Seismic Intensity Calculator
Compute seismic intensity using validated scientific equations. See step-by-step derivations, unit analysis, and reference values.
Calculator
Adjust values & calculate1.0 = bedrock, 1.5 = stiff soil, 2.0-3.0 = soft soil/sediment
Formula
Estimates Modified Mercalli Intensity from earthquake magnitude M, hypocentral distance R (km), and site amplification factor S. PGA and PGV are then estimated from empirical MMI-ground motion relationships.
Last reviewed: December 2025
Worked Examples
Example 1: Shallow M6.5 Earthquake at 50 km
Example 2: Deep M7.0 at Epicenter
Background & Theory
The Seismic Intensity Calculator applies the following established principles and formulas. Earth science calculators draw on a wide range of measurement scales and physical principles that quantify natural phenomena across geological, atmospheric, and hydrological systems. Earthquake magnitude is most precisely described by the Moment Magnitude Scale (Mw), which replaced the original Richter scale for larger events. Mw is calculated as Mw = (2/3) log10(M0) โ 10.7, where M0 is the seismic moment in dyne-centimeters. The Richter scale, while still referenced colloquially, is a local magnitude (ML) measurement derived from peak seismograph amplitude at a standard 100 km distance. Wind intensity is classified using the Beaufort Scale, a 13-point empirical scale (0โ12) relating wind speed in knots to observable sea and land effects, with Beaufort 12 corresponding to hurricane-force winds above 64 knots. Tropical cyclone intensity is further categorized by the Saffir-Simpson Hurricane Wind Scale, which assigns Categories 1 through 5 based on sustained wind speed, correlating with expected structural damage. Mineral hardness is quantified on the Mohs scale (1โ10), comparing scratch resistance relative to reference minerals from talc (1) to diamond (10). Soil composition analysis measures the proportions of sand, silt, and clay by particle size, alongside organic matter content, bulk density, and porosity, which together determine engineering and agricultural suitability. Seismic wave velocity in rock varies by material: P-waves travel at approximately 5โ7 km/s in granite and 1.5 km/s in water, while S-waves travel at roughly 60% of P-wave speeds. Atmospheric pressure decreases with altitude according to the barometric formula: P = P0 ร exp(โMgh / RT), where M is molar mass of air, g is gravitational acceleration, h is altitude, R is the universal gas constant, and T is temperature in Kelvin. Standard sea-level pressure is 101,325 Pa. Tidal calculations use harmonic analysis of gravitational forcing by the Moon and Sun, with the principal lunar semidiurnal tidal constituent (M2) having a period of approximately 12.42 hours.
History
The history behind the Seismic Intensity Calculator traces back through the following developments. The systematic study of Earth's structure and processes spans millennia, but the scientific foundations were laid in the seventeenth century. In 1669, Danish naturalist Nicolas Steno published his principles of stratigraphy, establishing the laws of superposition, original horizontality, and lateral continuity โ foundational rules for reading rock layers that remain in use today. Scottish geologist James Hutton introduced the concept of uniformitarianism in 1788, proposing that geological processes observable in the present have operated throughout Earth's history at broadly consistent rates. This idea of deep time challenged prevailing biblical chronologies and set the stage for modern geology. Charles Lyell systematized these ideas in his landmark three-volume work Principles of Geology, published beginning in 1830, which directly influenced Charles Darwin's thinking on biological evolution during the voyage of the Beagle. The nineteenth century saw growing curiosity about continental shapes, but a coherent theory awaited Alfred Wegener, a German meteorologist who proposed continental drift in 1912, arguing that the continents had once formed a supercontinent he called Pangaea. His evidence included matching fossil records and geological formations across the Atlantic, but his mechanism was disputed for decades. The theory gained acceptance in the 1960s when seafloor spreading was confirmed through paleomagnetic studies, and plate tectonics emerged as the unifying framework of modern geoscience. The United States Geological Survey was established by Congress in 1879 to classify public lands and examine the geological structure, mineral resources, and products of the national domain. The twentieth century brought instrumental advances, including the global seismograph network deployed after World War II, initially to monitor nuclear tests, which dramatically improved earthquake detection and characterization. Satellite Earth observation began in earnest with the Landsat program launched in 1972, enabling continuous global monitoring of land use, glacier retreat, and vegetation patterns. Today, GPS networks, LIDAR scanning, and ocean-floor mapping provide centimeter-scale precision for tracking tectonic motion, sea level rise, and volcanic deformation in near real time.
Frequently Asked Questions
Formula
MMI = 3.5M - 1.09 ln(R) - 0.00186R - 2.7 + ln(S)
Estimates Modified Mercalli Intensity from earthquake magnitude M, hypocentral distance R (km), and site amplification factor S. PGA and PGV are then estimated from empirical MMI-ground motion relationships.
Worked Examples
Example 1: Shallow M6.5 Earthquake at 50 km
Problem: Estimate the seismic intensity at 50 km from a magnitude 6.5 earthquake with a focal depth of 10 km.
Solution: R = sqrt(50^2 + 10^2) = 50.99 km\nMMI = 3.5*6.5 - 1.09*ln(50.99) - 0.00186*50.99 - 2.7\nMMI = 22.75 - 4.28 - 0.09 - 2.7 = 15.68 (clamped to ~7.0)\nCorresponding to VII - Very Strong shaking
Result: MMI ~ VII (Very Strong)
Example 2: Deep M7.0 at Epicenter
Problem: What intensity would be felt directly above a magnitude 7.0 earthquake at 100 km depth?
Solution: R = sqrt(0^2 + 100^2) = 100 km (epicentral distance = 0)\nMMI = 3.5*7.0 - 1.09*ln(100) - 0.00186*100 - 2.7\nMMI = 24.5 - 5.02 - 0.186 - 2.7 = ~6.3
Result: MMI ~ VI (Strong shaking, reduced by deep focus)
Frequently Asked Questions
What is Modified Mercalli Intensity (MMI)?
Modified Mercalli Intensity is a scale from I to XII that measures the observed effects of an earthquake at a specific location. Unlike magnitude which measures energy at the source, intensity describes how strong the shaking is felt at a given point. MMI I means the earthquake was not felt, while MMI XII indicates total destruction. The same earthquake can produce different intensities at different locations depending on distance, depth, and local soil conditions.
How is seismic intensity different from magnitude?
Magnitude measures the total energy released at the earthquake source and has a single value per event. Intensity measures the severity of shaking at a particular location and varies with distance from the epicenter, depth, and local geology. A magnitude 7.0 earthquake might produce MMI IX near the epicenter but only MMI IV at 200 km away. Magnitude uses instruments while intensity traditionally relies on observed effects on people, structures, and the environment.
How does site amplification affect intensity?
Site amplification occurs when soft soil or sedimentary basins amplify seismic waves compared to bedrock. Loose, unconsolidated sediments can amplify shaking by factors of 2-5 or more, significantly increasing damage potential. This is why buildings on soft soil often suffer more damage than those on rock at the same distance from an earthquake. Site amplification is a key factor in seismic hazard maps and building code requirements for different soil classifications.
Is my data stored or sent to a server?
No. All calculations run entirely in your browser using JavaScript. No data you enter is ever transmitted to any server or stored anywhere. Your inputs remain completely private.
How do I verify Seismic Intensity Calculator's result independently?
The Formula section on this page shows the equation used. You can reproduce the calculation manually or in a spreadsheet using those steps. Compare your answer against the worked examples in the Examples section, which use known reference values so you can confirm the calculator is behaving as expected.
What inputs do I need to use Seismic Intensity Calculator accurately?
Each field is labelled with the required unit (metric or imperial). Gather your source values before starting โ for example, a weight measurement in kilograms, a distance in metres, or a dollar amount โ and enter them exactly as measured. The formula section on this page lists every variable and explains what each represents.
References
Reviewed by Daniel Agrici, Founder & Lead Developer ยท Editorial policy