Enter the arrival time of first shear wave (s) and the arrival time of first compressional wave (s) into the Epicenter Distance Calculator. The calculator will evaluate and display the Epicenter Distance. 

Epicenter Distance Formula

The following formula is used to calculate the Epicenter Distance. 

ED = (S-P) * 8.4
  • Where ED is the Epicenter Distance (km)
  • S is the arrival time of first shear wave (s) 
  • P is the arrival time of first compressional wave (s) 

To calculate the epicenter distance, subtract the arrival time of the first compressional wave from the time of the first shear wave, then multiply the result by 8.4.

How to Calculate Epicenter Distance?

The following example problems outline how to calculate Epicenter Distance.

Example Problem #1:

  1. First, determine the arrival time of first shear wave (s).
    • The arrival time of first shear wave (s) is given as: 24.
  2. Next, determine the arrival time of first compressional wave (s).
    • The arrival time of first compressional wave (s) is provided as: 12.
  3. Finally, calculate the Epicenter Distance using the equation above: 

ED = (S-P) * 8.4

The values given above are inserted into the equation below and the solution is calculated:

ED = (24-12) * 8.4 = 100.8 (km)


What are shear waves and compressional waves?

Shear waves (S-waves) and compressional waves (P-waves) are types of seismic waves generated by earthquakes. P-waves are the first to arrive at a seismic station because they travel the fastest. They compress and expand the ground in the direction they are traveling. S-waves arrive after P-waves and move the ground up and down or side to side, perpendicular to the direction of wave travel.

Why is it important to calculate the epicenter distance?

Calculating the epicenter distance is crucial for determining the location of an earthquake. By knowing how far away the epicenter is from several different locations, seismologists can triangulate the exact location of the earthquake’s origin. This information is vital for assessing potential damage, issuing warnings, and understanding earthquake dynamics.

Can the epicenter distance formula be used for any type of seismic event?

The epicenter distance formula, as outlined, is specifically designed for calculating the distance of an observer from the epicenter of an earthquake based on the arrival times of P-waves and S-waves. While the basic principles might apply to different seismic events, the specific formula and its constants are tailored for earthquakes. For other seismic events, such as volcanic eruptions or explosions, different calculations and considerations might be necessary.