How this instrument works
The Gutenberg-Richter magnitude-energy relation converts an earthquake's magnitude into an estimate of the total seismic energy it radiated, expressed in joules. The relation is log₁₀(E) = 4.8 + 1.5M, where M is the earthquake's magnitude and E is energy in joules — rearranged, that gives E = 10^(4.8 + 1.5M), the formula this calculator applies directly.
Because the exponent on the magnitude term is 1.5, every whole-number step up multiplies the energy released by 10^1.5, about 31.6 times. That's why the scale feels deceptively gentle on paper: going from a 7.0 reading to a 6.0 one doesn't mean 'one-seventh less' energy, it means roughly 31.6 times less, and dropping from an 8.0 to a 6.0 means roughly 1,000 times less — two whole steps compounding to 31.6 × 31.6.
Modern seismology mostly reports moment magnitude (Mw), calculated from the physical size of a fault rupture, rather than the original 1930s Richter local magnitude (ML), which saturates and loses accuracy for very large earthquakes. The two scales are calibrated to agree closely for most events, which is why this energy relation applies regardless of which scale a report originally used. Note too that this figure is total radiated seismic energy at the source, not the shaking intensity felt at any one location, which depends heavily on distance, depth, and local ground conditions.
- Enter Earthquake magnitude — the reported value on the Richter or moment scale.
- Read Seismic energy released — the estimated energy radiated by the earthquake, in joules.
- Run the calculator twice with two different readings and compare the results directly to see exactly how many times more energy the larger earthquake released.
Worked example — a magnitude 6.0 earthquake
Enter 6.0 into Earthquake magnitude. Seismic energy released reads 63,095,734,448,000 joules, about 6.31 × 10^13 J: 10^(4.8 + 1.5 × 6.0) = 10^13.8.
For comparison, a 7.0 earthquake — one whole point higher on the scale — releases roughly 1.995 × 10^15 joules, about 31.6 times more energy than the 6.0 quake above, even though the reading itself only went up by 1.
Questions
Why does one point on the scale mean so much more energy?
Because the scale is logarithmic with a 1.5 exponent on energy, so each whole-number increase multiplies released energy by about 31.6× (10^1.5). An 8.0 earthquake releases roughly 1,000 times more energy than a 6.0 one — two whole steps compounding to about 31.6 × 31.6 — not merely 'two units more' the way the numbers might suggest at a glance.
Is this the same as how strong the shaking feels?
No — this figure is the total seismic energy radiated at the earthquake's source, not the shaking intensity felt at any particular location. Felt intensity depends heavily on distance from the epicenter, depth of the rupture, and local ground conditions, so two people a few kilometers apart during the same earthquake can experience very different shaking despite it having one single size rating and one single energy release.
What's the difference between Richter magnitude and moment magnitude?
Richter local magnitude (ML) was the original 1930s scale and loses accuracy — it 'saturates' — for very large earthquakes. Moment magnitude (Mw) is the modern standard, calculated from the physical size and slip of the fault rupture rather than a single seismograph reading. The two scales are calibrated to give similar numbers for most earthquakes, which is why this energy relation is commonly applied to either.
How much more energy does a 7.0 earthquake release than a 5.0?
About 1,000 times more. Going from 5.0 to 7.0 is two whole steps on the scale, and each step multiplies energy by roughly 31.6×, so two steps compound to about 31.6 × 31.6 ≈ 1,000×. Using this calculator's own figures, a 5.0 quake works out to about 2.00 × 10^12 joules and a 7.0 quake to about 2.00 × 10^15 joules — a thousandfold difference.
Where do the formula's constants, 4.8 and 1.5, come from?
They're empirically fitted values from the Gutenberg-Richter relation, developed by seismologists Beno Gutenberg and Charles Richter by comparing measured seismic wave energy against recorded readings across many real earthquakes. They aren't derived from first-principles physics alone — they're calibrated constants chosen to match observed data as closely as possible.