This RC time constant calculator works out how quickly a resistor–capacitor circuit charges and discharges, using the single relationship τ = R × C. Enter a resistance and a capacitance and the RC time constant calculator returns τ in seconds (plus the practical 5τ settling time and the corresponding filter cut-off frequency), so you can size a timing network, an anti-aliasing filter or a debounce circuit without reaching for a datasheet.
Clinical Tools Library · Electronics
RC Time Constant Calculator
Enter a resistance and a capacitance to get the time constant τ = R × C, the 5τ settling time, the filter cut-off frequency and a live charging curve. Built for engineers, technicians and students.
Inputs
Reverse check: R = τ / C = 10 kΩ · C = τ / R = 100 nF
| Time | Elapsed | Charged | Remaining (discharge) |
|---|
Voltage & current at a time
= 5 V × (1 − e^(−1.00)) = 3.16 V
Teach the error: the same number in different units
The most common RC mistake is reading capacitance in the wrong unit — a µF where a nF was meant is a 1000× error in τ. Below, your entered capacitance value (100) is applied at three neighbouring units, keeping R fixed. The highlighted card matches your current selection.
Formulas & reference data
Charging & discharging
Charging: VC(t) = VS(1 − e−t/τ). Discharging: VC(t) = V0 e−t/τ. Charging current: i(t) = (VS/R) e−t/τ.
The unit of τ is the second: one ohm × one farad = one second exactly, because the volts and amperes in the two SI definitions cancel.
Unit shortcuts
kΩ × µF = ms · kΩ × nF = µs · MΩ × µF = s · MΩ × pF = µs
Sources (verified current)
- NIST — The International System of Units (SI) · ohm and farad as SI derived units
- NIST — Definitions of the SI base units · the second
- OpenStax University Physics II (LibreTexts) — RC Circuits · 5τ convention, exponential model
- HyperPhysics, Georgia State University — Charging a Capacitor · derivation
- Electronics Tutorials — RC Charging Circuit & Time Constant · 63.2% / 5T
Last reviewed: July 2026 · Published by clinicaltoolslibrary.com
How the RC time constant calculator works
The RC time constant calculator multiplies your resistance by your capacitance and converts the result into convenient units. It expects resistance in ohms (Ω) and capacitance in farads (F); the unit selectors handle the prefixes for you, so 10 kΩ and 100 nF can be entered directly rather than as 10 000 Ω and 0.0000001 F.
Because the ohm and the farad are both SI derived units, their product resolves cleanly to seconds — one ohm multiplied by one farad is exactly one second. That is why τ needs no correction factor.
The tool assumes an ideal series RC network driven by a step input with a low-impedance source. Real components deviate: capacitor tolerance is often ±10 % or ±20 %, electrolytics drift with temperature and age, and source or trace resistance adds to R. Treat the output as a design starting point and confirm it on the bench.
RC time constant formula and units
τ = R × C
Where τ (tau) is the time constant in seconds, R is resistance in ohms and C is capacitance in farads. The same τ governs both charging and discharging of a series RC network, and it is the only parameter that sets the speed of the exponential response.
Calculating the time constant of an RC circuit step by step
- Convert the resistance to ohms (1 kΩ = 103 Ω; 1 MΩ = 106 Ω).
- Convert the capacitance to farads (1 µF = 10−6 F; 1 nF = 10−9 F; 1 pF = 10−12 F).
- Multiply the two. The answer is τ in seconds.
- Multiply τ by five to get the practical settling time — the point at which the circuit is treated as fully charged or fully discharged.
Unit shortcuts that avoid scientific notation
These identities let you calculate the RC time constant mentally, without converting anything:
- kΩ × µF = milliseconds
- kΩ × nF = microseconds
- MΩ × µF = seconds
- MΩ × pF = microseconds
Worked examples
Example 1 — a debounce filter. R = 10 kΩ, C = 100 nF. Using the shortcut above, 10 × 100 = 1000 µs, so τ = 1 ms. The node settles within roughly 5 ms, comfortably faster than a human keypress and slower than typical contact bounce.
Example 2 — a long timing delay. R = 1 MΩ, C = 4.7 µF gives τ = 4.7 s, and about 23.5 s to reach 99.3 %. With an electrolytic capacitor at ±20 % tolerance, the real τ could fall anywhere between roughly 3.8 s and 5.6 s — a reminder that RC timing is approximate unless you use precision parts.
Charging, discharging and the 5τ rule
A capacitor charging through a resistor follows VC(t) = VS(1 − e−t/τ), and discharging follows VC(t) = V0e−t/τ. In theory the capacitor never reaches the supply rail; in practice, engineers call the transient over after five time constants, when the remaining error is under 1 %. This convention is standard in university circuit texts and in practical RC charging tutorials alike.
| Elapsed time | Charged to (% of supply) | Remaining when discharging (%) | Practical meaning |
|---|---|---|---|
| 1τ | 63.2 % | 36.8 % | Definition of the time constant |
| 2τ | 86.5 % | 13.5 % | Still visibly settling |
| 3τ | 95.0 % | 5.0 % | Adequate for many logic thresholds |
| 4τ | 98.2 % | 1.8 % | Within 2 % of final value |
| 5τ | 99.3 % | 0.7 % | Conventionally “fully charged” |
Time to reach a specific voltage
To find how long the capacitor takes to reach an arbitrary fraction of the supply, rearrange the charging equation:
t = −τ × ln(1 − VC / VS)
For a 3.3 V logic threshold on a 5 V rail with τ = 1 ms, t = −1 ms × ln(1 − 0.66) ≈ 1.08 ms. Our capacitor charge time calculator automates this rearrangement if you need it repeatedly.
RC filter time constant and cut-off frequency
The same τ that describes a step response also sets the corner frequency of a first-order RC filter:
fc = 1 / (2πRC) = 1 / (2πτ)
At fc the output amplitude is 0.707 (−3 dB) of the input and the phase shift is 45°. The topology decides whether you get a low-pass or a high-pass response, but τ and fc are identical either way.
Low-pass versus high-pass
A low-pass filter takes its output across the capacitor: frequencies well below fc pass, higher frequencies roll off at 20 dB per decade. A high-pass filter takes its output across the resistor and does the reverse. Continuing Example 1, τ = 1 ms gives fc = 1 / (2π × 0.001) ≈ 159 Hz. See our low-pass filter calculator for the full magnitude and phase response.
Rise time and bandwidth
The 10 %–90 % rise time of a first-order RC network is tr ≈ 2.2τ, which yields the familiar bandwidth relationship tr × fc ≈ 0.35. This is why an oscilloscope probe’s capacitance, multiplied by the source impedance, quietly limits the edges you can observe. Component-level derivations of the underlying exponential are set out clearly in the Georgia State University HyperPhysics treatment of capacitor charging.
Educational reference, not a design sign-off. This page and the RC time constant calculator are provided for learning and estimation. Always confirm values against component datasheets, your own measurements and any applicable safety or compliance standard before committing a design. Nothing here is investigational or approved advice for a specific application.
Frequently asked questions
How do you calculate the RC time constant?
Multiply resistance in ohms by capacitance in farads: τ = R × C. A 10 kΩ resistor with a 100 nF capacitor gives τ = 10 000 × 0.0000001 = 0.001 s, or 1 ms.
How do you calculate the time constant of an RC circuit with resistors in series or parallel?
First reduce the network to a single equivalent resistance seen by the capacitor, then multiply by C. For resistors in series add them; for resistors in parallel use the reciprocal sum. Our Ohm’s law calculator helps with the reduction.
Why is the time constant 63.2 % and not 50 %?
Because 1 − 1/e = 0.632. The time constant is defined by the natural exponential, not by an arbitrary halfway point. The half-way time is a different quantity: t½ = τ × ln 2 ≈ 0.693τ.
What is the unit of the RC time constant?
Seconds. One ohm times one farad equals exactly one second, because the volts and amperes in the two definitions cancel. See the NIST definitions of the SI base units.
How is the RC filter time constant related to cut-off frequency?
They are reciprocals scaled by 2π: fc = 1 / (2πτ). A 1 ms time constant corresponds to a 159 Hz −3 dB corner frequency. Doubling τ halves fc.
How long does a capacitor take to fully charge?
Mathematically it never does, but after 5τ it is within 0.7 % of the supply voltage, which every practical design treats as fully charged. For τ = 1 ms that is 5 ms.
Does supply voltage change the RC time constant?
No. τ depends only on R and C. A higher supply voltage raises the final voltage and the peak current, but the shape and speed of the exponential are unchanged. Component values do matter — check tolerances with the resistor colour code calculator.
