How this calculator works
Magnitude describes the size of the seismic source, not the damage at a particular place. The Gutenberg-Richter energy relation links a surface-wave or local magnitude to the radiated seismic energy: each whole number adds about 1.5 to the base-10 logarithm of energy, which is the same as multiplying energy by about 31.6. That is why a magnitude 7 event releases roughly 32 times the energy of a magnitude 6 event, even though the ground motion only rises by a factor of 10. The comparison mode uses the same relation to report both ratios.
Formula
log10(E) = 1.5 M + 4.8, with E in joules, so E = 10^(1.5M + 4.8). TNT equivalent in tonnes = E / 4.184 x 10^9 J per tonne of TNT. Hiroshima equivalents = E / (15,000 tonnes x 4.184 x 10^9 J). For two magnitudes, energy ratio = 10^(1.5(M2 - M1)) and amplitude ratio = 10^(M2 - M1).
Worked example
A magnitude 6 earthquake releases 10^(1.5 x 6 + 4.8) = 10^13.8 = 6.31 x 10^13 J. That is 6.31 x 10^13 / 4.184 x 10^9 = 15,080 tonnes of TNT, or about 1.01 Hiroshima bombs. A magnitude 7 event releases 2.00 x 10^15 J, which is 31.6 times more energy and about 31.8 Hiroshima bombs.
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Frequently asked questions
Is this the Richter scale?
The energy relation grew out of the Richter and Gutenberg work and is still used as a convenient approximation. Modern reports usually quote moment magnitude, which is calibrated to agree with older magnitudes over most of the range. The energy estimate should be treated as an order-of-magnitude guide.
Why does the USGS show a different energy formula?
Several empirical relations exist. The USGS energy magnitude page uses log E = 5.24 + 1.44 Mw, while the older Gutenberg-Richter relation used here is log E = 1.5 M + 4.8. They differ by tens of percent, which is small on a scale that spans many orders of magnitude.
How much bigger is a magnitude 9 than a magnitude 5?
The difference is four magnitude units. Energy rises by 10^(1.5 x 4) = 10^6, one million times, and ground motion by 10^4, ten thousand times. The comparison mode reports both factors directly.
What is a Hiroshima bomb in this calculator?
It uses the common convention of 15 kilotons of TNT for the 1945 Hiroshima bomb, or 6.276 x 10^13 J. Weapon yields and the fraction of energy that becomes seismic waves vary, so the number is a rough scale comparison, not a prediction of damage.