconds. This RC pair is often used in 1 Hz low-pass filters.
FAQ
What does the RC time constant mean?
The time constant τ (tau) tells you how quickly a capacitor charges or discharges through a resistor. After 1τ, the capacitor reaches 63.2% of its final charge. After 5τ (five time constants), it's considered fully charged at 99.3%. This governs the speed of filters, timers, and signal transitions.
How do I convert µF and kΩ for the RC formula?
Use SI units directly: 1 µF = 1×10⁻⁶ F, 1 kΩ = 1×10³ Ω, 1 MΩ = 1×10⁶ Ω. For a 10 kΩ resistor and 100 µF capacitor: τ = 10,000 × 0.0001 = 1 second. The units multiply cleanly: Ω × F = seconds.
What is the RC circuit cutoff frequency?
The -3 dB cutoff frequency of a simple RC low-pass filter is f_c = 1 / (2π × R × C) = 1 / (2π × τ). For τ = 1 ms, f_c ≈ 159 Hz. Above this frequency, the output voltage drops by more than 3 dB (falls to 70.7% of input).
How many time constants to fully charge a capacitor?
Theoretically a capacitor never reaches 100%, but practically: 1τ = 63.2%, 2τ = 86.5%, 3τ = 95.0%, 4τ = 98.2%, 5τ = 99.3%. Five time constants is the engineering standard for 'fully charged.' For a 1 ms time constant, full charge takes about 5 ms.
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