Calculator Inputs
Formula Used
This calculator estimates epicentral distance from the difference between S-wave and P-wave arrival times. It assumes average seismic velocities along the travel path.
Here, Δt is the S-P time gap, D is epicentral distance, VP is P-wave speed, VS is S-wave speed, θ is angular distance, and R is Earth radius.
The model is useful for learning, quick checks, and approximate field estimates. Detailed seismology work may need layered Earth travel-time tables.
How to Use This Calculator
- Choose whether to enter a direct S-P difference or arrival clock times.
- Enter the time gap or the P-wave and S-wave arrival times.
- Provide average P-wave and S-wave velocities in kilometers per second.
- Select your preferred display unit for the main distance result.
- Adjust Earth radius if you want custom angular conversion.
- Set the number of decimal places to control precision.
- Click Calculate Distance to show results above the form.
- Use the export buttons to download CSV or PDF output.
Example Data Table
This example uses P-wave speed 6.00 km/s and S-wave speed 3.50 km/s.
| S-P Lag (s) | Distance (km) | Distance (miles) | Angular Distance (degrees) |
|---|---|---|---|
| 5 | 42.00 | 26.10 | 0.38 |
| 10 | 84.00 | 52.20 | 0.76 |
| 15 | 126.00 | 78.29 | 1.13 |
| 20 | 168.00 | 104.39 | 1.51 |
| 30 | 252.00 | 156.59 | 2.27 |
| 45 | 378.00 | 234.88 | 3.40 |
Frequently Asked Questions
1. What is epicentral distance?
Epicentral distance is the surface distance between a seismic station and the earthquake epicenter. It helps locate earthquakes and interpret seismic arrival records.
2. Why is the S-P difference important?
P waves travel faster than S waves. The bigger the arrival gap, the farther the earthquake is from the station. That gap is the main distance clue.
3. Which wave speeds should I enter?
Use average crustal or regional values if known. Common educational defaults are about 6.0 km/s for P waves and 3.5 km/s for S waves.
4. Is this result exact?
No. It is an estimate based on simplified average velocities. Real Earth structure varies with depth, rock type, and path geometry, so professional solutions use richer models.
5. Can I enter arrival clock times instead?
Yes. Switch the input mode to arrival times, then enter both wave arrivals in HH:MM:SS format. The calculator will determine the S-P difference automatically.
6. Why does the calculator also show degrees?
Angular distance is useful in seismology because many travel-time charts and global station maps use degrees rather than ground distance units.
7. What happens if S-wave speed is not lower?
The formula becomes invalid. S waves must be slower than P waves, otherwise the time-gap relationship no longer represents physical seismic behavior.
8. Can I download the calculation?
Yes. After calculating, you can download a CSV summary and chart dataset, or create a PDF report containing the main results and assumptions.