Earthquake Epicenter Intensity Calculator

Modified Mercalli Intensity Scale

The Richter or moment magnitude (Mw) scale measures the energy released at the earthquake source. The Modified Mercalli Intensity (MMI) scale measures how strongly shaking is felt at a specific location. MMI depends on both the earthquake magnitude and your distance from the epicenter.

Attenuation Formula

Ground shaking decreases with distance in a predictable way. A simplified attenuation relationship widely used for first estimates:

MMI = M - 2.5 x log10(R) + 1.5

where M is moment magnitude and R is the distance from the source in kilometers. This is a rough model; actual shaking depends on local soil conditions and fault type as well.

Distance to the epicenter is not distance to the earthquake

The epicenter is the point on the surface directly above the rupture. The rupture itself sits below it, at the focal depth, so the real path from source to your feet is the hypotenuse of a right triangle:

R = √(surface distance² + depth²)

Stand directly on the epicenter of a quake 30 km down and your surface distance is zero, but you are still 30 km from the earthquake. That is why the calculator asks for depth: without it, a deep event looks far more violent than it is. Depth also puts a hard ceiling on shaking, because R can never fall below the focal depth no matter how close you walk.

A quick sense of the numbers, for a magnitude 6.5 event:

Same earthquake, same spot on the map, and the difference between furniture moving and barely noticing is entirely the depth. Most damaging continental earthquakes are in the 5 to 15 km range.

MMI Scale Reference

I: Not felt. II-III: Felt by people at rest, objects may sway. IV: Dishes rattle, felt widely. V: Felt by nearly all, some objects fall. VI: Felt by all, slight structural damage. VII: Difficult to stand, moderate damage to ordinary buildings. VIII: Partial collapse of ordinary buildings, considerable damage to solid structures. IX-X: Severe to violent shaking, many well-built structures destroyed. XI-XII: Catastrophic, few structures standing.

Soil Amplification

Soft sediment and fill material can amplify ground motion by a factor of 2 to 5 compared to bedrock, which is worth roughly one to two full MMI steps. The 1989 Loma Prieta earthquake caused disproportionate damage in San Francisco Bay fill areas far from the epicenter for exactly this reason: the Marina District sits on rubble dumped after the 1906 quake, and it shook harder than solid ground much closer to the fault.

What this model will not tell you

It is a single equation fitted to averages, and real ground motion is messier than any single equation. Rupture direction matters (shaking runs ahead of a propagating rupture, which is why one side of a fault can be hit far harder than the other), basin geometry can trap and ring waves for a minute after the source has gone quiet, and the same soil that amplifies a slow, deep shake can damp a sharp one.

Use it to answer “roughly what did people feel there”, not to decide whether a building stands up. Actual USGS ShakeMaps combine this kind of relation with real instrument readings and thousands of “Did You Feel It” reports, and they routinely differ from a formula by a full intensity step.