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Band Pass Filter Calculator

Electronics & PhysicsCircuits and Components
High-pass stage (sets the low corner)
Low-pass stage (sets the high corner)
Centre frequency (Hz) —
Lower cutoff fL (Hz)
—
Upper cutoff fH (Hz)
—
Bandwidth (Hz)
—
Quality factor Q
—

A passive RC band-pass filter has two corners, each at f = 1/(2πRC). The high-pass pair sets the lower cutoff and the low-pass pair sets the upper one. With 10 kΩ and 220 nF, then 4.7 kΩ and 47 nF, the corners are 72.34 Hz and 720.48 Hz, the centre is their geometric mean, 228.3 Hz, and the bandwidth is 648.14 Hz.

About this tool

Hobbyists tuning an audio band, students checking a lab circuit and engineers sketching a sensor front end all need the same four numbers from a cascaded RC band-pass: where it starts to pass, where it stops, the middle, and how sharp it is. Enter the resistor and capacitor of the high-pass stage and of the low-pass stage, in kilohms and nanofarads, and the calculator returns the two -3 dB corners, the geometric centre frequency, the bandwidth and the quality factor Q, with the arithmetic laid out line by line. The model treats the two stages as independent. In a real unbuffered circuit the second stage loads the first, which lowers the peak and shifts the corners, especially when they are less than a decade apart; the tool warns in that case.

How to use it

  1. Enter the high-pass stage

    Type R1 in kΩ and C1 in nF. This pair sets the lower cutoff fL.

  2. Enter the low-pass stage

    Type R2 in kΩ and C2 in nF. This pair sets the upper cutoff fH, which must be above fL.

  3. Read the band

    The centre frequency, both corners, bandwidth and Q update as you type, with the working underneath.

Examples

Audio band: 10 kΩ/220 nF and 4.7 kΩ/47 nF

Resistor R1
10
Capacitor C1
220
Resistor R2
4.7
Capacitor C2
47

Result Centre frequency (Hz): 228.3
Lower cutoff fL (Hz): 72.34
Upper cutoff fH (Hz): 720.48
Bandwidth (Hz): 648.14
Quality factor Q: 0.352

  1. fL = 1 ÷ (2π × 10000 Ω × 220 nF) = 72.34 Hz
  2. fH = 1 ÷ (2π × 4700 Ω × 47 nF) = 720.48 Hz
  3. Centre = √(72.34 × 720.48) = 228.3 Hz
  4. Bandwidth = 720.48 − 72.34 = 648.14 Hz; Q = 0.352

The high-pass stage cuts below about 72 Hz and the low-pass stage above about 720 Hz, so the band is centred near 228 Hz, a decade wide.

1 kΩ with 1 µF and 10 nF

Resistor R1
1
Capacitor C1
1000
Resistor R2
1
Capacitor C2
10

Result Centre frequency (Hz): 1,591.55
Lower cutoff fL (Hz): 159.15
Upper cutoff fH (Hz): 15,915.49
Bandwidth (Hz): 15,756.34
Quality factor Q: 0.101

  1. fL = 1 ÷ (2π × 1000 Ω × 1000 nF) = 159.15 Hz
  2. fH = 1 ÷ (2π × 1000 Ω × 10 nF) = 15915.49 Hz
  3. Centre = √(159.15 × 15915.49) = 1591.55 Hz
  4. Bandwidth = 15915.49 − 159.15 = 15756.34 Hz; Q = 0.101

Corners at 159 Hz and 15.9 kHz are exactly two decades apart, so the centre lands at 1,591.55 Hz and Q is about 0.1.

How it is calculated

fL = 1 ÷ (2π·R1·C1); fH = 1 ÷ (2π·R2·C2); f0 = √(fL·fH); BW = fH − fL; Q = f0 ÷ BW

R1, C1
resistor (Ω) and capacitor (F) of the high-pass stage
R2, C2
resistor (Ω) and capacitor (F) of the low-pass stage
f0
centre frequency, the geometric mean of the corners
BW, Q
bandwidth in Hz and quality factor

Each first-order RC section has a -3 dB corner where the capacitor's reactance equals the resistance, at 1/(2πRC). Cascading a high-pass and a low-pass section passes the frequencies between the two corners. Because the response is symmetric on a logarithmic frequency axis, the centre is the geometric mean rather than the arithmetic average. Q is the centre divided by the bandwidth; a passive RC band-pass always has Q below 0.5, so it is a broad filter.

When not to use it

  • Active filters such as the Sallen-Key or multiple-feedback band-pass use different formulas.
  • LC or crystal resonant circuits need the resonance formula with inductance, not RC corners.
  • Narrow notch-like bands with Q above 0.5 cannot be built from two passive RC stages.

Common mistakes

  • Entering microfarads into the nanofarad field, which moves a corner by a factor of 1,000.
  • Averaging the two corners arithmetically instead of taking their geometric mean.
  • Using equal resistors in both stages without a buffer, so the second stage loads the first.
  • Entering the two stages the wrong way round, so the low-pass corner lies below the high-pass corner, leaving no passband.

Frequently asked questions

Why is the centre frequency a geometric mean?

Filter responses are symmetric on a logarithmic frequency scale. A band from 100 Hz to 10 kHz rolls off the same way one decade below 1 kHz as one decade above, so the middle is √(100 × 10,000) = 1 kHz, not the 5,050 Hz an ordinary average gives.

What does the -3 dB cutoff mean?

At each corner the output voltage has fallen to about 70.7 % of the passband level, which is half the power. The bandwidth this tool reports is the distance between those two half-power points.

Why is Q so low for an RC band-pass?

Two first-order passive sections cannot produce a sharp peak. Even with both corners at the same frequency the theoretical Q tops out at 0.5, and in practice loading pulls it lower. For a narrow band, use an active design or an LC resonator.

How do I stop the stages from loading each other?

Either put a unity-gain op-amp buffer between them or make the second stage's impedance much higher than the first, for example R2 at least ten times R1 with C2 scaled down to keep the same corner. The warning appears when the corners are under a decade apart, where loading is most visible.

Which order should the stages go in?

Either order gives the same ideal corners. Putting the high-pass first blocks DC from the following stage, which is the usual choice in audio paths. The calculator only needs to know which R and C belong to which corner.

How do I pick parts for a target band?

Choose a convenient capacitor, then solve R = 1/(2πfC) for each corner. For a 300 Hz to 3.4 kHz voice band with 100 nF and 10 nF, R1 comes out near 5.3 kΩ and R2 near 4.7 kΩ. Enter them here to confirm the result with standard values.

Cite this tool

Using this tool in an assignment, article or report? Copy a citation, or a link for your website.

APA

Tools Directory Editorial Team. (2026, October 18). Band Pass Filter Calculator. Tools Directory. Retrieved October 27, 2026, from https://tools.milunir.com/electronics-physics/circuits-and-components/band-pass-filter-calculator/

MLA

Tools Directory Editorial Team. “Band Pass Filter Calculator.” Tools Directory, 18 Oct. 2026, https://tools.milunir.com/electronics-physics/circuits-and-components/band-pass-filter-calculator/. Accessed 27 Oct. 2026.

Chicago

Tools Directory Editorial Team. “Band Pass Filter Calculator.” Tools Directory. Last modified October 18, 2026. Accessed October 27, 2026. https://tools.milunir.com/electronics-physics/circuits-and-components/band-pass-filter-calculator/.

Link<a href="https://tools.milunir.com/electronics-physics/circuits-and-components/band-pass-filter-calculator/">Band Pass Filter Calculator – Tools Directory</a>