Earthquake magnitude scales: Richter, moment magnitude and intensity

An earthquake magnitude is a logarithmic measure of size: each whole step up means about 10 times more ground-motion amplitude on a seismogram and about 32 times more energy released. So a magnitude 7 is not slightly bigger than a 6; it releases roughly 32 times the energy, and a magnitude 8 roughly 1,000 times. The numbers most news reports quote today are moment magnitudes (Mw), not the original Richter scale. I built the earthquake magnitude calculator to make those jumps concrete, and this guide explains what sits behind them.

A logarithmic scale

A logarithmic scale counts in multiplications rather than additions. On the original Richter scale, a magnitude is the base-10 logarithm of the largest wave amplitude recorded by a standard seismograph, corrected for distance. Ten times the amplitude adds one to the magnitude; a hundred times adds two. That is why magnitudes can be negative: a tremor with a tenth of the amplitude of a magnitude 0 is rated −1. If logarithms feel slippery, the log calculator lets you check that log₁₀ of 1,000 is 3, and Scientific notation explained, with e-notation and engineering notation covers the powers of ten that these numbers turn into.

Amplitude versus energy

Amplitude and energy grow at different rates. The energy released rises by a factor of 10 to the power 1.5 per magnitude step, which is 31.6, usually rounded to 32. The steps multiply:

• +0.2 magnitude ≈ 2 × the energy (10 to the power 0.3 ≈ 1.995);
• +1 magnitude ≈ 32 × the energy and 10 × the amplitude;
• +2 magnitudes = 1,000 × the energy and 100 × the amplitude;
• +3 magnitudes ≈ 31,600 × the energy.

To put absolute numbers on it, the calculator uses the Gutenberg–Richter energy relation, log₁₀ E = 1.5M + 4.8 with E in joules. A magnitude 6 comes out at about 6.3 × 10¹³ J, roughly 15 kilotons of TNT, similar to the Hiroshima bomb. A magnitude 9 is about 2 × 10¹⁸ J, around 480 megatons. Very large numbers like these are easier to read in powers of ten, which is why the scientific notation converter is handy alongside it.

From Richter to moment magnitude

Charles Richter introduced his scale in 1935 for local earthquakes in southern California, using the Wood–Anderson seismograph. It worked well for moderate, nearby quakes but had a known flaw: for very large earthquakes the measured waves stop growing in proportion to the earthquake, so the scale saturates and underestimates the biggest events. Later body-wave and surface-wave scales shared the problem.

The moment magnitude scale, defined by Thomas Hanks and Hiroo Kanamori in 1979, fixes this by starting from the seismic moment: the rigidity of the rock multiplied by the area of the fault that slipped and the average distance it slipped. That is a physical measure of the whole rupture, so it does not saturate. It was calibrated to match Richter values in the range where both work, which is why a news report can loosely say "Richter" while actually quoting Mw. The USGS uses moment magnitude for almost all earthquakes now, keeping local magnitude mainly for small, locally recorded ones.

Magnitude is not intensity

Magnitude describes the earthquake at its source and has one value per event. Intensity describes the shaking and damage at a particular place, and varies from town to town. The Modified Mercalli Intensity scale uses Roman numerals, from I (not felt) up through levels where buildings are destroyed, based on observed effects rather than a formula. A magnitude 6 directly under a city with weak buildings can cause far more damage than a magnitude 7 deep beneath a remote area. Depth, distance, local soil and building standards matter at least as much as the headline number, which is why I show typical effects in the calculator only as a rough guide.

Comparing two earthquakes

Enter two magnitudes in the calculator and it shows how many times more energy and amplitude the larger one has, the energy of each in joules and TNT, and a typical description. Some useful comparisons:

• A 7.0 against a 6.0: about 32 times the energy, 10 times the amplitude.
• A 9.1 against a 9.5: the 9.5 releases about 4 times as much energy, despite the small-looking gap.
• A 5.0 against a 7.0: the 7.0 releases 1,000 times the energy.

Two cautions. First, magnitude estimates are often revised in the hours after an event as more data arrives, so a first report of 7.2 can become 7.4. Second, energy figures from these relations are approximations; seismologists also define a separate energy magnitude (Me) for that reason. For everyday comparisons, though, the 10-times amplitude and 32-times energy rule is the right mental model.