What is a Low-Pass Filter?
A low-pass filter is an electronic circuit that allows signals with a frequency lower than a selected cutoff frequency (fc) to pass through while attenuating signals at higher frequencies. In other words, it blocks high frequencies and lets low frequencies pass — hence the name. Low-pass filters are widely used in audio systems, signal processing, power supplies, and communications to remove noise and unwanted high-frequency components.
How to Use the Low Pass Filter Calculator
Using this calculator is simple:
- Select the filter type — RC, RL, non-inverting op-amp, or inverting op-amp.
- Enter the component values — resistance, capacitance, inductance, or gain resistors depending on the selected type.
- Click Calculate to instantly get the cutoff frequency (fc), angular frequency (ωc), time constant (τ), and gain (for active filters).
The calculator is omnidirectional: you can freely mix metric and American unit systems. Use Ω / kΩ / MΩ for resistance, pF / nF / µF for capacitance, and µH / mH / H for inductance.
The Cutoff Frequency and −3 dB Point
The cutoff frequency (fc) is the key parameter of any low-pass filter. It marks the −3 dB point on the filter's Bode plot — the frequency at which the output power drops to half the input power (or the output voltage drops to 1/√2 ≈ 70.7% of the input voltage). Signals below fc pass with minimal attenuation; signals above fc are progressively attenuated.
Types of Low-Pass Filters
Passive Low-Pass Filters (RC and RL)
Passive filters use only resistors, capacitors, and inductors — no power supply is required.
RC Low-Pass Filter
The RC (Resistor-Capacitor) filter is the most common and simplest passive low-pass filter. A resistor is connected in series with the input, and a capacitor is connected from the output to ground.
- Cutoff frequency: fc = 1 / (2π × R × C)
- Time constant: τ = R × C
- Relation: fc = 1 / (2π × τ)
The RC filter is popular because capacitors are cheap, small, and widely available. It is used in audio tone control, power-supply decoupling, and anti-aliasing filters before ADC stages.
RL Low-Pass Filter
The RL (Resistor-Inductor) filter uses an inductor in series and a resistor to ground. Because inductors offer increasing inductive reactance (XL = 2π × f × L) at higher frequencies, they naturally impede high-frequency current — making them ideal for low-pass filtering in high-current or RF applications.
- Cutoff frequency: fc = R / (2π × L)
- Time constant: τ = L / R
RL filters are used in power electronics, motor drives, and RF chokes where large currents make capacitors impractical.
Active Low-Pass Filters (Op-Amp)
Active filters include an amplifier (typically an op-amp) and can provide gain while filtering. They do not load the source circuit and can drive low-impedance loads without signal degradation.
Non-Inverting Op-Amp Low-Pass Filter
This configuration passes the signal through an RC network and into the non-inverting (+) input of an op-amp. The output is in phase with the input, and the gain is set by resistors R1 and R2:
- Cutoff frequency: fc = 1 / (2π × R × C)
- Gain: G = 1 + R2 / R1
A gain ≥ 1 means the filter amplifies while it filters. This is useful in audio pre-amplifiers and sensor conditioning circuits where signal boost is needed.
Inverting Op-Amp Low-Pass Filter
In the inverting configuration, the feedback capacitor Cf is placed in parallel with the feedback resistor Rf. The signal enters through the input resistor Rin. The output is inverted (180° phase shift):
- Cutoff frequency: fc = 1 / (2π × Rf × Cf)
- Gain: G = −Rf / Rin
The inverting filter is preferred when a precise gain (including gain < 1 for attenuation) and phase inversion are acceptable. It is widely used in instrumentation amplifiers and active tone-control circuits.
Metric and American Unit Systems
This calculator fully supports both unit systems:
- Resistance: mΩ, Ω, kΩ, MΩ
- Capacitance: pF, nF, µF, mF (picofarads, nanofarads, microfarads, millifarads)
- Inductance: µH, mH, H (microhenries, millihenries, henries)
- Frequency output: Hz, kHz, MHz, GHz (auto-scaled)
- Time constant output: ns, µs, ms, s (auto-scaled)
Frequently Asked Questions
What is the −3 dB frequency?
The −3 dB frequency is another name for the cutoff frequency fc. At this point, the output power is halved (−3 dB ≈ 10 × log₁₀(0.5)), meaning the signal voltage drops to approximately 70.7% of the input. It marks the boundary between the passband and the stopband of the filter.
Can I use an inductor instead of a capacitor for a low-pass filter?
Yes! An RL filter uses an inductor in series with the load. As frequency increases, the inductor's reactance (XL = 2πfL) increases, blocking high-frequency signals. However, capacitors are generally preferred because they are smaller, cheaper, and have less parasitic resistance than inductors at most frequencies.
What is the time constant (τ) and why does it matter?
The time constant τ describes how quickly the filter responds to a sudden change in input signal. For an RC circuit, τ = R × C. The filter reaches approximately 63.2% of a step-input voltage in one τ, and about 99.3% after five τ. Knowing τ is essential for designing filters that track slow signals (large τ) or respond to fast changes (small τ).
Do active filters have better performance than passive filters?
Active filters (using op-amps) offer several advantages: they can provide voltage gain, they present a high input impedance (so they don't load the source), and they offer a low output impedance (able to drive loads directly). Passive RC/RL filters are simpler, require no power supply, and are used at very high frequencies where op-amps lose performance.
What is the difference between inverting and non-inverting op-amp filters?
Both achieve the same cutoff frequency but differ in phase and gain flexibility. The non-inverting filter preserves the signal phase (0° shift) and has a minimum gain of 1. The inverting filter introduces a 180° phase inversion and can have any gain including values less than 1 (attenuation), making it more flexible in many applications.