Calculators
RL Cutoff Frequency Calculator
Calculate RL filter cutoff frequency or solve R or L.
Calculate the ideal first-order RL cutoff frequency, or solve the resistance or inductance needed for a target cutoff. Processing stays local in your browser.
Result
1.5915494 kHz
RL time constant: 0.0001 s
The ideal relationship is fc = R/(2πL). Real inductors add winding resistance, parasitic capacitance, core loss, saturation limits, and frequency-dependent behavior that can shift a measured response.
About This Tool
A first-order resistor-inductor network has a characteristic cutoff frequency determined by its resistance and inductance. This calculator uses the ideal RL relationship to find that -3 dB frequency, or rearranges the equation to choose resistance or inductance for a target cutoff. It is useful for electronics study, simple passive filter design, current-smoothing analysis, and comparing RL behavior with RC circuits. All calculations run locally in your browser.
How To Use It
- Choose whether to solve for cutoff frequency, resistance, or inductance.
- Enter the two known values and select the matching engineering units.
- Read the calculated cutoff or component value. When solving cutoff frequency, the RL time constant is also shown.
- Use the result as an ideal starting point and account for inductor winding resistance, source/load impedance, parasitics, and component tolerance in a real circuit.
Examples
100 Ω and 10 mH
For R = 100 Ω and L = 10 mH, the ideal cutoff frequency is about 1.592 kHz and the RL time constant L/R is 100 µs.
Choose R for 1 kHz with 10 mH
For a 1 kHz target cutoff and L = 10 mH, R = 2πfL gives about 62.83 Ω.
Choose L for 1 kHz with 100 Ω
For a 1 kHz target cutoff and R = 100 Ω, L = R/(2πf) gives about 15.92 mH; a nearby standard inductor value will shift the nominal cutoff.
Useful Notes
RL cutoff frequency formula
For an ideal first-order series RL network, the characteristic cutoff is fc = R/(2πL), where R is the effective series resistance in ohms, L is inductance in henries, and fc is frequency in hertz. At this frequency the resistor and inductor reactance magnitudes are equal because XL = 2πfL = R.
Solving for resistance or inductance
The cutoff equation can be rearranged as R = 2πfcL or L = R/(2πfc). These forms are useful when one component is fixed and you want an ideal first-pass value for the other component.
Relationship to the RL time constant
The ideal RL time constant is τ = L/R seconds, which makes fc = 1/(2πτ). Increasing inductance or reducing resistance increases the time constant and lowers the cutoff frequency.
Low-pass and high-pass behavior
A series RL circuit can form a first-order low-pass or high-pass response depending on where the output is measured. The resistor voltage is low-pass with respect to the source voltage, while the inductor voltage is high-pass in the ideal unloaded model. Both share the same characteristic cutoff equation.
Use effective series resistance
The R in the ideal formula is the resistance that participates in the RL network, not automatically just one labeled resistor. Source resistance, load impedance, and the inductor's winding resistance can change the effective damping and therefore the measured cutoff.
Real inductor limitations
Inductors are not ideal across unlimited frequency. Winding resistance, parasitic capacitance, core loss, saturation, self-resonance, tolerance, and frequency-dependent inductance can make a real circuit depart from the simple first-order model.
FAQ
Why is the RL cutoff formula different from RC?
Capacitive reactance falls as frequency rises, while inductive reactance rises with frequency. Setting the relevant reactance magnitude equal to resistance gives fc = 1/(2πRC) for RC and fc = R/(2πL) for RL.
Does this work for both RL low-pass and high-pass filters?
Yes for the ideal first-order characteristic cutoff. The response type depends on whether output is taken across the resistor or the inductor.
Should I include the inductor's DC resistance?
When it is significant, winding resistance contributes to the effective series resistance and can shift the actual response. A precise model should include the circuit's relevant source, winding, and load impedances.
Why might my measured cutoff be different?
Common reasons include component tolerance, winding resistance, source/load impedance, parasitic capacitance, self-resonance, core losses, and measurement setup.
Can I use this above an inductor's self-resonant frequency?
No. Near and above self-resonance, parasitic capacitance substantially changes the inductor's behavior, so the simple ideal RL equation is no longer a reliable model.
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