What is the difference between RC, RL and LC filters?

RC and RL are first-order filters with -20 dB/decade roll-off. LC is second-order with -40 dB/decade — a sharper transition. RC uses resistor+capacitor, RL uses resistor+inductor, LC uses inductor+capacitor.

What is the -3 dB point?

-3 dB means the output power is halved (voltage is 70.7% of input). This is the universal definition of the cutoff frequency for all filter types.

How do I choose between RC and RL?

RC filters are more common because capacitors are cheaper, smaller and more readily available than inductors. RL filters are used at lower frequencies or in power applications where inductors are already present.

Filter Cutoff Frequency Calculator

f_c = 1/(2πRC)

f_c = R/(2πL)

f_c = 1/(2π√LC)

RC Filter — Enter R and C

Ω Resistance

C Capacitance

Enter component values

Cutoff Frequency Results

Cutoff fc
—
Hz

ω_c

—

rad/s

Period T_c

—

Time Constant τ

—

Gain at f_c

—

Roll-off

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Figure 1: The cutoff frequency f_c is where the filter output drops to −3 dB (70.7% of input voltage). Below f_c is the passband; above is the stopband with a roll-off slope.

Table of Contents

Fundamentals

What Is the Filter Cutoff Frequency?
Formulas by Filter Type

Worked Examples

Audio RC Filter
RF LC Filter
RL Power Filter

Deep Dive

Choosing the Right Filter Type
Understanding the -3 dB Point

Reference

Frequently Asked Questions
Related Filter Calculators

What Is Filter Cutoff Frequency?

The cutoff frequency (f_c) is the frequency at which a filter’s output drops to −3 dB (70.7% of input voltage, 50% of power). It marks the boundary between the passband and stopband. Every filter type — RC, RL, LC, active — has a characteristic cutoff frequency determined by its component values.

This calculator handles all three passive filter types. For more detailed analysis of each, use the dedicated RC Filter Calculator, RL Filter Calculator, or LC Filter Calculator.

Formulas by Filter Type

RC: f_c = 1/(2πRC) | τ = RC
RL: f_c = R/(2πL) | τ = L/R
LC: f_c = 1/(2π√LC) | 2nd order, −40 dB/decade

Worked Example — Audio RC Filter

Given: R = 10 kΩ, C = 100 nF

f_c = 1/(2π × 10000 × 100×10⁻⁹) = 159.2 Hz

This is a common bass-cut filter for audio. Frequencies below 159 Hz pass through; above 159 Hz they are progressively attenuated. The Low Pass Filter Calculator provides more detailed frequency response analysis.

Worked Example — RF LC Filter

Given: L = 250 µH, C = 100 pF

f_c = 1/(2π√(250×10⁻⁶ × 100×10⁻¹²)) = 1.007 MHz

Worked Example — RL Power Filter

Given: R = 100 Ω, L = 50 mH

f_c = 100/(2π × 0.05) = 318.3 Hz

Choosing the Right Filter Type

RC filters are simplest and cheapest — ideal for signal-level applications. RL filters handle high current better and are used in power circuits. LC filters offer steeper roll-off without resistive losses, used in RF and power supply filtering. The Butterworth Filter Calculator designs maximally-flat multi-order responses, and the Active Filter Calculator adds op-amp gain to overcome passive filter limitations.

Understanding the −3 dB Point

−3 dB means the output power is half the input power. In voltage terms, the output is 1/√2 = 0.707 of the input. This is a universal convention — all filter specifications use the −3 dB point as the cutoff frequency. The Band Pass Filter Calculator uses the same definition for its lower and upper cutoff frequencies.

Impedance Calculator: The Impedance Calculator explores how reactive impedance determines filter behaviour at different frequencies.

Frequently Asked Questions

What does first-order vs second-order mean?

The order refers to the number of reactive components (capacitors or inductors). First-order (RC, RL) has one, with −20 dB/decade roll-off. Second-order (LC) has two, with −40 dB/decade. Higher orders give sharper transitions but more complexity.

Can I use this for audio applications?

Yes. RC and LC filters are widely used in audio for tone shaping, crossovers, and anti-aliasing. The component values determine whether the filter operates at audio frequencies (20 Hz – 20 kHz) or at other ranges.

What is the phase shift at cutoff?

A first-order filter has −45° phase shift at fc (low-pass) or +45° (high-pass). A second-order filter has −90° at fc. Phase shift is important in feedback systems and audio where it affects sound quality.

How do I make a bandpass filter?

Combine a low-pass and high-pass filter in series, with the low-pass fc higher than the high-pass fc. The frequencies between the two cutoffs form the passband. The Band Pass Filter Calculator does this automatically.

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Last updated: March 2026