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Bessel Filter Group Delay Calculator

Enter the cutoff frequency (and order) to estimate the Bessel group delay.

How it is calculated

The tool uses a one-line approximation for the delay near DC: τ = 1 ÷ (2π × fc), where fc is the cutoff frequency in hertz and τ is in seconds. It is shown in scientific notation (seconds) and in milliseconds, τ(ms) = τ × 1000. The cutoff must be above zero. Notice that the order field has no effect: the formula does not use it, so changing the order from 2 to 8 gives exactly the same delay. A real Bessel filter's delay depends on its order and on how the cutoff is defined (for example the -3 dB point), so treat the result as a rough estimate of the order of magnitude, useful for comparing cutoffs, not a design value. Doubling fc halves the delay.

Worked example

A Bessel low-pass with a cutoff of 2000 Hz. Angular frequency: 2π × 2000 = 12,566.4 rad/s. Delay: 1 ÷ 12,566.4 = 7.9577 × 10⁻⁵ s, which is 0.0796 ms, or about 80 microseconds. A signal passing through this filter is therefore shifted by roughly 80 µs, and moving the cutoff up to 4000 Hz would halve that to about 40 µs.

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Common mistakes

  • Expecting the filter order to change the answer. The order box is informational here, so a 2nd-order and an 8th-order filter show the same delay; do not use the figure to compare orders.
  • Entering the cutoff in kHz. The field is in hertz, so 2 kHz must be typed as 2000, otherwise the delay is 1000 times too long.
  • Reading the result as the delay at every frequency. It is the low-frequency (near DC) value; for a real Bessel filter the delay is nearly flat in the passband but falls off toward and beyond the cutoff.
  • Treating it as the total latency of a circuit. Amplifiers, sampling, buffering and other stages add their own delays that this calculation does not include.
  • Confusing group delay in seconds with a phase shift in degrees. The delay is a time; the phase at a given frequency is a different quantity.

About this calculator

A Bessel filter is a type of low-pass filter designed to have a maximally flat group delay (also called linear phase response) in its passband, meaning all frequency components of a signal are delayed by nearly the same amount of time and the waveform's shape is preserved with minimal distortion. This calculator estimates that approximately constant delay at DC from the filter's cutoff frequency alone, using the approximation delay = 1/(2π × cutoff frequency). The filter order does not change the result, so treat it as a first estimate; the exact delay varies somewhat with order.

Because it preserves pulse shape so well, the Bessel filter is the go-to choice in audio crossover networks, oscilloscope input stages, telecommunications, and pulse/digital circuits where waveform fidelity matters more than a sharp cutoff — unlike Butterworth or Chebyshev filters, which trade phase linearity for steeper roll-off. Analog and RF engineers use group-delay figures like this one to predict how much a filter will smear or shift a signal in time before building it into a circuit.

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  • Editorial team

    Use the result to compare cutoffs, not to size a design. A 1000 Hz cutoff returns 1.5915 × 10⁻⁴ s (0.1592 ms) and 20000 Hz returns 7.9577 × 10⁻⁶ s, but the order box changes nothing: orders 2 and 8 print the same figure. A real Bessel filter's delay for a fixed cutoff grows with order. If two channels must stay time-aligned, check the filter's datasheet delay. What order and application are you working on?

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