The earthquake magnitude calculator above applies the published relations that connect seismic moment, moment magnitude, local magnitude and radiated energy. It is a teaching and conversion tool for earthquakes already recorded. It describes nothing about the future, and nothing on this page should be read as saying anything about what will happen anywhere.
Arb Digital publishes free physics calculators that name the convention they use, and earthquake magnitude needs that more than most subjects. There is no single quantity called "the magnitude". There are several scales, each defined by a different published relation, each with a range where it works and a range where it does not, and they are routinely quoted as though they were interchangeable. This page keeps them separate and says which one it is computing.
What This Earthquake Magnitude Calculator Does
It runs in three directions. Given a seismic moment in newton-metres, it returns the moment magnitude Mw. Given a peak amplitude on a Wood-Anderson response and an epicentral distance, it returns a local magnitude ML of the kind Richter originally defined. Given a magnitude published by a seismological agency, it returns the seismic moment and the radiated energy that correspond to it.
Alongside the headline figure it compares the event with a second magnitude you supply, showing the ratio in ground-motion amplitude and the ratio in radiated energy. Those are very different numbers for the same magnitude difference, and confusing them is the most common error people make with this subject.
How to Use It
- Choose what you are starting from. A seismic moment, a recorded amplitude with a distance, or a magnitude someone has already published.
- Enter that quantity. Seismic moment accepts scientific notation directly, which you will need, because moments span many orders of magnitude.
- Set the comparison magnitude to whichever event you want the ratios measured against.
- Read the headline magnitude and check which scale it is labelled as. The label changes with the mode, because the scales are genuinely different.
- Read the two ratios separately. The amplitude ratio and the energy ratio answer different questions and are never the same number.
The Formulas, and Which Scale Each One Belongs To
Moment magnitude. The scale used for significant earthquakes worldwide is Mw = (2/3)(log10M₀ − 9.1), with the seismic moment M₀ in newton-metres. This is the Hanks and Kanamori relation, published in the Journal of Geophysical Research in 1979 and later adopted in this SI form as the standard definition. Seismic moment itself is the product of the rigidity of the rock, the area of the fault that slipped and the average slip on it, so moment magnitude is anchored to the physical size of the rupture rather than to any instrument reading. The Bulletin of the Seismological Society of America is where much of the underlying calibration work for these scales was and continues to be published.
Local magnitude. Richter's original 1935 scale was defined for southern California from the peak amplitude on a Wood-Anderson torsion seismograph, with a distance correction. The modern southern California calibration, from Hutton and Boore's 1987 paper in the Bulletin of the Seismological Society of America, is ML = log10A + 2.76 log10Δ − 2.48, with A the amplitude in millimetres and Δ the epicentral distance in kilometres. That calibration is regional. Other networks use different distance terms fitted to their own crust, so the same recording processed by two networks can give slightly different local magnitudes.
Radiated energy. The Gutenberg-Richter energy relation, log10Es = 4.8 + 1.5M with Es in joules, is the classical estimate of the seismic energy radiated as waves. It is an empirical relation, not a definition, and real events scatter around it by a factor of several because the efficiency with which a rupture radiates energy varies. Treat the energy figure as an order-of-magnitude estimate.
Work the default through by hand. With M₀ = 1 × 1019 N·m, log10M₀ = 19, so Mw = (2/3)(19 − 9.1) = (2/3)(9.9) = 6.6. The energy relation then gives log10E = 4.8 + 1.5 × 6.6 = 14.7, so E = 5.01 × 1014 joules. Against a comparison magnitude of 6.0 the difference is 0.6, so the amplitude ratio is 100.6 = 3.98 and the energy ratio is 100.9 = 7.94. Check the local-magnitude mode too: an amplitude of 10 mm at 100 km gives ML = 1 + 2.76 × 2 − 2.48 = 4.04.
Magnitude Is Not Shaking — Intensity Is
This is the distinction that matters most and is most often lost. Magnitude is one number for the whole earthquake, describing the size of the rupture at its source. Intensity describes how strongly the ground shook at one particular place, and every earthquake has as many intensity values as there are places to measure it.
Intensity is reported on the Modified Mercalli Intensity scale or a regional equivalent, in Roman numerals, and it is assessed from observed effects and instrumental ground motion. It falls with distance from the source, it depends heavily on focal depth, and it depends enormously on what is under your feet: soft sediment and reclaimed ground amplify shaking substantially compared with rock, and basin geometry can focus and prolong it.
The practical consequence is that a shallow moderate earthquake directly beneath a soft-soil city can produce far more damaging shaking than a much larger deep one several hundred kilometres away. Comparing two earthquakes by magnitude alone tells you about the ruptures, not about what anyone experienced. Nothing on this page estimates intensity, ground motion or effect at any location.
Why One Magnitude Unit Is About 32 Times the Energy
Both the amplitude and the energy relations are logarithmic, but with different slopes, and that is the whole source of the confusion. Magnitude is defined from the logarithm of amplitude with a slope of 1, so one whole magnitude unit is a factor of 10 in recorded ground-motion amplitude. Energy scales with the 1.5 power in the exponent, so one whole magnitude unit is 101.5 ≈ 31.6 times the energy — the familiar "about 32 times" figure.
Two units is therefore a hundred times the amplitude and about a thousand times the energy. Both statements are correct; they are answers to different questions. When a report says one earthquake was "ten times bigger" than another, it is usually talking about amplitude, and the energy difference is far larger than that phrasing suggests. The EarthScope Consortium fact sheet on how often earthquakes occur sets out the same energy-per-magnitude-step relationship alongside how the frequency of events falls as magnitude rises.
Where Each Scale Stops Working
Local magnitude saturates. The Wood-Anderson instrument responds over a limited band of periods, and once a rupture becomes large enough that most of its energy arrives at longer periods than the instrument sees well, the recorded amplitude stops growing in proportion to the earthquake. Local magnitude consequently flattens out somewhere around the mid-6s, and no amount of extra rupture pushes it much higher. Surface-wave magnitude saturates too, at a higher level.
Moment magnitude does not saturate, because it is computed from the seismic moment of the whole rupture rather than from a band-limited instrument reading. That is precisely why it replaced the older scales for large events, and why the largest recorded earthquakes are always quoted as Mw. The scales agree reasonably well in the middle range, roughly between magnitude 3 and 6, which is why they can be used loosely there and why the habit of treating them as interchangeable survives into ranges where it is wrong.
Agencies also revise magnitudes. An early automatic solution is computed from a handful of nearby stations within minutes; a reviewed moment magnitude comes later from a full waveform inversion using a global network. A change in the published figure is normal processing, not a correction of an error. Research on how these determinations are made and refined is carried out at institutions such as the GFZ Helmholtz Centre for Geosciences section on the physics of earthquakes and volcanoes, and national agencies including the United States Geological Survey, the Japan Meteorological Agency and the British Geological Survey publish the authoritative figures for their regions.
Where This Sits Next to the Other Physics Tools
Everything on this page is logarithmic arithmetic applied to published seismological relations. If you want the underlying mathematics on its own, the logarithm calculator handles logarithms in any base and the exponent calculator handles the inverse. Seismic moments span so many orders of magnitude that the scientific notation converter is genuinely useful when reading figures out of a catalogue, and the energy converter moves the radiated energy estimate into whichever unit you need.
On the materials side, seismic moment depends on the rigidity of the rock, which is a shear modulus — the shear modulus calculator covers that quantity in its general engineering form. For the general logarithmic-ratio idea in a completely different setting, the decibel calculator does the same kind of arithmetic for sound.
Arb Digital builds free tools like this one because useful pages earn attention. If you want tools, calculators or content built for your own audience, we can help.
Browse All Free Tools Talk to Arb DigitalCommon Mistakes to Avoid
- Treating magnitude as a measure of shaking — magnitude describes the rupture; intensity describes the shaking at a place, and only intensity varies from street to street.
- Mixing the amplitude ratio with the energy ratio — one magnitude unit is 10 times the amplitude but about 32 times the energy, and quoting one figure for the other is wrong by a large factor.
- Using local magnitude for a large earthquake — it saturates in the mid-6s, so it systematically understates anything bigger.
- Comparing local magnitudes from different networks — the distance correction is regionally calibrated, so the same recording can yield slightly different values.
- Reading the energy figure as precise — the Gutenberg-Richter energy relation is empirical and real events scatter around it by a factor of several.
Related Free Tools From Arb Digital
Pair this with the logarithm calculator and the exponent calculator for the underlying arithmetic, and the scientific notation converter for reading seismic moments out of a catalogue. Convert the energy estimate with the energy converter, look at the same logarithmic-ratio idea in acoustics with the decibel calculator, and cover the rock-mechanics side with the shear modulus calculator and the stress and strain calculator. Everything Arb Digital publishes is on the free online tools hub.
Frequently Asked Questions
Richter's local magnitude is read from the peak amplitude on a Wood-Anderson instrument with a distance correction, and it was calibrated for southern California. Moment magnitude is computed from the seismic moment of the whole rupture, which is rigidity times fault area times average slip. They agree reasonably well in the middle of the range, but local magnitude saturates for large events and moment magnitude does not.
Because magnitude is defined from the logarithm of amplitude with a slope of one, while the energy relation has a slope of 1.5 in the exponent. One magnitude unit is therefore a factor of 10 in amplitude but 10 raised to the power 1.5, about 31.6, in radiated energy. Both statements describe the same step on the scale.
No. Magnitude describes the rupture, not the shaking at any location. A shallow moderate earthquake directly beneath soft ground can shake a place far harder than a much larger deep one hundreds of kilometres away. Damage relates to intensity, which depends on distance, depth, local ground conditions and what has been built there.
It is the physical measure of the size of the rupture: the rigidity of the rock multiplied by the area of the fault that slipped multiplied by the average slip across it. It has units of newton-metres and it is what moment magnitude is derived from, which is why moment magnitude is tied to the earthquake itself rather than to an instrument response.
Because the first figure is an automatic solution from a few nearby stations produced within minutes, and the reviewed figure comes later from a full waveform inversion using far more data. The revision is normal processing, and the reviewed moment magnitude from the responsible national agency is the one to use.
Not reliably. The distance term is a regional calibration fitted to a particular crust, and the version implemented here is the southern California one. Other networks fit their own distance corrections, so applying this formula outside its calibration region gives an approximate value rather than the figure that network would publish.
Not in the arithmetic, which will happily return any number. The physical limit comes from geology: the seismic moment depends on how much fault area can rupture at once and how much slip it can accumulate, so the largest possible earthquake in a region is set by the size and nature of the faults present there.
No. It converts between published magnitude scales and energy for events that have already been recorded, and nothing here forecasts, predicts or estimates the likelihood of anything. Hazard assessment is a separate discipline carried out by national seismological and geological agencies using methods this page does not implement.
This tool is provided for educational use only. It implements published magnitude and energy relations for recorded earthquakes and makes no forecast or prediction of any kind. It does not estimate shaking, intensity, damage or risk at any location. For authoritative magnitudes, hazard information and preparedness guidance, consult your national seismological agency — such as the United States Geological Survey, the Japan Meteorological Agency or the British Geological Survey — and the relevant emergency management authority.
