Estimate how long earthquake P and S waves take to travel a given distance in miles or km, or find the distance to a quake from the S−P arrival gap.
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Earthquake Travel Time Formula
Choose one of four explicit constant-speed solves. All assume a shared straight path and ignore earthquake depth and Earth layers.
S−P inverse: use the entered positive speeds with vP greater than vS to estimate the shared path length.
P/S travel times: divide the entered shared path distance by each constant speed.
Single-wave solves: travel time is distance divided by constant speed; speed is distance divided by positive time.
- t_P: P-wave travel time from source to station, in seconds
- t_S: S-wave travel time, in seconds
- S-P: difference between S and P arrival times, in seconds
- d : simplified common wave-path distance; not automatically a surface arc or epicentral distance
- d: distance traveled by the wave
- v : entered constant wave speed; 6.0 and 3.5 km/s are illustrative editable P/S assumptions
No travel-time table or IASP91 curve is loaded. All four modes use constant-speed arithmetic. Real seismic rays depend on Earth structure, source depth and phase identification; use validated seismic travel-time methods for event analysis.
Reference Values
Hypothetical constant-speed pairs for arithmetic comparison only; these do not classify Earth layers or supply regional measured velocities:
| Hypothetical pair | P speed (km/s) | S speed (km/s) |
|---|---|---|
| Scenario 1 | 6 | 3.5 |
| Scenario 2 | 6 | 4 |
| Scenario 3 | 8 | 4 |
| Scenario 4 | 8 | 5 |
| Scenario 5 | 10 | 6 |
Illustrative S−P conversion with vP = 6 km/s and vS = 3.5 km/s, assuming a common path and ignoring depth:
| S−P interval | P time (s) | Path (km) | Path (mi) |
|---|---|---|---|
| 10 s | 14 | 84 | 52.20 |
| 30 s | 42 | 252 | 156.59 |
| 60 s | 84 | 504 | 313.17 |
| 180 s | 252 | 1512 | 939.51 |
| 300 s | 420 | 2520 | 1565.86 |
| 480 s | 672 | 4032 | 2505.37 |
Worked Example
A station records P at 10:00:30 and S at 10:01:30, a 60-second interval. With hypothetical constant speeds 6 and 3.5 km/s, shared path d = 60 × 6 × 3.5 / (6 − 3.5) = 504 km; tP = 84 seconds and tS = 144 seconds. This is not a table-based epicenter solution. Real event location requires multiple observations and a suitable Earth model.
FAQ
Why does S-P time tell you the distance? P waves move faster than S waves, so the gap between their arrivals grows with distance. A short S-P means the quake was nearby; a long S-P means it was far away. Each station only needs its own clock for this, not a synchronized network.
Does earthquake depth change the answer? Yes. This calculator has no depth input and no depth-specific travel-time table. Shared ray-path distance differs from horizontal or surface distance, and actual phase paths depend on source depth and Earth structure.
When is a constant-speed model useful? Use this simplified model for declared constant-speed scenarios or classroom arithmetic. It does not implement a table mode and should not replace validated regional/global seismic methods.
What is an epicentral distance in degrees? Epicentral angular distance describes the surface arc from the epicenter to a station. This tool omits a degree output because its estimated path length is not automatically that surface arc.
