How to Calculate Frequency Bandwidth
Bandwidth describes how wide a slice of the frequency spectrum a signal, filter, antenna, or resonant circuit actually uses or passes. It is defined as the difference between the upper cutoff frequency (f_H) and the lower cutoff frequency (f_L) of the response: BW = f_H − f_L. In electronics, those cutoffs are almost always the −3 dB (half-power) points — the frequencies where the output power has dropped to half its peak value. This calculator takes those two cutoffs and derives the bandwidth, the center (resonant) frequency, the quality factor, and the fractional bandwidth.
Center frequency and Q factor
For a bandpass response, the center or resonant frequency is the geometric mean of the two −3 dB points: f_0 = √(f_L × f_H). This isn't just a convenient average — for the classic RLC bandpass filter, the product of the lower and upper cutoff frequencies is exactly equal to the square of the resonant frequency (f_L × f_H = f_0²), so the geometric mean gives the true center of the passband on a logarithmic frequency axis. From there, the quality factor is Q = f_0 / BW. Q measures selectivity: a high-Q circuit (Q ≫ 1) has a narrow bandwidth relative to its center frequency and a sharp, peaked response — useful for tuning in one radio station and rejecting its neighbors. A low-Q circuit has a broad, gentle response that passes a wide swath of frequencies, which is what you want in a general-purpose audio amplifier.
Practical notes
- Narrowband shortcut: when Q is large (BW ≪ f_0), the geometric mean f_0 = √(f_L × f_H) is nearly identical to the simpler arithmetic mean (f_L + f_H) / 2, so many datasheets use that approximation without meaningful error.
- Fractional bandwidth: BW / f_0 (often shown as a percentage) is unit-independent, so it lets you compare a narrowband AM filter against a wideband Wi-Fi channel on equal footing even though their absolute frequencies differ by orders of magnitude.
- Keep units consistent: enter f_L and f_H in the same unit (Hz, kHz, MHz, or GHz) — mixing units before converting is the most common source of bandwidth-calculation errors.
- −3 dB isn't the only convention: some RF and optical specifications use −1 dB, −6 dB, or null-to-null bandwidth instead of the standard −3 dB (half-power) points, so confirm which convention a given datasheet is using before comparing numbers.