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When news reports say an earthquake was "magnitude 6", most people imagine a scale like a ruler, where 6 is a bit more than 5. It is not. Charles Richter built the magnitude scale on a logarithm, and once you see his definition the numbers start to mean something. This post covers who he was, how his 1935 scale works, his own worked example, and the mistakes students make with it.
Who was Charles Richter?
A tribute by Clarence Allen in the Bulletin of the Seismological Society of America records that Richter was born on a farm in Ohio in 1900, took his A.B. at Stanford in 1920 and his Ph.D. at Caltech in 1928, and spent almost his whole career at the Seismological Laboratory in Pasadena. He died in 1985. Allen writes that Richter is best known for introducing the word "magnitude" into seismology and for the local magnitude scale, and he rates Richter's 1958 book Elementary Seismology as his greatest contribution.
What problem was Richter solving?
Before 1935, earthquakes were compared by intensity: how strongly people felt them and how much damage they did. In his paper An Instrumental Earthquake Magnitude Scale (1935), Richter points out the flaw. In southern California many shocks happen in almost unpopulated areas or under the sea, so felt reports say little about the earthquake itself. He wanted a number based "directly on instrumental indications". He credits H. O. Wood with suggesting the word "magnitude", to distinguish it from intensity.
How did Richter define magnitude?
Richter's definition is precise. The magnitude of a shock is "the logarithm of the maximum trace amplitude, expressed in microns, with which the standard short-period torsion seismometer ... would register that shock at an epicentral distance of 100 kilometers."
So a shock that would write a trace of 1 micron (0.001 mm) at 100 km is magnitude 0. Richter stresses that 0 does not mean "no shock"; it is just the reference shock. A shock of magnitude 1 has ten times the recorded amplitude, magnitude 2 has 100 times, and so on.
Real seismographs are rarely exactly 100 km away, so he published a table of how the reference shock's amplitude falls with distance. To find a magnitude, you take log of the measured amplitude and subtract the table value for that distance.
Worked example: using the definition
Richter's paper gives a real case: the shock of 15 February 1932, recorded with an amplitude of 3 mm at a station 100 km away.
At 100 km, the reference shock writes 0.001 mm, so the table value is log 0.001 = −3.
log 3 = 0.477.
Magnitude = 0.477 − (−3) = 3.48.
Richter lists exactly 3.48 for that station. Five other stations, from 39 km to 345 km away, gave magnitudes from 3.13 to 3.54, a spread of only 0.41, which he found "surprisingly small".
Now compare two earthquakes. A magnitude 6 and a magnitude 4 differ by 2 units, so the amplitudes differ by 10² = 100 times.
Energy is different. The US Geological Survey says each whole-number step means a tenfold increase in measured amplitude but about 32 times more energy release. Two steps therefore mean about 32 × 32 ≈ 1,000 times the energy, since 32 is close to 10^1.5. Richter's 1935 paper assumed amplitude ratio was the square root of energy ratio, which would make it 100 times per step; Gutenberg later related magnitude to energy directly, and the 32-times figure is what USGS gives today.
If logarithms are rusty, our post on John Napier and logarithms shows why they turn huge ratios into small, usable numbers.
What mistakes do students make?
Reading magnitude as linear. Magnitude 6 is not "50 percent bigger" than 4; its amplitude is 100 times larger.
Using amplitude and energy interchangeably. One step is 10 times the amplitude but about 32 times the energy.
Confusing magnitude with intensity. One earthquake has one magnitude; intensity, which NCERT's Interior of the Earth chapter describes on the Mercalli scale from 1 to 12, varies from place to place.
Assuming the Richter scale is still the standard. USGS says the original local scale is now mainly used for small, locally recorded earthquakes; for others it uses moment magnitude, based on the fault area, the slip and the rock's rigidity.
When a log calculation keeps going wrong, the Fermi Problem Library has worked problems with a step-by-step solver that explains the reasoning rather than printing an answer.
What role did Beno Gutenberg play?
Richter's paper tests the scale on twenty-one well-recorded earthquakes that Gutenberg had studied. The NAS memoir of Gutenberg says Gutenberg influenced the 1935 paper, and that the two men extended magnitude to distant and deep earthquakes. The local scale was mainly Richter's. You can read more in our post on Beno Gutenberg and the depth of Earth's core.
What can students learn from Richter's way of working?
Richter accepted that "precision in this matter was neither expected nor required" and still made the rule exact. He tested it across many stations and reported the spread honestly. That is a good model for any measurement: define it clearly, check it independently, and say how uncertain it is.
Try one now: a shock writes 20 mm at 100 km. Work out its magnitude, then the magnitude of a shock with one-tenth that amplitude.
