Earthquake Magnitude Energy Calculator (Richter and Moment Magnitude)
Convert an earthquake magnitude into the seismic energy it releases (joules, TNT, Hiroshima bombs, electricity), its seismic moment and size class, compare two magnitudes by energy and shaking amplitude, or turn an energy back into a magnitude, with the Gutenberg–Richter or USGS energy relation.
How it works
Radiated energy: log₁₀ E = 1.5 M + 4.8 (E in joules; Gutenberg–Richter / Kanamori), or log₁₀ E = 1.44 M + 5.24 (Choy & Boatwright, USGS) · Seismic moment M₀ = 10^(1.5 M + 9.1) N·m · Energy ratio = 10^(1.5 (M₁ − M₂)) · Amplitude ratio = 10^(M₁ − M₂) · 1 ton TNT = 4.184 × 10⁹ J
Magnitude is a logarithmic measure of earthquake size. Each whole step multiplies the wave amplitude recorded on a seismogram by 10 and the radiated seismic energy by 10^1.5 ≈ 31.6, so an M7 releases about 32 times the energy of an M6 and about 1,000 times that of an M5. The original Richter (local) scale of 1935 saturates above about M6.5, so agencies now report moment magnitude (Mw), which is defined from the seismic moment M₀ (rigidity × fault area × slip) as Mw = ⅔ (log₁₀ M₀ − 9.1) and agrees with Richter for small and moderate quakes. Kanamori showed that radiated energy is roughly M₀ ÷ 20,000, which gives the classic Gutenberg–Richter energy relation log₁₀ E = 1.5 M + 4.8 in joules; the USGS quotes the alternative empirical fit of Choy and Boatwright, log₁₀ E = 1.44 M + 5.24, which you can select under More options. The calculator turns magnitude into joules, tons of TNT (4.184 GJ per ton), Hiroshima bombs (about 15 kilotons) and electricity, works backwards from an energy to a magnitude, and compares two quakes. It also shows the USGS size class, the typical strongest shaking near the epicentre on the Modified Mercalli scale and how many such quakes happen each year worldwide. Energy says nothing about local damage, which depends on depth, distance, soil and construction.
Worked example
For M 6 with the default relation, log₁₀ E = 1.5 × 6 + 4.8 = 13.8, so E = 10^13.8 = 6.31 × 10¹³ J. Dividing by 4.184 × 10⁹ J per ton gives 15.08 kilotons of TNT, about 1.01 Hiroshima bombs (6.28 × 10¹³ J each) or 17.53 GWh of electricity. The seismic moment is 10^(1.5 × 6 + 9.1) = 1.26 × 10¹⁸ N·m. Compared with an M 5, the energy is 10^1.5 = 31.6× more and the shaking amplitude 10× more. M 6 is in the USGS “strong” class (6–6.9), with typical strongest shaking of VII–IX near the epicentre and about 130 such quakes a year worldwide.
Sources: USGS: Earthquake magnitude, energy release and shaking intensity · USGS: How much bigger is a magnitude 8.7 than a 5.8? · USGS: Magnitude types · Seismic magnitude scales — Wikipedia
Frequently asked questions
Why does one magnitude step mean about 32 times the energy?
Energy grows with magnitude by a factor of 10^1.5 per unit, and 10^1.5 = 31.6. Two steps are 31.6² ≈ 1,000 times. The recorded wave amplitude only grows 10 times per step, which is why people often underestimate the jump from M6 to M7.
Is this the Richter scale or moment magnitude?
Modern reports use moment magnitude (Mw). It was designed to match the Richter local magnitude for small and moderate quakes but, unlike Richter, does not saturate for large ones. The energy relation applies to moment magnitude, so use the magnitude the USGS or your national agency reports.
How many atomic bombs is an earthquake?
With 1 ton of TNT = 4.184 GJ and the Hiroshima bomb at about 15 kilotons, an M6 releases about one Hiroshima bomb of seismic energy, an M7 about 32 and an M9 about 32,000. The comparison is only about energy; an explosion releases it in a fraction of a second at a point, an earthquake over seconds to minutes along a fault.
How many small earthquakes equal one big one?
Divide the energies: it takes about 32 M5 quakes, 1,000 M4 quakes or 31,600 M3 quakes to release the energy of one M6. That is why small quakes cannot “relieve” enough stress to prevent a large one.
What is the biggest earthquake ever recorded?
The 1960 Valdivia, Chile earthquake at Mw 9.5. With log₁₀ E = 1.5 M + 4.8 it released about 1.1 × 10¹⁹ J, roughly 2,700 megatons of TNT, about 180,000 times the energy of an M6.
What magnitude is dangerous?
There is no single threshold. Quakes below M4 are rarely damaging; M5–6 can damage weak buildings near the epicentre; M7 and above can cause widespread destruction. A shallow quake under a city is far more dangerous than a deep or distant one of the same magnitude.
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This calculator is for educational purposes. Double-check important results before acting on them.