Cutoff Frequency Calculator
Calculate cutoff frequency, angular frequency, and time constant for RC, LC, and RL filters.
About cutoff frequency
Cutoff frequency marks the boundary between a filter's passband and the region where signals are increasingly attenuated. For a first-order RC filter, the magnitude at cutoff is 1 divided by the square root of 2 of its passband value, corresponding to approximately minus 3 decibels. The angular cutoff frequency is ωc = 1/(RC), and ordinary frequency is fc = ωc/(2π). The product RC is the time constant, which describes how quickly the circuit responds to a step input. An RL filter follows the same first-order response with the roles of resistance and reactance rearranged. Its angular cutoff frequency is ωc = R/L, its ordinary cutoff frequency is R/(2πL), and its time constant is L/R. RC low-pass and high-pass circuits share the same cutoff equation when they use the same component values. RL low-pass and high-pass arrangements likewise share one cutoff magnitude even though the output is taken across a different component. An ideal LC resonant network uses fc = 1/(2π√(LC)). The calculator also reports √(LC) as its characteristic time scale and 1/√(LC) as angular frequency. Real LC filters include source resistance, load resistance, and component losses that determine bandwidth and damping. Consequently, resonance and a practical minus-3-decibel edge are not always identical. More complete designs may need filter order, topology, quality factor, and termination impedance. Enter resistance in ohms, capacitance in farads, and inductance in henries. Unit conversion is especially important because typical capacitors are specified in microfarads, nanofarads, or picofarads, while inductors may be millihenries or microhenries. One microfarad is 0.000001 farad and one millihenry is 0.001 henry. A missed prefix can shift the result by factors of thousands or millions. This calculator is useful for initial audio, sensor, power-supply, and radio-frequency estimates. It applies ideal lumped-component equations and does not account for component tolerance, equivalent series resistance, parasitic capacitance, self-resonance, loading, or frequency-dependent behavior. Verify critical designs with component data sheets, circuit simulation, and bench measurements.
Cutoff frequency examples
The same component values can be checked against standard filter equations.
| Filter and components | Cutoff result | Typical use |
|---|---|---|
| RC: 1,000 Ω and 1 µF | 159.155 Hz | A low-frequency sensor or audio stage. |
| RL: 100 Ω and 0.1 H | 159.155 Hz | A first-order inductive filter. |
| LC: 10 mH and 1 µF | 1,591.549 Hz | An ideal resonant network. |
How to calculate filter cutoff
- Select the RC, LC, or RL filter model.
- Convert component ratings to ohms, farads, and henries.
- Enter the two positive component values shown for the model.
- Select Calculate to obtain cutoff and angular frequency.
- Review the time scale before applying the ideal result to a real circuit.
Frequently asked questions
What does minus 3 dB mean at cutoff?
It means voltage magnitude has fallen to about 70.7 percent of the passband value for a first-order filter. Under the same impedance, that corresponds to half the power.
Is cutoff frequency the same for low-pass and high-pass filters?
The standard first-order RC or RL equation gives the same boundary frequency for either response. The selected output component determines whether frequencies above or below that boundary pass.
Why must I convert microfarads to farads?
The equations use base SI units, so prefixes must be converted before calculation. One microfarad equals one millionth of a farad.
Is LC resonance always the practical cutoff?
No, an ideal LC calculation gives its natural resonant frequency. Resistance, loading, topology, and quality factor determine the actual passband edges.
How do component tolerances affect the answer?
Actual component values shift the measured cutoff from the nominal result. Use worst-case tolerance analysis when the frequency boundary is critical.