Earthquake Magnitude & Energy Calculator
Turn an earthquake’s magnitude into the energy it released. Get joules, tonnes of TNT and seismic moment, work out moment magnitude from a fault’s size and slip, and compare two earthquakes.
How to Use
- Pick a mode: From magnitude, From seismic moment, From fault slip, or Compare two earthquakes.
- Enter a moment magnitude (Mw), a seismic moment in N·m or dyne·cm, or the fault’s length, width, slip and rigidity (30 GPa is a common value for crustal rock).
- In From fault slip, use Find to choose the unknown: the magnitude from a given slip, or the average slip a target magnitude needs.
- Read the radiated energy in joules and tonnes of TNT, the seismic moment and the magnitude. The answer field and the first readout are highlighted.
- See the earthquake on the magnitude scale beside historic quakes and TNT marks, and check Show Work for each step.
Worked Example
The 2011 Tōhoku earthquake. The USGS gives it Mw 9.1. Its seismic moment is M₀ = 10^(1.5 × 9.1 + 9.1) = 10^22.75 = 5.623 × 10²² N·m, and the radiated energy is log₁₀ E = 1.5 × 9.1 + 4.8 = 18.45, so E = 2.818 × 10¹⁸ J. Dividing by 4.184 × 10⁹ J per tonne of TNT gives 673.6 megatonnes.
Tōhoku against San Francisco 1906. The magnitudes differ by 9.1 − 7.9 = 1.2. The energy ratio is 10^(1.5 × 1.2) = 10^1.8 = 63.10, and the ratio of seismogram amplitudes is 10^1.2 = 15.85.
The common mistake: treating magnitudes as a linear scale, or one step as ten times the energy. A magnitude 8 is not twice a magnitude 4: the difference of 4 is 10^(1.5 × 4) = 1,000,000 times the energy. And a magnitude 7 releases 31.62 times the energy of a 6, not 10 times; the factor of 10 is for the amplitude of the shaking on a seismogram.
Show Work
Formulas
From Richter to Moment Magnitude
Charles Richter, working with Beno Gutenberg at Caltech, published the first magnitude scale in 1935 for southern California earthquakes: the logarithm of the largest swing on a standard Wood–Anderson seismometer, corrected for distance. The logarithm is why each step is a factor of ten in amplitude. In 1956 Gutenberg and Richter linked magnitude to energy with log E = 11.8 + 1.5M in ergs, which is the 4.8 + 1.5M in joules used here.
Scales based on wave amplitude saturate for the biggest earthquakes, because a long rupture keeps adding energy at periods the instruments do not measure. Keiiti Aki defined the seismic moment in 1966, a direct measure of the size of the fault slip, and Hiroo Kanamori built the moment magnitude on it in 1977, with Thomas Hanks and Kanamori giving the general form in 1979. The IASPEI (International Association of Seismology and Physics of the Earth’s Interior) standard of 2013 fixes the constant at 9.1 for M₀ in N·m.
Magnitudes for the preset earthquakes are from the USGS earthquake catalogue: 9.5 for Chile in 1960, the largest ever recorded, 9.1 for Tōhoku in 2011 and 7.9 for San Francisco in 1906. The energy relation is an average: individual earthquakes of the same magnitude can radiate several times more or less energy, so treat the joule and TNT figures as estimates.
About This Tool
This calculator turns a moment magnitude into radiated energy, TNT equivalent and seismic moment; turns a seismic moment into a magnitude, with the older Hanks–Kanamori constant for comparison; finds the magnitude a fault’s size and slip produce, or the slip a target magnitude needs; and compares two earthquakes’ energy and shaking. It places each earthquake on a magnitude scale beside historic quakes and TNT marks, or draws the fault with its length, width and slip.
Everything runs in your browser; nothing you enter is sent anywhere.
Related tools: Logarithm Calculator, pH Calculator, and Nuclear Binding Energy Calculator.
Frequently Asked Questions
How much energy does an earthquake release?
Gutenberg and Richter’s energy relation, log₁₀ E = 1.5M + 4.8 with E in joules, gives the energy radiated as seismic waves. A magnitude 5.0 releases 1.995 × 10¹² J, about 476.9 tonnes of TNT; a 7.0 releases 1.995 × 10¹⁵ J (476.9 kilotonnes); the Mw 9.1 Tōhoku earthquake of 2011 released about 2.818 × 10¹⁸ J, or 673.6 megatonnes.
How much bigger is each step on the magnitude scale?
Each whole step multiplies the shaking amplitude on a seismogram by 10 and the energy by 10^1.5 = 31.62. Two steps are 1,000 times the energy, and even 0.1 is 1.413 times. The 1960 Chile earthquake (9.5) released 3.981 times the energy of Tōhoku (9.1), although the numbers differ by only 0.4.
What is moment magnitude?
It is the magnitude seismologists use for large earthquakes, based on the seismic moment M₀ = μAD: rock rigidity times fault area times average slip. Then Mw = ⅔(log₁₀ M₀ − 9.1) with M₀ in N·m, the IASPEI standard form. A 20 km × 10 km fault slipping 1 m in 30 GPa rock has M₀ = 6 × 10¹⁸ N·m, which is Mw 6.452.
Is moment magnitude the same as the Richter scale?
They are set to agree for moderate earthquakes, but Richter’s 1935 local magnitude is read from the peak swing of one kind of seismometer and stops growing for the largest quakes: it saturates. Moment magnitude keeps growing with the fault size, so it is the one quoted for great earthquakes, such as USGS’s Mw 9.1 for Tōhoku (the Japan Meteorological Agency gives 9.0) and Mw 7.9 for San Francisco in 1906.
How far must a fault slip to make a magnitude 7 earthquake?
Mw 7.0 needs a seismic moment of 10^(1.5 × 7 + 9.1) = 3.981 × 10¹⁹ N·m. On a fault 50 km long and 15 km deep in 30 GPa rock (an area of 7.5 × 10⁸ m²), the average slip is 3.981 × 10¹⁹ ÷ (3 × 10¹⁰ × 7.5 × 10⁸) = 1.769 m.
How do I use the Earthquake Magnitude & Energy Calculator?
Just type your numbers. The answer shows up right away — there is no button to press. Change anything and it updates by itself.
Does it cost anything or need an account?
No. The tool is completely free, there is no account to create, and it keeps working offline after the page first loads.
Is anything I type uploaded?
No. The tool works entirely on your device, so the values you enter never leave your browser.
Common Use Cases
Comparing earthquakes
Tōhoku (9.1) against San Francisco 1906 (7.9): a difference of 1.2 means 63.10 times the energy and 15.85 times the shaking amplitude.
Making sense of news reports
A magnitude 6.0 releases about 6.31 × 10¹³ J, the energy of 15.08 kilotonnes of TNT.
Fault scenarios
Find the average slip a target magnitude needs: Mw 7.0 on a 50 km × 15 km fault in 30 GPa rock needs 1.769 m.
Seismic moment catalogues
Convert a moment tensor result to a magnitude: M₀ = 10²⁰ N·m is Mw 7.267, or 7.300 with the older Hanks–Kanamori constant.
Teaching logarithms
Show why a 0.1 change matters: it is 1.413 times the energy, so a 6.5 releases 5.623 times as much as a 6.0.
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