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Interaural time difference (ITD) calculator

Enter the azimuth of a sound source, the radius of the head, the air temperature and a frequency to get the interaural time difference, the maximum difference, the interaural phase difference, the frequency limit for phase cues and the angle that a 10 microsecond change represents.

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Results

Interaural time difference (Woodworth)

381 µs

Speed of sound
343.2 m/s
Maximum difference (source at 90°)
655 µs
Interaural phase difference of the tone
68 °
Under 180°: the phase gives a clear cue to the direction
Highest frequency with unambiguous phase at 90°
763 Hz
Angle change for a 10 µs change in ITD
1.3 °

The interaural time difference calculator gives the delay between the two ears for a sound source at a given azimuth, with the maximum delay, the phase difference of a tone and the angular resolution, from the head radius and the temperature.

How the calculation works

  • Enter the azimuth of the source and the head radius.
  • Enter the temperature and the frequency of a tone.
  • Read the ITD, the phase and the resolution.

Example

At 20 °C the speed of sound is 343.2 m/s. A source at 45° (0.785 rad) and a head radius of 8.75 cm give an interaural time difference of (0.0875 / 343.2) × (0.785 + sin 45°) = 381 µs. The maximum, at 90°, is 655 µs. For a tone of 500 Hz the phase difference is 360 × 500 × 381 µs = 68°. Near the front, 10 µs corresponds to about 1.3°.

Why it matters

The calculator helps students of hearing science, audio engineers who work on spatial audio and binaural recording, and anyone curious about how two ears give the direction of a sound.

Good to know

The model treats the head as a sphere and gives the delay for a source far away, and the real head, with the shape of the ears and the shoulders, gives results that differ by several percent from the values computed here. The size of the head varies between people and between children and adults, which means that the cues must be recalibrated during growth. The resolution is best in front of the listener, where the smallest detectable change of the azimuth is about one degree, and gets worse for sources to the side, where the delay changes slowly with the angle. At the side, other cues such as the shape of the outer ear, which colors the sound above 4 kHz, help to tell front from back. Spatial audio on headphones uses these delays with level differences and filters, called head-related transfer functions, to create a source outside the head. The speed of sound used is that of dry air and changes slightly with the humidity.

The critical band calculator treats the frequency analysis of the ear, the loudness calculator converts phons and sones, the sound distance calculator treats the fall of level with distance and the ear canal calculator treats the resonance of the ear.

Frequently asked questions

What is the interaural time difference?

It is the delay between the arrival of a sound at the near ear and the far ear. It is zero for a source straight ahead and grows to about 650 microseconds for a source at the side, and the brain uses it to locate low-frequency sounds.

What is the Woodworth formula?

Woodworth modeled the head as a rigid sphere. The sound travels a straight part, then bends around the sphere. The delay is (r / c) × (θ + sin θ), with the head radius r, the speed of sound c and the azimuth θ in radians.

Why does the brain use level differences at high frequencies?

Above about 1.5 kHz the wavelength is shorter than the head, so the phase is ambiguous, but the head casts a sound shadow, which creates level differences between the ears. The two cues, time and level, cover the low and the high frequencies.

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Results are estimates provided for information purposes. They do not replace professional advice.

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