Each increase of one unit on the Richter scale represents a tenfold increase in the amplitude, but the energy released rises by about 31.6 times. Comparing earthquakes of magnitude 4.0 and 5.0, how many times more energy is released by the 5.0 earthquake?

A one-magnitude rise releases about 31.6 times more energy, so a 5.0 quake frees roughly 31 times the energy of a 4.0.

Ten times refers to the amplitude increase, not the energy increase.

Hundred times would be the amplitude change over two whole magnitude steps, not one energy step.

A rise of only 1.25 times badly understates the sharp energy jump per unit.

Each whole step multiplies both ground motion tenfold and released energy about thirty-onefold.

This logarithmic scaling is why even a small magnitude difference means a huge energy difference.