1,591.5494
Hz
1.591549
kHz
10,000
rad/s
0.0001
s
0.0000001
10,000
1/s
1,591.5494
Hz
1.591549
kHz
10,000
rad/s
0.0001
s
0.0000001
10,000
1/s
The Cutoff Frequency Calculator determines the -3 dB frequency of first-order RC and RL filter circuits. The cutoff frequency (also called the corner frequency, break frequency, or half-power frequency) is the most important parameter of any filter—it defines the boundary between the passband (frequencies that are passed through) and the stopband (frequencies that are attenuated).
First-order filters are the simplest and most fundamental filter circuits in electronics. An RC filter uses a resistor and capacitor, while an RL filter uses a resistor and inductor. Depending on the configuration (which component is in series and which is in shunt), these can function as either low-pass or high-pass filters. Regardless of configuration, the cutoff frequency is determined by the same formula.
For an RC filter, the cutoff frequency is fс = 1/(2πRC). As frequency increases in a low-pass RC filter, the capacitor's reactance decreases, eventually shunting more signal to ground. At the cutoff frequency, the capacitive reactance equals the resistance, and the output is attenuated by 3 dB (reduced to 70.7% of the input voltage, or 50% of the input power).
For an RL filter, the cutoff frequency is fс = R/(2πL). As frequency increases, the inductor's reactance increases, eventually blocking the signal. At the cutoff frequency, the inductive reactance equals the resistance, producing the same -3 dB attenuation.
The time constant (τ) is the reciprocal of the angular cutoff frequency: τ = RC for RC circuits or τ = L/R for RL circuits. It characterizes the circuit's transient response—how quickly it responds to step changes. The circuit reaches 63.2% of its final value after one time constant.
First-order filters roll off at 20 dB per decade (6 dB per octave) beyond the cutoff frequency. This calculator helps engineers quickly determine the cutoff frequency for a given component combination, or work backward to select components for a desired cutoff frequency. It is an essential tool for designing audio filters, anti-aliasing filters, EMI suppression circuits, sensor signal conditioning, and power supply decoupling networks.
The cutoff frequency calculator uses the standard first-order filter formulas:
RC Filter:
$$f_c = \frac{1}{2\pi RC}$$
$$\tau = RC$$
RL Filter:
$$f_c = \frac{R}{2\pi L}$$
$$\tau = \frac{L}{R}$$
Angular Cutoff Frequency:
$$\omega_c = 2\pi f_c = \frac{1}{\tau}$$
At the Cutoff Frequency:
The voltage gain is:
$$|H(f_c)| = \frac{1}{\sqrt{2}} \approx 0.707 \quad \Rightarrow \quad 20\log_{10}\left(\frac{1}{\sqrt{2}}\right) = -3.01 \text{ dB}$$
The phase shift is ±45° (the sign depends on whether the filter is low-pass or high-pass).
The cutoff frequency defines where the filter transitions from passing signals to attenuating them. Below fс, a low-pass filter passes signals with minimal attenuation; above fс, signals are increasingly attenuated at 20 dB/decade. The -3 dB gain at fс means the output power is half the input power. The time constant indicates the speed of the circuit's transient response—smaller time constants mean faster response. The 45° phase shift at cutoff is the midpoint between 0° (in the passband) and 90° (deep in the stopband).
Inputs
Results
A 1 kΩ resistor with a 0.01 µF (10 nF) capacitor creates a filter with a cutoff frequency of 15.9 kHz—suitable as a simple anti-aliasing filter for audio sampling at 44.1 kHz.
Inputs
Results
A 50Ω load with a 100 mH inductor gives a cutoff of 79.6 Hz. This RL filter attenuates switching noise above 80 Hz in a power supply, while passing the 60 Hz fundamental with minimal loss.
The cutoff frequency (fс) is the frequency at which a filter's output power drops to half of its passband value, corresponding to a -3 dB reduction in voltage gain. It marks the boundary between the passband (frequencies passed with minimal attenuation) and the stopband (frequencies significantly attenuated). For first-order filters, fс = 1/(2πRC) for RC circuits or fс = R/(2πL) for RL circuits.
At -3 dB, the output power is exactly half the input power (10^(-3/10) ≈ 0.5), and the output voltage is 1/√2 ≈ 70.7% of the input voltage. This is the point where the reactive impedance equals the resistance, making it a natural mathematical boundary. It is universally adopted as the standard definition for filter bandwidth in engineering.
In a low-pass RC filter, the output is taken across the capacitor (frequencies below fс pass, above are attenuated). In a high-pass RC filter, the output is taken across the resistor (frequencies above fс pass, below are attenuated). Both have the same cutoff frequency formula; only the output tap point differs. Similarly for RL filters, but with inductor and resistor roles swapped.
A first-order filter rolls off at 20 dB per decade (equivalently, 6 dB per octave) beyond the cutoff frequency. This means that at 10 times the cutoff frequency, the signal is attenuated by 20 dB (to 10% voltage). For steeper rolloff, cascaded filter stages or higher-order designs (Butterworth, Chebyshev) are used.
RC filters are preferred in most applications because capacitors are smaller, cheaper, lighter, and have lower losses than inductors. RL filters are used when inductors are already present in the circuit (e.g., in power supplies or RF circuits), when the load impedance is very low, or when DC current must pass through the filter without voltage drop (since inductors have near-zero DC resistance).
The time constant τ (tau) characterizes the circuit's speed of response to sudden changes. After a step input, the output reaches 63.2% of its final value in one time constant, 86.5% in two, and 95% in three. τ = RC for RC circuits and τ = L/R for RL circuits. A smaller time constant means a faster response and a higher cutoff frequency, since ωс = 1/τ.
Roboculator Team
The Roboculator Team explains calculations, planning tools, and practical formulas in clear language for real-life situations.
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