Earthquake Distance Calculator (S-P Time)
Estimate how far away an earthquake struck from the delay between the fast P-wave and the slower S-wave at your location.
How it works
d = Δt ÷ (1/Vs − 1/Vp) · where Δt = S-wave arrival − P-wave arrival
P (primary) waves travel faster than S (secondary) waves, so they always arrive first. The gap between the two arrivals grows with distance because the faster wave pulls further ahead the longer both have travelled. Measuring that S−P time and dividing by the difference of the wave slownesses gives the distance to the source — the single-station method used to draw the circles that triangulate an epicentre.
Worked example
With Vp = 6.0 km/s and Vs = 3.5 km/s, the slowness difference is 1/3.5 − 1/6.0 = 0.119 s/km. A 20-second S−P gap gives d = 20 ÷ 0.119 ≈ 168 km. A common rule of thumb, "distance ≈ 8 km per second of delay," is just the reciprocal of that factor.
Sources: Seismic wave — Wikipedia
Frequently asked questions
Why do you need three stations to find an epicentre?
S−P time gives distance but not direction, so one station only tells you the quake lies somewhere on a circle. Drawing the distance circles from three separated stations produces a single intersection point — the epicentre.
Are P- and S-wave speeds really constant?
No — they vary with rock type and depth, typically 5–8 km/s for P and 3–4.5 km/s for S in the crust. The defaults here are representative crustal values; using locally calibrated speeds improves accuracy.
What is the difference between P and S waves?
P waves are compressional, pushing and pulling the ground in the direction of travel, and move fastest. S waves are shear waves that move the ground side to side, travel slower, and cannot pass through liquids like the outer core.
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This calculator is for educational purposes. Double-check important results before acting on them.