Earthquake Distance Calculator

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.