What is the cutoff frequency of a low-pass filter?

The cutoff frequency (f_c) is the frequency at which the output signal power drops to half of the input power — a voltage reduction to approximately 70.7% (1/√2), also called the -3 dB point. For an RC filter: f_c = 1 / (2π·R·C). For an RL filter: f_c = R / (2π·L).

What is the time constant (τ) and why does it matter?

The time constant τ is the product R·C (for RC filters) or the ratio L/R (for RL filters). It describes how quickly the filter responds to a step input — the output reaches about 63.2% of its final value after one time constant. It is also related to the cutoff frequency by f_c = 1 / (2π·τ).

What is the difference between an RC and an RL low-pass filter?

Both are first-order passive low-pass filters with identical frequency response shapes. An RC filter uses a resistor in series and a capacitor to ground; it is easier to tune (capacitors are cheap and available in many values). An RL filter uses a resistor in series and an inductor to ground; inductors are bulkier and more expensive but handle higher currents without saturation issues.

What does -3 dB mean in filter design?

Decibels (dB) measure signal level ratios on a logarithmic scale. A -3 dB change means the power is halved and voltage drops to about 70.7%. The -3 dB point is the standard definition of a filter's cutoff frequency because it marks the boundary between the passband and the transition to attenuation.

How do I choose between a low-pass filter and a high-pass filter?

Use a low-pass filter when you want to keep low frequencies and remove high-frequency noise or interference (e.g., audio smoothing, power supply filtering). Use a high-pass filter when you want to block DC or low-frequency content and pass higher frequencies (e.g., coupling stages, removing mains hum).

What unit prefixes does this calculator accept?

Enter values with standard SI prefixes: k (kilo, ×10³), M (mega, ×10⁶), m (milli, ×10⁻³), µ or u (micro, ×10⁻⁶), n (nano, ×10⁻⁹), p (pico, ×10⁻¹²). For example: 10k = 10,000 Ω, 100n = 100 nF, 4.7u = 4.7 µF.

Low-Pass Filter Calculator

Name: Low-Pass Filter Calculator
Availability: InStock
Author: Nham Vu

Enter resistor and capacitor (or inductor) values to instantly calculate the cutoff frequency, time constant, and -3 dB point for your low-pass filter.

Filter Type

Resistance (R)

Accepts: 1k, 10k, 1M, 470 etc.

Capacitance (C)

Accepts: 100n, 4.7u, 1000p etc.

Test Frequency (optional)

See gain and phase at this frequency.

Filter Results

Cutoff Frequency (f_c)

—

-3 dB point

Time Constant (τ)

—

Angular Cutoff (ω_c)

—

rad/s

Reactance at f_c

—

Formula Reference

f_c = 1 / (2π · R · C)

τ = R · C

ω_c = 1 / τ = 2π · f_c

|H(f)| = 1 / √(1 + (f / f_c)²)

∠H(f) = -arctan(f / f_c)

Summary