Group Delay Calculator for Audio Phase Alignment

Group Delay Calculator

Estimate audio group delay from phase slope, filter type, FIR length, acoustic spacing, and sample rate.

🎵Presets

🎛Calculator Inputs

Used to convert milliseconds into samples.
Used for cycles, phase rotation, and wavelength.
Measured phase slopeGroup delay = - phase slope / angular frequency slope

For measured data, use unwrapped phase. A falling phase trace normally gives a positive group delay.

Filter and FIR modelChoose a common audio approximation for crossover, all-pass, port, or FIR latency
Delay = (taps - 1) / 2 samples.
Use for processor latency or a delay line.
Acoustic offsetDistance is converted through the speed of sound at the selected temperature
Positive value adds acoustic delay.
Speed of sound = 331.3 + 0.606T m/s.
Used to mark when delay is a large fraction of a cycle.
Total group delay
0 ms
including acoustic offset
Sample delay
0
samples at selected rate
Cycle fraction
0
cycles at target frequency
Distance equivalent
0 ft
sound travel distance

📊Reference Specs

48
samples per ms at 48 kHz
0.89
ms per foot near 20°C
343
meters per second sound
360
degrees per one cycle
Calculation typeCore formulaBest useWatch item
Measured phase slope-(Δphase / 360) / ΔfrequencyAnalyzer exports and crossover tracesPhase must be unwrapped
Linear phase FIR(taps - 1) / (2 x sample rate)Convolution EQ, FIR crossovers, limitersLatency rises with tap count
First-order all-pass1 / (pi x fc x (1 + r²))Small phase trims near one cornerDelay halves above and below fc
Second-order all-passQ / (pi x f0) near centerSharper phase rotation around one bandHigh Q narrows the delay peak
Acoustic offsetdistance / sound speedDriver depth, mic spacing, sub alignmentTemperature changes sound speed

🎧Common Audio Cases

ScenarioTypical bandDelay rangePractical interpretation
Subwoofer crossover50 to 120 Hz3 to 15 msOften audible as weak or lumpy summing if unmatched
Studio monitor crossover1.5 to 3 kHz0.05 to 0.6 msSmall in time, but still meaningful in phase
Ported enclosure tuning30 to 70 Hz8 to 30 msDelay peaks around the tuning region
Room microphone spacingFull range0.9 ms per ftUse samples or milliseconds to line up transients
Linear phase mastering EQProgram wide10 to 100 msLatency is predictable from tap length

📐Frequency Delay Grid

FrequencyOne cycle45° tolerance90° tolerance
40 Hz25.00 ms3.13 ms6.25 ms
80 Hz12.50 ms1.56 ms3.13 ms
250 Hz4.00 ms0.50 ms1.00 ms
1 kHz1.00 ms0.13 ms0.25 ms
4 kHz0.25 ms0.03 ms0.06 ms

💡Calculation Tips

Phase traces: When the analyzer wraps at +/-180°, unwrap the trace before measuring slope. A wrapped trace can make a smooth delay look like a sudden negative spike.
Alignment checks: Compare the final delay to the period of the crossover frequency. Milliseconds that look small can still be a large phase angle at high frequencies.

Group delay refer to the phenomenon where the different frequency within an audio signal travel at different speeds through an audio system. Because different frequencies within an audio signal experiences more delay than others, the signal can become smear out. As a result, low frequencies may arrive at the listener at a different time than mid frequencies, making the audio signal sound disconnectedly.

For instance, an low frequency of a kick drum may not be heard at the same time as the bass note due to group delay. Group delay is mathematically define as the time derivative of phase. Phase refers to the position of a sound wave within the cycle of that sound wave at a specific moment in time.

What Is Group Delay in Sound Systems

Group delay measure the movement of the envelope of that sound wave. When a person utilize an equalizer or a crossover, those equalizer and crossovers shift the phase of the audio signal. If the phase is shift in a linear manner, each frequency will experience the same delay, which is often not perceivable by human ear.

However, if the phase is not linear shifted, different frequencies will experience different delay. Different amounts of delay occurs most frequent when a person employs filter, such as a Butterworth filter or a Linkwitz-Riley filter. Both of these filter types has the potential to alter the phase of a sound signal rapid near the corner frequency of that filter.

Such rapid alteration to the phase of a sound signal create alteration to the group delay of that signal, as well. Thus, frequencies that is present near the corner frequency of that filter will experience a different amount of delay than those that are located away from that corner frequency. This different amount of delay for the frequencies near the corner frequency relative to the other frequencies is why sounds reproduced through a subwoofer crossover can feel disconnect from the remaining sound system’s mid-frequency sound.

To control the group delay of a system, a person must understand how filter can impact the phase of a sound system. More specific, if a person employ a crossover to separate the low frequencies from the mid frequencies of an audio system, the crossover will introduce phase shift to those frequencies. These phase shift create group delay, and group delay create a time difference between each of those sound system’s frequency.

Thus, if a person notice that the low frequencies of the system are smear relative to the other frequencies of the system, the person may be experiencing group delay that is create as a result of the phase shift of the system’s crossover or equalizer. For these reason, group delay is both a result of the phase shift of those filters, as well as a result of the difference in timing of each of the sound system’s frequencies.

Group Delay Calculator for Audio Phase Alignment

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