Find RL cutoff frequency and time constant instantly. Check reactance, impedance, and angular frequency quickly. Export results and review examples for faster circuit analysis.
Cutoff frequency: fc = R / (2πL)
Angular cutoff frequency: ωc = R / L
Time constant: τ = L / R
Inductive reactance: XL = 2πfL
Impedance: Z = √(R² + XL²)
Resistor output gain: |H| = R / √(R² + XL²)
Inductor output gain: |H| = XL / √(R² + XL²)
The cutoff point appears when XL equals R. At that point the magnitude is 0.707 of the reference value. That is the familiar -3 dB point.
| Resistance | Inductance | Cutoff Frequency | Time Constant | Note |
|---|---|---|---|---|
| 100 Ω | 10 mH | 1.592 kHz | 100 µs | Fast response circuit |
| 220 Ω | 47 mH | 744.73 Hz | 213.64 µs | Common filter range |
| 1 kΩ | 100 mH | 1.592 kHz | 100 µs | Higher resistance design |
| 470 Ω | 1 H | 74.80 Hz | 2.128 ms | Lower cutoff example |
RL circuits appear in filters, sensors, and control systems. The cutoff frequency marks the point where output magnitude drops to 70.7 percent of the reference level. In a simple series RL network, this point happens when inductive reactance equals resistance. That balance changes how the circuit passes low or high frequencies. Knowing the cutoff helps you predict behavior before building the circuit. It also helps students connect equations with real electrical response.
The cutoff frequency formula for a series RL circuit is fc = R / (2πL). Resistance raises the cutoff. Inductance lowers it. Small inductors push the cutoff upward. Large inductors push it downward. The angular cutoff frequency is ωc = R / L. The time constant is τ = L / R. These values work together. The time constant describes transient behavior, while the cutoff frequency describes sinusoidal response. Both are useful during design and troubleshooting.
This calculator accepts resistance, inductance, and optional operating frequency inputs. It can also solve for resistance or inductance when the target cutoff is known. That makes it useful for reverse design work. You can test a low-pass output across the resistor or a high-pass output across the inductor. When you enter an operating frequency, the tool also estimates reactance, impedance, gain, phase angle, and output voltage. Those extra values make comparisons easier during homework, lab work, and field analysis.
Use consistent units before reviewing the result. Ohms, henries, and hertz are the base units. The form accepts common engineering units to save time. Always check that resistance and inductance are positive. A very small inductance can create a high cutoff. A very large inductance can create a low cutoff. These trends are normal. They reflect the direct relationship between resistance and cutoff, and the inverse relationship between inductance and cutoff.
In practice, RL cutoff calculations support filter shaping, noise control, current smoothing, and timing studies. They also help when choosing standard resistor and inductor values. After you compute the cutoff, compare it with the expected signal range. That simple step prevents poor attenuation or unwanted phase shift. A clear calculator speeds design checks and reduces manual mistakes. It also gives learners a better view of how circuit theory becomes measurable performance directly.
It is the frequency where the output magnitude reaches 70.7 percent of the reference level. In a simple RL circuit, this happens when inductive reactance equals resistance.
A larger inductor creates more reactance at the same frequency. Because cutoff occurs when reactance equals resistance, more inductance means that balance is reached at a lower frequency.
Higher resistance requires a higher inductive reactance to reach the cutoff condition. That means the frequency must rise before XL becomes equal to R.
Output across the resistor behaves like a low-pass response. Output across the inductor behaves like a high-pass response. The cutoff frequency stays the same for both views.
The time constant shows how quickly current changes after a step input. It is useful for transient analysis, while cutoff frequency is more useful for sinusoidal steady-state response.
Yes. Choose the correct solve mode, enter the known values, and the calculator will reverse the formula to estimate the missing design value.
Operating frequency lets the tool calculate reactance, impedance, gain, phase angle, current, and output voltage. That gives a better view of actual circuit behavior.
Yes. It helps students verify formulas and helps designers compare circuit choices quickly. Export features also make documentation easier during reports or lab records.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.