Enter the distance to the earthquake epicenter and the average velocity of seismic waves to calculate the travel time of the waves to your location.
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Earthquake Travel Time Formula
The calculator uses three different methods depending on which inputs you have.
Mode 1: P & S arrivals. The S minus P time is converted to epicentral distance using a standard travel-time table.
S-P = t_S - t_P → Distance from travel-time table
Mode 2: Distance table. Given a distance, the P and S travel times are read from the same table.
t_P = f(Δ), t_S = t_P + (S-P)(Δ)
Mode 3: Simple speed. Travel time is distance divided by a constant wave speed.
t = d / v
- 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
- Δ: epicentral distance in degrees of arc (1° ≈ 111.195 km)
- d: distance traveled by the wave
- v: seismic wave speed (typically 6.0 km/s for crustal P, 3.5 km/s for crustal S)
The P & S arrivals mode interpolates the IASP91 travel-time curve to turn an S-P interval into a distance. The distance table mode runs that same curve in reverse to predict when each phase will arrive at a station. The simple speed mode skips the table and uses constant velocity, which is fine for short crustal paths but loses accuracy at teleseismic distances because real wave speed increases with depth.
Reference Values
Typical seismic wave speeds in the upper Earth:
| Layer | P-wave (km/s) | S-wave (km/s) |
|---|---|---|
| Sediments | 2.0–4.0 | 1.0–2.5 |
| Upper crust | 5.5–6.2 | 3.2–3.6 |
| Lower crust | 6.5–7.2 | 3.7–4.1 |
| Upper mantle | 7.8–8.4 | 4.4–4.7 |
| Lower mantle | 11–14 | 6.5–7.3 |
Quick S-P interval to distance conversion (shallow earthquake, ~33 km depth):
| S-P interval | Distance (°) | Distance (km) | Distance (mi) |
|---|---|---|---|
| 10 sec | ~0.7° | ~80 | ~50 |
| 30 sec | ~2.3° | ~255 | ~160 |
| 1 min | ~5.2° | ~580 | ~360 |
| 3 min | ~18° | ~2,000 | ~1,240 |
| 5 min | ~35° | ~3,890 | ~2,420 |
| 8 min | ~70° | ~7,780 | ~4,830 |
Worked Example
A station records the P wave at 10:00:30 and the S wave at 10:01:30. The S-P interval is 60 seconds. Looking that up on the travel-time curve gives an epicentral distance of about 5.2°, or roughly 580 km from the station. To locate the actual epicenter, you need three stations: draw a circle of that radius around each, and the intersection point is the epicenter.
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, but not much for shallow events. The travel-time table used here assumes a focal depth near 33 km. Deep-focus earthquakes (300+ km) arrive a bit earlier than the table predicts, especially at short distances.
When should you use the simple speed mode instead of the table? Use the constant-speed mode for short crustal paths, classroom problems, or when you already know the wave speed in your medium. Use the table mode for regional or global distances where waves dive into the mantle and average speed changes with depth.
What is an epicentral distance in degrees? Seismologists measure distance along the Earth's surface as an angle from the epicenter to the station, with the Earth's center as the vertex. One degree equals about 111.195 km. Degrees are used because travel-time curves are spherical, not flat.
