Design RC and RL low-pass filters by calculating cutoff frequency, gain, phase shift, rolloff rate, rise time, and frequency response table.
A low-pass filter allows signals below a certain cutoff frequency to pass while attenuating higher frequencies. It is one of the most widely used circuits in electronics — found in audio systems (removing hiss), power supplies (smoothing ripple), anti-aliasing before ADCs, sensor signal conditioning, and radio receivers.
The most basic implementations use a resistor-capacitor (RC) or resistor-inductor (RL) network. The cutoff frequency is the point where the output drops to −3 dB (70.7%) of the input level. Above cutoff, the signal is progressively attenuated at a rate that depends on the filter order.
This Low-Pass Filter Calculator handles both RC and RL topologies with support for 1st through 3rd order filters. Enter component values and a test frequency to see the cutoff frequency, gain, phase lag, rolloff rate, time constant, and rise time. A full frequency response table shows how the filter behaves across the spectrum, and preset buttons cover audio, RF, and power supply applications.
Use this page to move quickly from component values to cutoff frequency, attenuation, and time response when designing a simple analog low-pass stage. It is handy when you want to compare a few resistor-capacitor or resistor-inductor choices without re-deriving the same transfer function each time. It also keeps the frequency and step-response views together so you can judge both filtering and delay at once.
RC Low-Pass: fc = 1 / (2π × R × C) RL Low-Pass: fc = R / (2π × L) Gain: G(f) = −10n × log₁₀(1 + (f/fc)²) dB Phase: φ = −n × arctan(f/fc) Rolloff: n × 20 dB/decade Rise Time: t_rise ≈ 2.2 × τ
Result: fc = 19,894 Hz, Gain at 10 kHz = −1.07 dB
A 1 kΩ / 8 nF RC low-pass has a 19.9 kHz cutoff. At 10 kHz (below cutoff), the signal passes with minimal attenuation of about 1 dB.
A low-pass filter preserves slower signal content while suppressing faster variation. In practice that means less high-frequency noise, smoother power rails, and cleaner inputs to amplifiers, converters, and control systems.
The same component values control both the frequency response and the time response. Lowering the cutoff improves noise rejection, but it also slows the circuit down. That tradeoff is why time constant and rise time matter alongside the -3 dB point.
Simple RC and RL stages are great for first-pass design, but loading, source impedance, parasitic elements, and required passband flatness can all change the real response. If the filter is part of a critical signal chain, verify the final circuit in simulation or measurement.
The frequency at which output power drops to half (−3 dB). Below cutoff, the filter passes signals; above cutoff, it increasingly attenuates them.
It is a low-pass filter placed ahead of an ADC so frequencies above the useful measurement band are attenuated before sampling can fold them back into the digitized signal. That helps keep unwanted high-frequency content from appearing as false lower-frequency signals.
RC is simpler and cheaper for most applications. RL filters are used in power circuits where inductors provide better performance.
A 1st-order filter rolls off at 20 dB/decade. Each additional order adds another 20 dB/decade of rolloff, giving a steeper transition band.
τ = RC (or L/R) — the time for the output to reach 63.2% of a step input. It characterizes the filter's speed of response.
For a first-order response, the 10 to 90 percent rise time is about 2.2 times the time constant. That is a quick way to estimate how slowly the filter will respond to a step.