P-wave / S-wave epicenter distance calculator

Estimate epicenter distance from the S-P gap and back-calculate the event time with a simple classroom model for earthquake records.

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Example preset

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Inputs

Velocity presets

Results

S-P interval
Epicenter distance (approximate)
P wave running time
Omori coefficient k (this Vp/Vs conversion)
S wave running time
Origin time estimated from P-wave arrival
Origin time estimated from S-wave arrival
Origin time difference

Graph (distance - running time)

Enter values to draw the travel-time curve.

How it's calculated

With a constant-speed model, the travel times are tP = D / Vp and tS = D / Vs.

Because S-P = Δt = tS - tP, the epicenter distance D is estimated with the following relation.

D = Δt / (1/Vs - 1/Vp) = Δt × Vp × Vs / (Vp - Vs)

Many worksheets rewrite this as D = k × (S-P), where k = Vp × Vs / (Vp - Vs).

In arrival-time mode, the event time is estimated from T0 = Tp - D/Vp or T0 = Ts - D/Vs.

Note: This is a classroom approximation and does not model depth-dependent velocity, crustal structure, or path effects.

FAQ

What is the S-P interval?

This is the time difference between the arrival of P waves and the arrival of S waves. In general, the farther from the epicenter the longer S-P will be.

Is epicenter distance the same as hypocenter distance?

No. This page estimates horizontal epicenter distance with a simplified constant-speed model. It does not reconstruct the full hypocenter geometry.

Which Vp and Vs values should I use?

Use the values given in your class materials when available. Textbook defaults are only a learning reference because actual seismic velocities vary by region and depth.

What should I do if the S wave arrival time is smaller than the P wave?

If the S-wave arrival is on the next day, turn on the next-day option. Also check both arrival times for possible typos.

Can this result be used for disaster prevention decisions?

No. This page is for classroom estimation only. Use official earthquake bulletins and local emergency guidance for real decisions.

How to use this earthquake lesson page

This page is for classroom-style estimation from the P-wave and S-wave arrival gap. Treat the result as a learning aid for reading seismic records, not as an operational disaster-response tool.

Recommended classroom flow

  1. Confirm the arrival times first and correct obvious input mistakes before interpreting the result.
  2. Use the default P-wave and S-wave speeds unless your class materials specify different values.
  3. Compare the estimated distance with the origin time calculation and discuss why regional assumptions can change both answers.

What to verify before using the output

Check whether the S-wave really arrives after the P-wave and whether the record crosses midnight. If either assumption is wrong, the calculated distance and origin time will both become misleading.

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