Seismic Wave Travel Time Calculator

Seismic travel-time estimates for P- and S-wave arrivals

Estimating when seismic energy reaches a station starts with a simple relationship between source distance and wave velocity. Seismic Wave Travel Time Calculator applies that relationship to a primary wave and, when supplied, a secondary wave: enter the source-to-receiver distance in kilometers and the velocities in kilometers per second to obtain arrival times. The result is a straight-line, constant-velocity estimate rather than a complete Earth model.

For earthquake observations, classroom exercises, and preliminary survey planning, a direct travel-time calculation makes the effect of each assumed velocity visible. The primary and secondary arrivals are calculated independently over the same entered distance, so their displayed gap comes from the difference in travel times—not from adding or averaging the input values.

The guidance below explains the distance and velocity fields, the division used for each seismic arrival, and the assumptions to review before treating a timing estimate as evidence about an event or subsurface structure.

What this seismic arrival-time calculator calculates

This seismic calculator answers how long a wave traveling at a specified constant speed would take to cover the entered source-to-station distance. It always calculates the primary-wave arrival when distance and primary velocity are positive. If you also enter a positive secondary velocity, it calculates a second arrival over that same path and reports the absolute time gap between them.

The tool does not infer an earthquake location, depth, ray path, rock type, or velocity from a seismogram. Those choices remain yours. It is most useful after you have selected a distance and one or two representative velocities and want a transparent timing check for that stated scenario.

How to calculate P- and S-wave travel times

1. Enter Distance to Source (km) as the source-to-station path distance used in your scenario.
2. Enter Primary Wave Velocity (km/s) for the primary arrival you want to estimate.
3. Optionally enter Secondary Wave Velocity (km/s, optional) to calculate a second arrival and its gap from the primary arrival.
4. Select Compute to calculate the seismic arrival time or update the arrival comparison.
5. Check that the result is shown in seconds and minutes and that faster velocities produce earlier arrivals for the same distance.

When comparing several earthquakes, stations, or survey assumptions, retain the distance and velocities with each result. A copied summary records the displayed primary arrival and, when available, the comparison table and arrival gap.

Choosing source distance and seismic wave velocities

Seismic travel-time estimates depend entirely on the path distance and the velocity values entered here. Because the form uses kilometers and kilometers per second, the quotient is seconds. A value expressed in meters per second or a distance taken from a different geometry will produce a timing result that may be numerically valid but unsuitable for the seismic question being asked.

• Distance to Source (km): use the source-to-station distance or modeled path length that matches your intended straight-line calculation.
• Primary Wave Velocity (km/s): enter the constant velocity selected for the primary-wave scenario. It must be greater than zero.
• Secondary Wave Velocity (km/s, optional): enter a second positive velocity only when you want a second travel-time estimate for the same distance.
• Shared path assumption: the calculator applies both velocities to the single distance field, so do not use the secondary field for a different station or a different path length.

If field or catalog information supports a range rather than one velocity, calculate more than one case. A slower assumed velocity lengthens the reported arrival time; a faster assumed velocity shortens it. That approach makes the uncertainty in the velocity assumption easier to see than presenting one arrival as exact.

Seismic travel-time equation used by this calculator

For each seismic wave entered in the form, the calculator divides distance by velocity. With distance d in kilometers and velocity v in kilometers per second, travel time t is returned in seconds:

For the optional secondary-wave comparison, the calculator evaluates the same equation twice and takes the absolute difference between the two times. The primary velocity is v_P, the secondary velocity is v_S, and the displayed arrival gap is:

These equations describe a constant-velocity path. They do not add separate segments, apply depth corrections, or model bending, reflections, or velocity changes along the route. Consequently, distance changes affect each travel time proportionally when velocity is held fixed, while velocity changes affect travel time inversely when distance is held fixed.

Worked seismic arrival example: 120 km with primary and secondary velocities

Consider a 120 km source-to-station distance, a primary velocity of 6 km/s, and a secondary velocity of 3.5 km/s. The calculator evaluates each wave separately over the 120 km path; it does not combine these unlike quantities into a total.

• Primary arrival: 120 km ÷ 6 km/s = 20.00 seconds, or 0.33 minutes.
• Secondary arrival: 120 km ÷ 3.5 km/s = 34.29 seconds, or 0.57 minutes when rounded for display.
• Arrival gap: |34.29 − 20.00| = 14.29 seconds using the displayed values.

This example shows why a lower secondary velocity produces a later arrival over the same distance. If a result conflicts with that pattern, first verify that the distance is in kilometers, both velocities are positive and in kilometers per second, and both wave speeds describe the same modeled route.

Distance sensitivity for the 120 km seismic example

Holding the example velocities at 6 km/s for the primary wave and 3.5 km/s for the secondary wave, changing only the source distance changes both arrival times in direct proportion. The values below are travel-time outputs from the calculator equation, rounded to two decimal places.

For fixed velocities, a longer seismic path delays both arrivals and increases this P–S timing difference. Change the actual distance or either velocity in the form to test the assumptions relevant to your station, event, or survey line rather than relying on the example values.

Reading primary, secondary, and arrival-gap results

The seismic result panel lists the primary-wave arrival in seconds and minutes. When a valid secondary velocity is present, it also lists each velocity and arrival in a comparison table and states the absolute arrival gap in seconds. The gap is zero only when the two computed travel times are the same.

A useful check is to change one field at a time. At a fixed distance, raising a velocity should make that wave arrive earlier. At a fixed velocity, increasing distance should make that wave arrive later. If the secondary velocity is lower than the primary velocity, the secondary arrival will be later for the shared path; if you enter it as higher, the calculator will simply report the earlier secondary arrival and the absolute difference.

The page’s result text notes that an arrival gap can be used in epicenter-distance work, but this calculator alone does not triangulate an epicenter. Real location methods use observations from multiple stations and appropriate travel-time models. Use this output as a transparent single-path estimate, then combine it with the data and methods required by your analysis.

Limits of this constant-velocity seismic travel-time model

This seismic travel-time calculator intentionally uses a single distance and constant velocity for each wave. That makes the relationship easy to inspect, but real seismic propagation can involve layered materials, changing velocities, curved ray paths, source depth, phase identification, and local structure that are not represented by a direct distance-over-velocity calculation.

• Units: enter distance in kilometers and wave velocity in kilometers per second so the calculated travel time is in seconds.
• Path geometry: the entered distance is treated as one modeled path, not automatically as epicentral distance, hypocentral distance, or a layered ray length.
• Constant velocity: each wave is assigned one speed for its entire route, even though real materials may alter wave speed and direction.
• Secondary comparison: the optional velocity produces a second direct-path estimate; it does not identify a seismic phase or verify that the two arrivals were observed.
• Displayed rounding: arrivals and gaps are shown to two decimal places, so small differences from unrounded hand calculations are expected.

For hazard decisions, formal earthquake location, or detailed geophysical interpretation, compare these first-pass estimates with authoritative observations and a model appropriate to the region and phase. The calculator is most valuable when its assumptions are documented alongside the distance and velocities that produced the reported arrival times.