Shaking Intensity from Peak Ground Acceleration (MMI)

Understanding the PGA to Mercalli intensity calculator — concept and principle

Peak ground acceleration (PGA) is what strong-motion instruments record; Modified Mercalli Intensity (MMI) is what people feel and what buildings suffer. This calculator converts a PGA value into an estimated MMI using the empirical relation of Worden et al. (2012), the type of conversion used in shaking maps such as USGS ShakeMap.

Acceleration is a measurement; MMI translates it into what people feel and what buildings suffer.

How it is calculated

Convert PGA from %g to cm/s²: PGA = (%g / 100) × 981.
Take the base-10 logarithm, log PGA.
If log PGA ≤ 1.57: MMI = 1.78 + 1.55 × log PGA.
If log PGA > 1.57: MMI = −1.60 + 3.70 × log PGA.
The description is the MMI rounded to the nearest whole level and clamped between I and X.

The break point 1.57 corresponds to about 37 cm/s², or roughly 3.8% g.

The principle

Intensity is not measured by an instrument; it is assigned from reports of what people felt and what happened to structures. Worden and colleagues paired many such intensity observations in California with nearby recorded ground motions and fitted a straight line in log space. Two segments were needed: at weak shaking, intensity rises slowly with acceleration; once shaking is strong enough to cause damage, it rises much faster. A logarithm is used because perceived effects scale with ratios of acceleration, not with absolute differences, much like sound loudness.

Worked example

Input: PGA = 20% g.
0.20 × 981 = 196.2 cm/s².
log₁₀ 196.2 = 2.29270, which is above 1.57, so the high-range equation applies.
MMI = −1.60 + 3.70 × 2.29270 = 6.882986311.
Rounded to 7: VII Very strong.

Each point is the calculator re-run with only “Peak ground acceleration (%g)” changed; the gold point is the default example. Change the inputs above and this chart follows your numbers.

Peak ground acceleration (%g)	MMI (Worden 2012)
5	4.655364343
10	5.769175327
15	6.420712986
20	6.882986311
25	7.241553359
30	7.53452397
40	7.996797295

How to read the result

Where does your result fall?

Roughly: I to III, felt by few or none; IV to V, felt by most, dishes rattle, unstable objects may fall; VI, felt by all with slight damage; VII, negligible damage in well-built buildings but considerable damage in poorly built ones; VIII and above, considerable damage even in ordinary buildings. With this relation, about 1% g gives MMI ≈ 3.3, 10% g ≈ 5.8 and 40% g ≈ 8.0. The full scale goes up to XII, but the label list here stops at X.

Common mistakes

Entering PGA in g (0.2) instead of %g (20).
Confusing intensity with magnitude: a single earthquake has one magnitude but many intensities, falling off with distance.
Treating the decimal MMI as exact; intensity data scatter by about one level around such fits.

Keep in mind: This is an empirical regression based mainly on California data. Local soils, building types and the frequency content of shaking change the effects, so use it as an estimate, not a damage assessment or structural design input.

Frequently asked questions

Why not use peak velocity instead?

Worden et al. also give a PGV relation, and velocity often correlates better with damage at higher intensities. PGA is used here because it is the most widely reported value.

Does Korea use the Mercalli scale?

Yes, the Korea Meteorological Administration reports intensity on the 12-level Modified Mercalli scale.

Sources: C. B. Worden, M. C. Gerstenberger, D. A. Rhoades and D. J. Wald (2012), Bulletin of the Seismological Society of America 102(1), 204–221 · H. O. Wood and F. Neumann (1931), Modified Mercalli intensity scale of 1931, Bulletin of the Seismological Society of America 21(4)

Checked 8 Nov 2026. Standard textbook formulas in SI units, computed in your browser. For learning and estimates — real designs must follow your local codes and be checked by a qualified engineer.

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