Low Pass Filter Calculator

Compute cutoff frequency (–3 dB point), gain (dB) & phase shift for passive RC or RL low‑pass filters. Visualize magnitude and phase Bode plots.

1 μF = 1e-6 F
? Audio LPF (3.4 kHz) : R=1kΩ, C=0.047μF
? Standard RC : R=1kΩ, C=1μF (159 Hz)
⚡ RL Power : R=10Ω, L=10mH (159 Hz)
? Anti-aliasing : R=1kΩ, C=0.1μF (1.59 kHz)
? Subsonic (0.5 Hz) : R=100kΩ, C=3.18μF
Local computation: All calculations run inside your browser. No data is sent to any server.
Filter Parameters & Response
Cutoff frequency fc = — Hz
Attenuation at fc : -3.01 dB (half-power point)
Gain at test freq : — dB  |  —°
Transfer function magnitude : |H(f)| = —
Filter type : RC Low-Pass
Component values : R = 1000 Ω, C = 1 μF
Roll-off rate : -20 dB/decade
Magnitude Response (Bode Plot)
Gain (dB) –3 dB reference line Cutoff frequency marker
Phase Response (Bode Plot)
Phase (°) Cutoff frequency marker 0° reference

1st Order Low‑Pass Filter: Theory & Practical Insight

A low-pass filter (LPF) attenuates frequencies above the cutoff frequency \(f_c\) and passes frequencies below it. The simplest passive implementations are the RC and RL networks. These filters are fundamental in audio crossovers (woofers), anti-aliasing before ADCs, power supply smoothing, and noise reduction. The cutoff frequency is defined where the output power drops by half (−3 dB relative to the passband).

For RC: \( f_c = \frac{1}{2 \pi R C} \)    |    For RL: \( f_c = \frac{R}{2 \pi L} \)

The voltage transfer function magnitude and phase are derived from the voltage divider:
\( H(j\omega) = \frac{1}{1 + j\omega RC} \) (RC case). The magnitude in dB: \( |H|_{dB} = 20 \log_{10}\left( \frac{1}{\sqrt{1+(f/f_c)^2}} \right) = -10\log_{10}\left(1+(f/f_c)^2\right) \). Phase angle: \( \phi = -\arctan(f/f_c) \). Below \( f_c \), gain approaches 0 dB; above \( f_c \), roll‑off is –20 dB/decade.

Design Methodology & Key Specifications

  • Cutoff frequency selection: Choose \( f_c \) to pass desired signals and reject higher frequencies. For audio, a 3.4 kHz LPF removes high-frequency noise while preserving voice.
  • Impedance matching: Ensure load impedance is much larger than filter output impedance to avoid loading effects. Our calculator assumes ideal source and load.
  • Component tolerances: Use 1% resistors and 5–10% capacitors for predictable cutoff.

For real‑world circuits, source and load impedances affect the response. The formulas above assume an ideal voltage source and infinite load. Our Bode plots visualize the ideal response as a solid first approximation.

Real‑World Applications

Audio woofer crossover
A low-pass filter sends low frequencies to a subwoofer. Typical values: R=8Ω, L=3.3mH yields fc ≈ 386 Hz.
Anti-aliasing filter
Before an ADC, a LPF removes frequencies above Nyquist. Example: fc = 20 kHz for audio ADC.
Engineering insight – Active vs Passive: Active low-pass filters using op-amps provide gain and buffering, but the same cutoff formulas apply for first-order. Passive RC/RL filters are still widely used in high-frequency designs and power applications.

Step‑by‑Step Calculation & Bode Interpretation

Our solver determines \(f_c\) from your R and C (or L). It then reconstructs the Bode magnitude and phase plots over a frequency range spanning 0.01×\(f_c\) to 100×\(f_c\) on a logarithmic scale. The magnitude plot reveals the characteristic –20 dB/decade slope above cutoff and the flat passband below. The phase plot shows the transition from 0° to –90°, with –45° at \(f_c\). The –3 dB line crossing at \(f_c\) validates the design. Use the test frequency input to evaluate gain or phase at any specific point – ideal for checking attenuation at unwanted harmonics.

Example: Designing an Anti-Aliasing Filter for Audio ADC

For a 44.1 kHz sampling rate, the Nyquist frequency is 22.05 kHz. A first-order LPF with fc = 20 kHz (R=1kΩ, C≈7.96 nF) attenuates frequencies above 22.05 kHz by about –1.5 dB at 22 kHz and provides additional attenuation beyond. Our tool instantly verifies the design.

Frequently Asked Questions

Both are first-order low-pass filters. RC uses a resistor and capacitor; RL uses a resistor and inductor. RC is more common due to cost and size, but RL filters are used in power supplies and RF where inductors are practical.

At \(f = f_c\), the magnitude of the transfer function is \(1/\sqrt{2} \approx 0.707\). Converting to decibels: \(20\log_{10}(0.707) = -3.01\) dB. This marks the half-power point, a standard bandwidth definition.

The plots use the exact transfer function evaluated at 200 logarithmically spaced points, ensuring high visual accuracy. They match theoretical curves within 0.1 dB and 0.1°.
References & Further Reading: All About Circuits – Low-pass Filters, Horowitz & Hill “The Art of Electronics”, Wikipedia: Low-pass filter.
Reviewed by GetZenQuery tech team — last update May 2026.