Earthquake Magnitude Calculator
Compare two earthquakes and see how much more ground motion and energy the larger one carries, convert a seismic moment to moment magnitude (or back again), or work out a Richter-style local magnitude from a seismogram amplitude and a distance. Every formula is shown with its source. Runs entirely in your browser — free, no sign-up.
Results
2.0
Magnitude difference
100
Ground-motion amplitude ratio
1,000
Energy ratio
Earthquake A has 100 times the seismogram amplitude of earthquake B and releases about 1,000 times as much energy.
Radiated energy of each earthquake
| Earthquake | Magnitude | Energy (joules) | Roughly equal to |
|---|---|---|---|
| A | 7.0 | 2.00 × 10¹⁵ | 477 kilotons of TNT |
| B | 5.0 | 2.00 × 10¹² | 477 tons of TNT |
Energy uses log₁₀E = 1.5M + 4.8 (E in joules), the Gutenberg–Richter relation. It is an estimate of radiated seismic energy, not of the damage an earthquake does.
How to Use the Earthquake Magnitude Calculator
- 1. Choose the question. Compare two earthquakes takes two magnitudes. Moment magnitude converts between seismic moment and Mw, or builds the moment from a fault's length, width and slip. Local magnitude applies Richter's method to a seismogram.
- 2. Enter your numbers. Exponents can be typed as 4e19 or 4 × 10^19. For a local magnitude, give the peak trace amplitude in millimetres and either the distance in kilometres or the S−P time in seconds.
- 3. Read the results. The cards show the ratios, magnitudes and moments; the working lists every substitution so you can copy the steps into a lab report.
- 4. Mind the scale. Energy comes from log₁₀E = 1.5M + 4.8, and the local magnitude uses a Southern California calibration — the notes under each result say what each one assumes.
What a Magnitude Number Means
Earthquake magnitude is a logarithmic scale. Each whole-number step is a tenfold increase in the amplitude of the ground motion recorded on a seismogram, and roughly 32 times more energy released — the USGS gives both figures. The energy factor comes from the Gutenberg–Richter relation log₁₀E = 1.5M + 4.8, with E in joules, so one unit is 10^1.5 = 31.6. A magnitude 7.0 therefore releases about 2.00 × 10¹⁵ joules, close to 477 kilotons of TNT, while a magnitude 5.0 releases a thousandth of that.
| Magnitude difference | Amplitude ratio | Energy ratio |
|---|---|---|
| 0.5 | 3.16 | 5.62 |
| 1.0 | 10 | 31.6 |
| 2.0 | 100 | 1,000 |
| 2.5 | 316 | 5,623 |
Amplitude ratio = 10^Δ; energy ratio = 10^(1.5Δ), where Δ is the difference in magnitude.
Radiated energy is not the same as damage. How hard the ground shakes at a site depends on depth, distance, the rock and soil underneath, and the direction in which the fault ruptured. Seismologists report that separately, as shaking intensity.
Moment Magnitude (Mw)
Moment magnitude is the scale seismologists use for anything but the smallest earthquakes, because it does not saturate for great earthquakes. It starts from the seismic moment, M₀ = μ × A × D: the rigidity of the rock (μ, about 30 gigapascals in typical crust), the area of the fault that slipped (A) and the average slip (D). Hanks and Kanamori (1979) defined Mw so that it matches older scales where they overlap. In SI units, Mw = ⅔ (log₁₀M₀ − 9.1) with M₀ in newton-metres — the form USGS publishes. In the original centimetre-gram-second units, the same formula is Mw = ⅔ log₁₀M₀ − 10.7 with M₀ in dyne-centimetres; converting 10.7 exactly gives 9.05, which is why you will meet both 9.05 and 9.1 in textbooks.
Worked example: a fault that slipped 2 m
Rigidity 30 GPa, rupture 100 km long × 20 km wide, average slip 2 m.
M₀ = 30 × 10⁹ Pa × (100 km × 20 km = 2 × 10⁹ m²) × 2 m = 1.20 × 10²⁰ N·m.
Mw = ⅔ (log₁₀(1.20 × 10²⁰) − 9.1) = 7.32.
Going the other way, a Mw 7.0 earthquake has a seismic moment of 3.98 × 10¹⁹ N·m, or 3.98 × 10²⁶ dyne·cm. The calculator also prints USGS's rough energy estimate from moment magnitude, log₁₀E = 5.24 + 1.44 Mw, beside the Gutenberg–Richter value, so you can see how much the two differ.
Richter Local Magnitude (ML)
Charles Richter's 1935 scale compares the peak amplitude A on a Wood-Anderson seismograph with the amplitude A₀ that a reference earthquake of magnitude 0 would give at the same distance: ML = log₁₀A − log₁₀A₀(r). Richter fixed the scale by defining 1 mm of trace at 100 km as ML 3.0. This calculator uses the distance correction Hutton and Boore (1987) fitted for Southern California: ML = log₁₀A + 1.110 log₁₀(r/100) + 0.00189 (r − 100) + 3.0, with A in millimetres and r the distance from the focus in kilometres. It reduces to Richter's definition at 100 km.
Worked example: a 12 mm trace at 85 km
log₁₀(12) = 1.079.
Correction = 1.110 × log₁₀(85/100) + 0.00189 × (85 − 100) + 3.0 = 2.893.
ML = 1.079 + 2.893 = 3.97.
If you have the S−P time instead of a distance, the calculator multiplies it by 8 km per second, the usual rule of thumb for crustal earthquakes; you can change that factor. The formula was fitted to data between about 10 and 700 km, and the calculator warns you outside that range. Local magnitudes from other regions use their own corrections, so treat a Southern California formula applied elsewhere as an estimate.
Frequently Asked Questions
- How much more energy does a magnitude 8 earthquake release than a magnitude 7?
- About 32 times more. Energy grows by 10^1.5 = 31.6 for every whole magnitude unit, while the recorded ground-motion amplitude grows by 10. Two units apart is about 1,000 times the energy and 100 times the amplitude.
- What is the difference between the Richter scale and the moment magnitude scale?
- The Richter scale (ML) is measured from the peak amplitude on a particular kind of seismograph at a known distance, so it saturates around magnitude 7 and is tied to its regional calibration. Moment magnitude (Mw) is derived from the physical size of the rupture — rigidity, fault area and slip — and stays accurate for the largest earthquakes. News reports now almost always quote Mw.
- Is a magnitude 6 earthquake twice as big as a magnitude 3?
- No. Magnitude is logarithmic, so a 3-unit gap is a factor of 1,000 in amplitude and about 32 thousand in energy. Dividing magnitudes is a common mistake; always compare the difference.
- Can an earthquake have a negative magnitude?
- Yes. The scale has no lower limit, and sensitive instruments record microearthquakes below zero — for example, ML −1 means an amplitude ten times smaller than ML 0 at the same distance. Magnitude 0 is not the absence of an earthquake.
- Why does the moment magnitude formula use 9.1 or 10.7?
- They are the same relation in different units. With seismic moment in dyne-centimetres, Hanks and Kanamori's constant is 10.7; with moment in newton-metres, it becomes 9.05 by exact conversion, and USGS publishes 9.1. The difference is 0.03 magnitude units — far below what anyone can measure.
- What is seismic moment?
- Seismic moment, M₀, is the fundamental measure of an earthquake's size: rigidity of the rock times the area that ruptured times the average slip, in newton-metres. Doubling the slip on the same fault doubles M₀, which raises Mw by ⅔ log₁₀2 = 0.2.