Earthquake Calculator

Compare two earthquake magnitudes with the Gutenberg-Richter energy relation to see how many times greater the shaking amplitude and the radiated energy are, in joules and TNT-equivalent tons.

Quick Facts

Formula
Gutenberg-Richter energy-magnitude relation
log10(E) = 1.5M + 4.8, with E in joules — each whole magnitude point is about 31.6× more energy and 10× more shaking amplitude.

Your Results

Calculated
Magnitude difference
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Mw(B) minus Mw(A)
Shaking amplitude ratio
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10^(difference) — relative peak ground motion
Energy release ratio
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10^(1.5 × difference) — relative seismic energy
Energy released (Earthquake B)
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Gutenberg-Richter estimate, in joules

Ready

Enter two earthquake magnitudes and press Calculate.

Understanding the Earthquake Magnitude Comparison Calculator

The magnitude scales used to size earthquakes — the original Richter local-magnitude scale and the moment magnitude (Mw) scale seismologists use today — are logarithmic, not linear. A difference of just one or two points on the scale corresponds to a huge difference in shaking and energy. This calculator applies the standard Gutenberg-Richter energy-magnitude relation to two magnitudes you enter and reports the amplitude ratio, the energy ratio, and the total energy released by the larger event.

The formulas

Two relationships, both from the work of Beno Gutenberg and Charles Richter, describe how the scale behaves:

  • Amplitude ratio: because the magnitude scale is base-10 logarithmic in peak ground-motion amplitude, two earthquakes whose magnitudes differ by ΔM = MB − MA differ in amplitude by a factor of 10ΔM. A one-point increase means about 10× the amplitude recorded on a seismometer.
  • Energy ratio: radiated seismic energy scales faster than amplitude. The energy ratio between the two earthquakes is 101.5 × ΔM, so each whole magnitude point is roughly 31.6× more energy, and two points is roughly 1,000× more energy.
  • Absolute energy: the Gutenberg-Richter energy-magnitude relation (1956) estimates the seismic energy radiated by a single earthquake of magnitude M as log10(E) = 1.5M + 4.8, with E in joules. This calculator applies it to Earthquake B to give a concrete energy figure, then converts it to TNT-equivalent tons using 4.184 × 109 joules per ton of TNT.

Why a "small" number is a big deal

Because the scale is logarithmic, small differences compound quickly: a magnitude 7.0 earthquake releases about 31.6 times the energy of a 6.0, roughly 1,000 times the energy of a 5.0, and about 31,600 times the energy of a 4.0. Moving from magnitude 6.5 to 7.5 is not a modest increase — it represents roughly 32 times more energy released at the source.

What this calculator does not model

Magnitude measures the energy released at the earthquake's source. It does not, by itself, tell you how strongly the ground shakes at a particular location — that depends on distance from the epicenter, depth of rupture, local soil conditions, and building design. Those effects are captured by separate intensity scales, like the Modified Mercalli Intensity scale, and by ground-motion attenuation models, not by magnitude alone.

Frequently Asked Questions

What is the Gutenberg-Richter formula?
It is the energy-magnitude relation published by Beno Gutenberg and Charles Richter: log10(E) = 1.5M + 4.8, where E is the radiated seismic energy in joules and M is the earthquake's magnitude. It converts a magnitude into an approximate energy figure and lets you compare energy between earthquakes of different sizes.
How much stronger is a magnitude 7 earthquake than a magnitude 6?
One whole point on the magnitude scale means about 10 times the peak ground-motion amplitude and about 31.6 times (10^1.5) the radiated energy. So a magnitude 7 releases roughly 31.6 times more energy than a magnitude 6, and about 1,000 times more than a magnitude 5.
Is moment magnitude the same as the Richter scale?
They are closely related but not identical. The original Richter (local magnitude) scale was developed for Southern California seismometers and saturates for very large earthquakes. Moment magnitude (Mw), based on the physical seismic moment of the fault rupture, is what seismologists now use for medium-to-large earthquakes, and it is calibrated to give similar numbers to the classic Richter scale for the events Richter originally measured. This calculator's formulas apply to either scale in the ranges they are commonly quoted.
Does a higher magnitude always mean more damage at your location?
No. Magnitude measures energy released at the earthquake's source, not shaking intensity at a given place. Distance from the epicenter, depth of rupture, local soil and geology, and building construction all affect how strongly a specific location shakes and how much damage results — which is why separate intensity scales, like the Modified Mercalli Intensity scale, exist to describe felt effects.

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