Quick answer
An RC circuit has time constant τ = RC and cutoff frequency f_c = 1 ÷ (2πRC). 10 kΩ with 10 µF gives τ = 100 ms and f_c = 1.5915 Hz.
Enter the resistance and capacitance and optionally a time. The calculator returns τ, cutoff frequency and charge percentage.
Related tools: Voltage Divider Calculator: Output voltage of a two-resistor divider. RLC Impedance Calculator: Impedance and phase angle of a series RLC circuit. RMS Voltage Calculator: Convert between RMS, peak and peak-to-peak voltage of a sine wave.
How to use the RC Circuit Calculator
- Enter resistance (Ω) (above 0).
- Enter capacitance (µF) (above 0).
- Optionally, enter time since charging began (optional) (ms) (0 or more).
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| Resistance | A number, in Ω | > 0 |
| Capacitance | A number, in µF | > 0 |
| Time since charging began (optional) (optional) | A number, in ms | ≥ 0 |
Formula and method
Formula
τ = RC; f_c = 1 ÷ (2πRC); charge = 1 − e^(−t ÷ τ)
IEEE-754 double precision; shown to the decimals indicated.
A capacitor charging through a resistor from a fixed source.
Worked examples
These examples are verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: Resistance = 10000; Capacitance = 10.
| Result | Value |
|---|---|
| Time constant τ | 100 ms |
| Cutoff frequency | 1.5915 Hz |
| Charge after t | — |
Example 2
Inputs: Resistance = 4700; Capacitance = 0.47; Time since charging began (optional) = 2.
| Result | Value |
|---|---|
| Time constant τ | 2.209 ms |
| Cutoff frequency | 72.0484 Hz |
| Charge after t | 59.5615% |
The first line is the headline result (time constant τ). Below it the rC Circuit Calculator lists cutoff frequency and charge after t, which describe the same case from other angles. IEEE-754 double precision; shown to the decimals indicated.
Charging
After one time constant a capacitor charges to 63.2% of the supply; after 5τ it is about 99.3% charged. Charge fraction = 1 − e^(−t/τ). With τ = 100 ms, full charge takes about 0.5 s.
Filtering
The same circuit works as a low-pass filter: signals below f_c pass and those above are attenuated at 20 dB per decade. The cutoff is the −3 dB point.
How the result changes with resistance
Holding every other input at the first worked example, this table changes only resistance. It shows how sensitive the answer is to that one value; each row was produced by running this calculator.
| Resistance | Time constant τ | Cutoff frequency | Charge after t |
|---|---|---|---|
| 5000 | 50 ms | 3.1831 Hz | — |
| 10000 | 100 ms | 1.5915 Hz | — |
| 20000 | 200 ms | 0.7958 Hz | — |
| 40000 | 400 ms | 0.3979 Hz | — |
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- Resistance: entering "0" shows "Resistance must be greater than 0." beside that field and no result.
- Capacitance: entering "0" shows "Capacitance must be greater than 0." beside that field and no result.
Choosing between the RC Circuit Calculator and similar calculators
Each row shows what a related calculator on this site asks for and what it returns, so you can pick the one that matches your question.
| Calculator | You enter | It returns |
|---|---|---|
| [Voltage Divider Calculator](/engineering/voltage-divider-calculator/) | input voltage, r1 and r2 | Output voltage |
| [RLC Impedance Calculator](/engineering/rlc-impedance-calculator/) | resistance, inductance and capacitance | Impedance |
| [RMS Voltage Calculator](/engineering/rms-voltage-calculator/) | i know the and voltage | RMS voltage |
| [Parallel Plate Capacitor Calculator](/engineering/parallel-plate-capacitance-calculator/) | plate area, plate separation and relative permittivity εr | Capacitance |
| [Current Divider Calculator](/engineering/current-divider-calculator/) | total current, r1 and r2 | Current through R1 |
Background: electrical circuits
Ohm's law links voltage, current and resistance: V = I × R, so I = V ÷ R and R = V ÷ I. Power is P = V × I, which also equals I² × R and V² ÷ R.
These relations hold for ohmic components, where resistance is constant. Diodes and transistors are non-linear, and in AC circuits with reactive parts impedance (Z) takes the place of resistance. Check component ratings and local electrical code before relying on any calculation.
Assumptions and limitations
- About 99% charged after five time constants
Use results as engineering estimates and check them against the governing standards, safety factors and a qualified engineer's judgement before relying on them.
If a required value is empty, not a number, or outside its allowed range, the form marks that field with a message and shows no result instead of a misleading number. The automated checks deliberately try invalid entries for resistance and capacitance to confirm this.
Frequently asked questions
What is a time constant?
The time for the capacitor to reach 63.2% of full charge.
How do I lower the cutoff frequency?
Increase the resistance or the capacitance, since f_c = 1 ÷ (2πRC); doubling either halves the cutoff.
What are the units of RC?
The product RC is in seconds: ohms times farads give the time constant, so 10 kΩ × 10 µF is 0.1 s.
What does the RC Circuit Calculator calculate?
Time constant, cutoff frequency and charge level of an RC circuit. It returns Time constant τ, Cutoff frequency and Charge after t.
What formula does the RC Circuit Calculator use?
τ = RC; f_c = 1 ÷ (2πRC); charge = 1 − e^(−t ÷ τ). A capacitor charging through a resistor from a fixed source.
What do I need to enter in the rC Circuit Calculator?
You enter Resistance (Ω) and Capacitance (µF). Optional: Time since charging began (optional) (ms).
How is the result rounded or limited?
IEEE-754 double precision; shown to the decimals indicated. About 99% charged after five time constants.
What is an example of a rC Circuit result?
With resistance 10000 and capacitance 10, the time constant τ is 100 ms.
Can I rely on this calculator for a decision?
Use results as engineering estimates and check them against the governing standards, safety factors and a qualified engineer's judgement before relying on them. For this calculator in particular: About 99% charged after five time constants.
Related calculators
- Voltage Divider Calculator — Output voltage of a two-resistor divider.
- RLC Impedance Calculator — Impedance and phase angle of a series RLC circuit.
- RMS Voltage Calculator — Convert between RMS, peak and peak-to-peak voltage of a sine wave.
- Parallel Plate Capacitor Calculator — Capacitance of two parallel plates.
- Current Divider Calculator — Current through each of two parallel resistors.
- Inductive Reactance Calculator — Reactance of an inductor at a frequency.
Sources
- OpenStax, University Physics Volume 2 (Rice University): electricity, circuits and thermodynamics
Content last reviewed 2026-11-04. Formulas and worked examples are checked by automated tests against independently computed values.