Earthquake Magnitude & Energy Calculator

When an earthquake occurs, it releases body waves: fast primary compression waves (P-waves) and slower secondary shear waves (S-waves). Because they travel at different speeds through the Earth's crust, the time delay between their arrivals at a seismograph station increases with distance.

By measuring this time delay (P-S delay), we can calculate the distance to the earthquake epicenter. Standard crustal velocities average 6.0 km/s for P-waves and 3.5 km/s for S-waves, yielding an epicenter distance multiplier of approximately 8.4 kilometers per second of delay.

Distance (km) = Δ t × (V_p × V_s) / (V_p - V_s)

While magnitude measures the energy released at the earthquake source, intensity measures the shaking and damage observed at a specific location. One earthquake has a single magnitude but a different intensity at every point on the map, because ground motion decays with distance and is amplified or damped by the ground it travels through.

Peak ground acceleration (PGA) is the usual instrumental measure of that shaking, expressed as a percentage of gravity. The USGS publishes a fixed scale that maps PGA onto the Modified Mercalli intensity levels, and this tool applies that published scale: the band edges in %g are 0.17, 1.4, 3.9, 9.2, 18, 34, 65 and 124.

What this tool does not do is predict PGA from a magnitude and a distance. Doing that properly needs a ground-motion model calibrated for a specific region, fault style and site class, and different published models disagree with each other by a factor of two or more. An earlier version of this page estimated PGA from magnitude and distance using an equation that matched no published model and read roughly an order of magnitude low, which put a damaging earthquake in the "no damage" band. That estimate has been removed rather than replaced with a guess. For a real event, the USGS ShakeMap for that earthquake reports the acceleration directly.

Switch between the Energy, Distance, and Intensity tabs depending on what you want to analyze. Energy compares two magnitudes and shows how much stronger one earthquake's energy release and ground amplitude are relative to the other. Distance takes the P-S wave arrival delay (in seconds) from a seismogram and estimates how far away the epicenter was. Intensity takes a peak ground acceleration in %g and tells you which Modified Mercalli band it falls in, with the perceived-shaking and potential-damage labels the USGS attaches to that band.

Magnitude is not measured directly. What seismologists compute is the seismic moment: the rigidity of the rock multiplied by the area of fault that slipped multiplied by how far it slipped. That product, in newton metres, is what a magnitude is derived from, and agencies publish it for every significant earthquake.

The relation is Hanks and Kanamori’s, from 1979: Mw = (2/3) × (log10(M0 in N·m) − 9.1). In the CGS units the original paper used it reads Mw = (2/3) log10(M0 in dyne·cm) − 10.7, and the two are the same relation: a newton metre is 10^7 dyne centimetres, and two thirds of seven is the 4.667 separating the constants.

A factor of ten in moment moves the magnitude by two thirds of a unit, which is the whole reason the scale is logarithmic: the moments involved span more than ten orders of magnitude between an earthquake you can feel and one that moves a coastline.

This is also why moment magnitude replaced the Richter scale for large events. The original Richter measure saturates (above roughly magnitude 7 it stops distinguishing between earthquakes that differ enormously in the energy they release) while moment magnitude does not.

On the Energy tab with the default inputs (magnitude 6.0 vs. 5.0), the magnitude 6.0 event releases about 6.31 × 10¹³ joules of energy, roughly 15,080 tons of TNT equivalent. Compared to the magnitude 5.0 event, that is an energy ratio of 31.6x and a ground-motion amplitude ratio of 10x, confirming the rule that each whole-number magnitude step multiplies energy by about 31.6.

On the Distance tab, a 10-second P-S wave delay at standard crustal velocities (6.0 km/s and 3.5 km/s) works out to an epicenter roughly 84 km away. On the Intensity tab, entering 20%g puts you in the 18-34%g band: Modified Mercalli VII, described by the USGS as "Very strong" shaking with "Moderate" potential damage. Drop the same entry to 12%g and it falls into the 9.2-18%g band, MMI VI, "Strong" shaking with "Light" damage, one band lower for a little over half the acceleration.

If you track other physical or environmental measurements, the Metal Detector Target Depth Estimator and Geocaching Coordinates Distance & Bearing Solver use similar distance-and-signal math applied to different outdoor hobbies.