Earthquake Distance Calculator
Estimate the distance from a seismograph station to an earthquake epicenter using the arrival time difference between P and S seismic waves. Useful for seismology education and rapid preliminary epicenter location.
About this calculator
Earthquakes generate two types of body waves: primary (P) waves, which are compressional and travel fastest, and secondary (S) waves, which are shear waves that arrive later. Because the two wave types travel at different but predictable speeds through the Earth's crust, the time gap between their arrivals at a seismograph station is proportional to the distance to the epicenter. The simplified formula used here is: Distance (km) = (S-wave arrival time − P-wave arrival time) × 8. The factor 8 km/s represents an approximate average velocity difference constant derived from typical crustal P-wave (~6 km/s) and S-wave (~3.5 km/s) speeds. This is a standard educational approximation; precise epicenter location uses multiple stations and more detailed velocity models.
How to use
Suppose a seismograph records the P wave at t = 20 seconds and the S wave at t = 46 seconds after the earthquake origin time. Step 1 — Calculate the S–P time gap: 46 − 20 = 26 seconds. Step 2 — Multiply by 8: 26 × 8 = 208 km. The seismograph station is approximately 208 km from the earthquake epicenter. Repeating this with at least two other stations and triangulating the results pinpoints the epicenter location on a map.
Frequently asked questions
Why do P waves and S waves arrive at different times at a seismograph station?
P waves are compressional waves that push and pull rock particles in the direction of travel, making them the fastest seismic waves with typical crustal speeds of 5–8 km/s. S waves are shear waves that move rock particles perpendicular to travel, making them slower at roughly 3–5 km/s. The greater the distance to the earthquake source, the larger the time gap between the two arrivals. This predictable difference is the foundation of the S–P method for distance estimation.
How accurate is the S minus P wave method for locating an earthquake epicenter?
The S–P method using a single station gives only a distance estimate, not a direction, so the epicenter could lie anywhere on a circle of that radius around the station. Using three or more stations and triangulating the circles yields a unique intersection point. The factor of 8 is an approximation that works reasonably well for shallow crustal earthquakes but can be less accurate for deep-focus events or in regions with unusual geology. Professional seismologists use three-dimensional velocity models and software like SEISAN or HYPOINVERSE for precise location.
What is the minimum number of seismograph stations needed to locate an earthquake epicenter?
A minimum of three seismograph stations are needed to triangulate an epicenter using the S–P time difference method. Each station provides a circle of possible epicenter locations; three circles ideally intersect at a single point. In practice, four or more stations are used to improve accuracy and account for measurement error. Modern seismic networks use dozens of stations and automated algorithms to locate earthquakes within seconds of their occurrence.