Logarithmic scale

A logarithmic scale is a nonlinear scale used when there is a large range of quantities. Common uses include the earthquake strength, sound loudness, light intensity, and pH of solutions.

It is based on orders of magnitude, rather than a standard linear scale, so each mark on the scale is the previous mark multiplied by a value.

Common usages

The following are examples of commonly used logarithmic scales, where a larger quantity results in a higher value:

  • Richter magnitude scale and moment magnitude scale (MMS) for strength of earthquakes and movement in the earth.
  • bel and decibel and neper for acoustic power (loudness) and electric power;
  • cent, minor second, major second, and octave for the relative pitch of notes in music;
  • logit for odds in statistics;
  • Palermo Technical Impact Hazard Scale;
  • logarithmic timeline;
  • counting f-stops for ratios of photographic exposure;
  • rating low probabilities by the number of 'nines' in the decimal expansion of the probability of their not happening: for example, a system which will fail with a probability of 10−5 is 99.999% reliable: "five nines".
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    While today’s ocean water remains basic, the pH scale is logarithmic and the drop of 0.1 units translates to about a 30 percent increase in acidity.
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