Acoustic delay, distance and the temperature nobody accounts for

Every loudspeaker alignment, every microphone placement and every impulse-response measurement comes down to one conversion: distance to time. The usual figure is 343 m/s, or 2.915 ms per metre, and the usual mistake is treating it as a constant. The speed of sound in air varies by about 0.6 m/s per degree Celsius, which is small enough to ignore for a quick estimate and large enough to ruin a careful one.

The calculator converts between distance, time and samples, and reports how much the answer moves for each degree of temperature error so you can judge whether it matters for what you are doing.

The numbers worth knowing by heart

• 331.3 m/s at 0 °C.
• 343.2 m/s at 20 °C, which is the source of the usual 343.
• 2.914 ms per metre at 20 °C, or 1 ms per 34.3 cm.
• 139.9 samples per metre at 48 kHz, and 128.4 at 44.1 kHz.
• 7.15 mm per sample at 48 kHz, so one sample of misalignment is under a centimetre of path difference.

Those last two figures are the ones that decide whether you need sub-sample delay resolution. At 48 kHz a single sample is 7 mm, which is below the precision of most physical placement, so whole-sample delay is usually enough — until you are aligning two drivers on the same baffle, where a fraction of a sample starts to matter.

Temperature, and why it is not a detail

The speed of sound rises by about 0.6 m/s per degree Celsius near room temperature — roughly 0.17% per degree. For a fixed distance that is a delay change of the same fraction in the opposite direction: at 5 m and 20 °C the delay is 14.568 ms, and at 25 °C it is 14.445 ms. The difference is 0.123 ms, which is 42 mm of path.

So a five-degree error in the assumed temperature moves a five-metre alignment by about four centimetres. In a room where the air at the microphone is 26 °C while the mixing position is 21 °C, that is a real offset rather than a rounding error. It is also why a measurement made in a cold room and a correction applied in a warm one will disagree in a way that looks like a bad microphone.

The corrections that follow from this are straightforward. Use the actual air temperature where the sound travels, not the thermostat's reading. Prefer relative measurements over absolute ones — an impulse response already contains the correct delay, so if you can measure it, measure it. And if you must predict, state the temperature you assumed, because a delay figure without one is unreproducible.

Humidity, pressure and the rest

Humidity matters far less than temperature but not nothing: saturated air at 20 °C is about 0.36% faster than dry air, which is 0.05 ms over five metres — a millimetre or two of path, well below placement tolerance. It becomes worth including in high-precision outdoor work and in any measurement where the air is deliberately humidified.

Pressure is the parameter people expect to matter and it does not. In the ideal-gas relation, density falls in proportion to pressure, and the two effects cancel: sound speed depends on temperature and gas composition, not on the barometer. A change from a high-pressure day to a low-pressure one moves the speed of sound by less than 0.01%.

What does matter, and is often forgotten, is wind and air movement. Sound travelling with the airflow is faster and against it slower, which is why outdoor measurements drift and why a measurement made with a fan running is not reproducible. This calculator does not model it, because a steady airflow is not a property of the air but of your specific geometry.

Where this shows up in practice

• Loudspeaker and subwoofer alignment. The delay between two sources is a path difference; at 5 m and 20 °C that is 699 samples at 48 kHz, round to 699 or 700 depending on which side you would rather be wrong on.
• Crossovers between a horn and a cone. The acoustic centres are not where the boxes suggest, so the prediction is a starting point and the measurement is the answer.
• Microphone arrays and beamforming. The steering delays are computed from the same c, and a 1% error in c is a 1% steering error — for a 16-element array at 4 kHz that is enough to move a null noticeably.
• Distance measurement by echo. Time a reflection and convert. The error contribution from temperature is the dominant one over any real distance, so measure the temperature as well.
• Room modes. The wavelength scaling with temperature means room mode frequencies drift slightly with the weather — a 0.17% shift is 0.4 Hz at 230 Hz, which is below the practical resolution of the measurement but real.

Five mistakes worth avoiding

1. Using 343 m/s without stating a temperature. It is 331.3 m/s at 0 °C and 355 m/s at 35 °C; the single number hides a 7% range.
2. Confusing round trip with one way. An echo measurement double-counts the path; a delay setting does not.
3. Rounding samples before combining. Sum the times first, then round once, or the errors accumulate with every stage.
4. Assuming whole samples are enough. At 44.1 kHz a sample is 7.8 mm, which is fine for placement but not for driver alignment.
5. Ignoring airflow. A steady wind is a bias that looks exactly like a wrong speed of sound, and it changes when the fan does.

Summary

Convert through time, not distance: work out the delay in seconds from the path and the speed of sound at the actual temperature, then multiply by the sample rate. Report the temperature with the result, and when the answer matters, measure the impulse response instead of predicting it.

Values shown are engineering aids rather than measurements; see the disclaimer and the tool index.