What is a band-pass filter?

A band-pass filter (BPF) is a circuit that allows signals within a defined frequency range (the passband) to pass through while attenuating frequencies outside that range. The passband is bounded by the lower (-3 dB) cutoff frequency f1 and the upper (-3 dB) cutoff frequency f2.

What is the center frequency formula for an RLC band-pass filter?

The resonant center frequency is f0 = 1 / (2π × √(L × C)), where L is in henries and C is in farads. This is also the frequency of maximum output voltage.

How is bandwidth calculated?

For a series RLC band-pass filter the -3 dB bandwidth is BW = R / (2π × L). The lower cutoff is f1 = f0 − BW/2 and the upper cutoff is f2 = f0 + BW/2 (exact for high-Q circuits; the calculator uses the precise quadratic formula).

What is the Q factor and why does it matter?

The quality factor Q = f0 / BW = (1/R) × √(L/C). A high Q means a narrow, selective passband; a low Q means a wide passband. In radio applications Q values of 50–200 are common; in audio applications Q might be 0.7–10.

What topology does this calculator assume?

This calculator models the series RLC band-pass filter, where R, L, and C are connected in series and the output is measured across R. This is the most common textbook topology.

Why do the cutoff frequencies differ from f0 ± BW/2?

The simple approximation f1 ≈ f0 − BW/2 holds for high-Q filters. For low-Q filters the exact quadratic solution gives slightly asymmetric cutoffs around f0. This calculator always uses the exact formula.

Band-Pass Filter Calculator

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

Enter R, L, and C values to instantly compute the center frequency, bandwidth, Q factor, and upper/lower -3 dB cutoff frequencies of an RLC band-pass filter.

Component Values

Resistance (R)

Inductance (L)

Capacitance (C)

Signal Frequency — optional, for gain & phase

Results

Enter component values and click Calculate

Center Frequency (f₀)

—

Lower Cutoff (f₁)

—

−3 dB lower edge

Upper Cutoff (f₂)

—

−3 dB upper edge

Bandwidth (BW)

—

f₂ − f₁

Quality Factor (Q)

—

f₀ / BW

Impedance at Resonance

Z min

—

= R

XL = XC

—

at f₀

Time Constant

—

τ = L/R

Key Formulas

f₀ = 1 / (2π√(LC))

BW = R / (2πL)

Q = f₀ / BW

Summary

Enter R, L, and C values to instantly compute the center frequency, bandwidth, Q factor, and upper/lower -3 dB cutoff frequencies of an RLC band-pass filter.

How it works

Enter the resistance (R) in ohms, kilohms, or megohms.
Enter the inductance (L) in microhenries, millihenries, or henries.
Enter the capacitance (C) in picofarads, nanofarads, or microfarads.
Click Calculate to compute f0, BW, Q, and the upper/lower cutoff frequencies.
Optionally enter a signal frequency to see the gain and phase response at that point.
Use the Reset button to clear all fields and start over.

Use cases

Design RF bandpass filters for radio receivers and transmitters.
Verify component values for audio equalizer circuits.
Compute the Q factor to assess filter selectivity.
Determine the -3 dB bandwidth of a resonant LC tank circuit.
Select inductor and capacitor values for a target center frequency.
Analyze filter response at a specific signal frequency.
Teach or learn RLC resonance theory with instant numerical feedback.
Cross-check simulation results against hand calculations.

Frequently Asked Questions

Last updated: 2026-06-09 · Reviewed by Nham Vu