RC Time Constant Calculator
Solve τ = R · C in any direction — time constant from resistance and capacitance, or work backwards to find R or C. Includes a circuit diagram, live charge/discharge curves, step-by-step math, tolerance sensitivity, and companion metrics like cutoff frequency and rise time.
Closing the switch connects V₀ across the series combination of R and C. The capacitor voltage VC climbs exponentially toward V₀, and the time it takes to cover 63.2% of that gap is exactly τ = R · C — independent of the supply voltage.
R ↑ — slower charge
τ scales linearly with resistance. Doubling R doubles τ, so the capacitor takes twice as long to reach any given fraction of V₀. Current is limited more, so charge accumulates more slowly.
C ↑ — slower charge
τ also scales linearly with capacitance. A bigger capacitor holds more charge at the same voltage, so it takes proportionally longer to fill through the same resistor.
Independent of V₀
τ never depends on the supply voltage. Raising V₀ makes the capacitor charge to a higher final voltage, but the shape of the curve — and the time to reach 63.2% — stays identical.
Time-domain vs. frequency-domain
τ is the time-domain face of the same circuit whose frequency-domain face is the cutoff fc = 1/(2πRC). A large τ means a low cutoff frequency, and vice versa.
How to Use This Calculator
The RC relation links three quantities: resistance R, capacitance C, and the time constant τ = R · C. Pick which one you want the tool to solve, then fill in the other two.
1. Choose what to solve for
Pick τ (time constant from R and C), R (resistance from τ and C), or C (capacitance from τ and R) — the tool rearranges the formula automatically.
2. Pick a preset, or type your own values
Use the quick pills (100 Ω → 1 MΩ, 1 pF → 100 µF, 1 ns → 10 s) or type any custom value and choose its unit from the dropdown.
3. Read the result and steps
The result card shows the solved value with an auto-selected unit plus engineering (×10ⁿ) notation. The step-by-step panel shows exactly how the number was reached.
4. Study the charge/discharge chart
The plot shows both exponential curves normalised to V₀, with the 63.2% point at t = τ marked, so you can see the 1τ–5τ settling behaviour at a glance.
5. Switch to Advanced for more depth
Advanced mode adds a tolerance sensitivity panel, plus cutoff frequency, half-life, 10–90% rise time, energy stored and peak current companion metrics.
6. Convert τ to frequency, or copy the result
Use the τ → cutoff frequency converter further down the page to see the frequency-domain equivalent, or "Copy result" to grab the solved value.
What This Tool Offers
Built around the fundamental RC relation τ = R · C, the first-order circuit result behind every filter, debounce circuit, and timing delay in electronics.
Solve all three directions
Go from R and C to τ, from τ and C to R, or from τ and R to C — the formula is rearranged for you.
Full SI unit handling
Enter resistance in Ω / kΩ / MΩ / GΩ, capacitance in pF → F, and time in ns → hours. The solver auto-picks the cleanest display unit.
Live exponential chart
See the capacitor charging and discharging curves plotted side by side, with the 63.2% / 1τ point marked and 1τ–5τ gridlines.
Annotated circuit diagram
A labelled series RC schematic showing the source, switch, resistor, capacitor, current direction and capacitor voltage.
Tolerance sensitivity
See exactly how a ±1% shift in R and C compounds into the time constant — practical worst-case analysis for real components.
Companion RC metrics
Advanced mode reports cutoff frequency, angular cutoff, half-life, 10–90% rise time, 5τ settling, stored energy and peak current.
Reference Tables & Conversions
A τ → cutoff-frequency converter, plus lookup tables for charge levels, common RC combinations, and time constants in other circuit types.
τ → cutoff frequency & settling estimator
Capacitor Charge & Discharge vs. Time
How far along the exponential curve the capacitor is at each multiple of τ. After 5τ the transient is conventionally considered finished.
| Time | Charged (% of V₀) | Discharged (remaining %) | Typical use |
|---|---|---|---|
| 0.5τ | 39.3% | 60.7% | — |
| 1τ | 63.2% | 36.8% | Definition of τ |
| 2τ | 86.5% | 13.5% | — |
| 3τ | 95.0% | 5.0% | Common "settled" rule of thumb |
| 4τ | 98.2% | 1.8% | — |
| 5τ | 99.3% | 0.7% | Full settle for most designs |
Common RC Combinations
Typical resistor/capacitor pairings and the time constant and cutoff frequency they produce.
| R | C | τ | Cutoff fc | 5τ settle |
|---|---|---|---|---|
| 1 kΩ | 1 nF | 1 µs | 159.2 kHz | 5 µs |
| 1 kΩ | 100 nF | 100 µs | 1.59 kHz | 500 µs |
| 10 kΩ | 10 nF | 100 µs | 1.59 kHz | 500 µs |
| 4.7 kΩ | 10 µF | 47 ms | 3.39 Hz | 235 ms |
| 100 kΩ | 1 µF | 100 ms | 1.59 Hz | 500 ms |
| 10 kΩ | 100 µF | 1 s | 159.2 mHz | 5 s |
| 1 MΩ | 1 µF | 1 s | 159.2 mHz | 5 s |
Time Constants Across Circuit Types
| Circuit | Time constant | Notes |
|---|---|---|
| RC series | τ = R · C | First-order; exponential charge/discharge |
| RL series | τ = L / R | First-order; current rises exponentially |
| RLC series (underdamped) | τ = 2L / R | Envelope decay; resonant ω₀ = 1/√(LC) |
What Does τ = R · C Measure?
The RC time constant τ is the characteristic time of a resistor–capacitor circuit. It answers a simple question: how long does the capacitor take to get most of the way to its final voltage? The answer is τ — the time to cover 63.2% of the remaining gap. It is the single number that describes the speed of any first-order RC network, from a simple debounce filter to an audio tone control.
The RC Time Constant Formula
The defining relationship is:
Rearranged for the other two unknowns:
The voltage across the capacitor while charging from 0 toward V₀ follows:
and while discharging from V₀ toward 0:
RC Time Constant Variables
| Symbol | Meaning | Unit |
|---|---|---|
| τ | Time constant — time to reach 63.2% (charging) | seconds (s) |
| R | Series resistance | ohms (Ω) |
| C | Capacitance | farads (F) |
| V₀ | Supply / initial voltage | volts (V) |
| fc | Cutoff frequency, 1/(2πRC) | hertz (Hz) |
How R and C Affect the Time Constant
Because τ is the product R · C, it grows linearly with either component. Doubling the resistor doubles τ; doubling the capacitor doubles τ; doubling both quadruples it. Notice what is missing from the formula: the supply voltage. τ is a property of the R and C alone, which is why the same circuit responds at the same speed whether it runs on 3.3 V or 24 V.
In the frequency domain, the very same circuit is a low-pass filter with cutoff fc = 1/(2πRC). A long time constant means a low cutoff frequency, and a short time constant means a high one — two views of the identical physical behaviour.
RC Time Constant Calculation Examples
R = 10,000 Ω · C = 1 × 10⁻⁴ F
τ = 10,000 × 1 × 10⁻⁴
τ = 1 s
C = 1 × 10⁻⁸ F
R = 1 × 10⁻⁴ / 1 × 10⁻⁸
R = 10,000 Ω = 10 kΩ
R = 4,700 Ω · τ = 0.047 s
C = 0.047 / 4,700
C = 1 × 10⁻⁵ F = 10 µF
Frequently Asked Questions
It is the time required for the capacitor voltage to change by 63.2% of the total change it is heading toward. While charging, that means reaching 63.2% of V₀; while discharging, that means falling to 36.8% of the starting voltage. It is the natural timescale of the circuit.
Because the response is exponential, not linear. Substituting t = τ into V₀(1 − e−t/τ) gives V₀(1 − e⁻¹) = V₀(1 − 0.3679) = 0.6321 · V₀. The number falls out of the mathematics of the exponential, not from an arbitrary choice. If you want 50%, that happens at t = τ · ln 2 ≈ 0.693τ.
Technically never — an exponential only approaches its final value asymptotically. In practice, 5τ brings the capacitor to 99.3% of V₀, which is close enough that engineers treat the transient as finished. That is why "5τ" appears as the settling time throughout this tool.
No. τ = R · C contains no voltage term at all. Raising V₀ raises the final voltage the capacitor charges to, but the percentage-versus-time curve — and therefore the time to reach 63.2% — is completely unchanged. This is a distinctive property of linear RC circuits.
By fc = 1 / (2πτ), which is the same as fc = 1/(2πRC). The time constant and the −3 dB cutoff frequency carry identical information about the circuit, just expressed in the time domain versus the frequency domain. Use the converter above to move between them.
Very many. Switch debounce circuits, RC low-pass and high-pass filters, 555 timer timing networks, power-on reset delays, audio tone controls, integrators and differentiators, camera flash charging, and sample-and-hold circuits all have τ = RC at their core.
Because τ is a product, relative errors add. A +1% resistor combined with a +1% capacitor gives ≈ +2.01% in τ; −1% in both gives ≈ −1.99%. Electrolytic capacitors in particular are often specified at ±20%, which dominates the total error budget — see the tolerance sensitivity panel in Advanced mode.
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| τ | Time constant | s |
| R | Resistance | Ω |
| C | Capacitance | F |
What it means
The time constant τ (tau) of an RC circuit is the product of resistance R and capacitance C: τ = R*C, measured in seconds. It is the time required for the capacitor voltage to reach approximately 63.2% of its final value during charging (or to fall to 36.8% during discharging) when subjected to a step input. After 5 time constants (5τ), the transient is considered essentially complete (over 99%). This parameter is fundamental for understanding the speed of response of RC circuits, which are used in filters, timing circuits, and signal shaping. The time constant determines the cut‑off frequency of a low‑pass filter (f_c = 1/(2πτ)). In digital circuits, the RC time constant affects the rise and fall times of signals and the propagation delay. Example: With R=1kΩ and C=100µF, τ = 1000 * 100e-6 = 0.1 seconds. The capacitor charges to 6.32V (assuming 10V supply) in 0.1s and reaches 9.9V in 0.5s (5τ).
Worked example
RC Time Constant – Practical Example
Real‑World| Parameter | Value |
|---|---|
| R | 1 kΩ = 1000 Ω |
| C | 100 µF = 100×10⁻⁶ F |
| Formula | τ = R · C |
Common mistakes
- Units: R in ohms, C in farads → τ in seconds.
- Charging: After one time constant, the voltage reaches 63.2% of the final value.
- Discharging: After one time constant, the voltage drops to 36.8% of the initial value.
- Steady state: After 5τ, the capacitor is considered fully charged (error <1%).
- Assumption: Ideal capacitor and resistor; the source is ideal and constant.
Applications
The RC time constant τ = R·C is the time required for a capacitor to charge to approximately 63.2% of the final voltage (or discharge to 36.8%) when a step voltage is applied. This parameter is fundamental to timing circuits, filters, and transient analysis. Engineers use it to design timing delays, to set the cutoff frequency of RC filters, and to control the rise and fall times of signals. In power supplies, it determines the ripple voltage. In digital circuits, it affects the propagation delay of CMOS gates. By understanding the RC time constant, professionals can design circuits with predictable timing and frequency response. This formula is a cornerstone of analog and mixed‑signal design.
- Timing circuits (delays, oscillators, pulse generators)
- RC filter design (low‑pass, high‑pass, band‑pass)
- Power supply smoothing and ripple reduction
- Signal conditioning and waveform shaping
- Educational introduction to transients and frequency response
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