The loudness converter gives the loudness in sones of sounds specified in phons, the loudness ratio between two sounds and the phon level that matches a loudness in sones.
How the calculation works
- Enter the loudness level of the two sounds in phons.
- Enter a loudness in sones.
- Read the sones, the ratio and the phons.
Example
A sound at 60 phons has a loudness of 2^((60 − 40) / 10) = 4.00 sones and a sound at 70 phons has 2^((70 − 40) / 10) = 8.00 sones, so the second is 2.00 times as loud. A loudness of 16 sones corresponds to 40 + 10 × log₂(16) = 80.0 phons.
Why it matters
The calculator helps acoustics and audio students, sound designers, environmental noise officers and anyone who wants to understand why a 10 dB louder noise is heard as twice as loud.
Good to know
The sone scale follows the law of Stevens, with a loudness that increases as a power of the sound intensity, and the exponent of about 0.3 on intensity gives the doubling per 10 phons for levels above 40 phons. Below 40 phons, the loudness grows more quickly and the formula used here is a power law with an exponent of 2.64 on the ratio of the phon values, which is the form recommended in the standards for the lower range. The equal-loudness contours of ISO 226, which link the sound pressure level to the phon level at each frequency, must be used to find the phon level of a tone that is not at 1000 Hz. For a complex noise, the loudness is computed by summing the contributions of the critical bands, using the methods of Zwicker or Moore and Glasberg, which also include the effects of masking. The phon is not an absolute scale of annoyance, and the perceived loudness depends on duration, on the listener and on the context, so a calculator gives an average trend.
Related tools
The critical band calculator treats frequency analysis, the sound localization calculator treats directional cues, the decibel addition calculator combines levels and the noise exposure calculator treats safe durations.