Earthquake Distance Calculator
Estimate earthquake epicenter distance from P-wave and S-wave arrival time difference using the Wadati method.
Includes wave speed constants and examples.
Earthquake epicenter distance is calculated using the time difference between the arrival of P-waves (primary, compressional waves) and S-waves (secondary, shear waves). P-waves travel faster through Earth than S-waves, so the gap between their arrivals reveals how far the seismic station is from the earthquake source.
Core formula: Distance (km) = (t_S − t_P) × V_P × V_S ÷ (V_P − V_S)
Simplified using the empirical “8 seconds per 100 km” rule for continental crust: Distance (km) = (t_S − t_P in seconds) × 8
Or more precisely (using average crust wave velocities): Distance (km) = (Δt in seconds) ÷ (1/V_S − 1/V_P)
Where:
- t_P = time of P-wave arrival at the seismometer
- t_S = time of S-wave arrival at the seismometer
- Δt = t_S − t_P (the lag between P and S arrival)
- V_P = P-wave velocity ≈ 6.0–8.0 km/s (average ~6.0 km/s in crust)
- V_S = S-wave velocity ≈ 3.5–4.5 km/s (average ~3.5 km/s in crust)
What each variable means:
- P-waves (Primary) — compressional waves; travel through solid and liquid rock; arrive first; cause the initial gentle shaking felt before an earthquake
- S-waves (Secondary) — shear waves; travel only through solid rock; arrive second; cause the main destructive shaking
- Epicenter — the point on Earth’s surface directly above the earthquake focus (hypocenter)
- Three-station triangulation — to locate the epicenter on a map, you need distance measurements from at least 3 seismometer stations; the epicenter lies at the intersection of three circles drawn around each station
Seismic wave velocity reference:
- P-wave in granite: ~5.5–6.5 km/s
- P-wave in mantle: ~8.0–9.0 km/s
- S-wave in granite: ~3.0–3.5 km/s
- S-wave does not propagate in liquid (Earth’s outer core is detected as a shadow zone)
Worked example: Seismograph records P-wave at 14:22:10 UTC and S-wave at 14:22:58 UTC.
Δt = 58 − 10 = 48 seconds
Using simplified formula: Distance = 48 × 8 = 384 km from this seismometer station
Using precise formula (V_P = 6.0 km/s, V_S = 3.5 km/s): Distance = 48 ÷ (1/3.5 − 1/6.0) = 48 ÷ (0.2857 − 0.1667) = 48 ÷ 0.1190 = 403 km
The earthquake epicenter is approximately 384–403 km from this station.