Tsunami Travel Time Calculator
Calculate tsunami propagation speed and arrival time from ocean depth and distance using shallow water wave theory (v = √(g·d)).
About this calculator
This calculator applies shallow-water wave theory to estimate how fast a tsunami travels across the open ocean and how long it takes to reach a coastline. Because a tsunami's wavelength (often 100+ km) is enormous compared to the ocean's depth, the wave behaves as a "shallow water" wave everywhere -- even in water thousands of meters deep -- so its speed depends only on gravitational acceleration and water depth: v = √(g·d). This is why tsunamis race across deep ocean basins at speeds comparable to a jet airliner (500-900 km/h) and only slow down as they approach shore.
The calculator also estimates shoaling amplification using Green's Law, which compares the average ocean depth along the wave's path to a representative 10 m coastal shelf: as water shallows, the wave slows and its height grows to conserve energy, which is the physical mechanism behind a tsunami's destructive runup. This model uses a single average ocean depth for the entire path and a fixed assumed period (20 minutes) to estimate wavelength -- real tsunamis generated by different mechanisms (undersea earthquakes, landslides, volcanic collapse) have periods that can range from a few minutes to over an hour, and real bathymetry varies enormously along any given path, so this is a simplified planning estimate, not a substitute for an official tsunami warning system's numerical modeling.
Inputs
Results
Tsunami Speed
713.1 km/h
Travel Time
1.4 hours
How to Use This Calculator
- Enter Average Ocean Depth and Distance to Coast.
- Review Tsunami Speed (km/h) and Travel Time (hours).
- Use Speed (knots) and Travel Time (minutes) to inform your decision.
How the result changes with Average Ocean Depth
| Average Ocean Depth | Tsunami Speed | Travel Time |
|---|---|---|
| 2,000 | 504.3 km/h | 1.98 hours |
| 3,000 | 617.6 km/h | 1.62 hours |
| 6,000 | 873.4 km/h | 1.14 hours |
| 10,000 | 1,127.6 km/h | 0.89 hours |
What each input means
- Average Ocean Depth
- Average depth of the ocean along the wave path in meters. Average ocean depth is ~3,700 m.
- Distance to Coast
- Distance from the tsunami source to the point of interest in kilometers.
How this is calculated
Worked example, using the default values
- Identify Input ParametersAverage Ocean Depth = 4000, Distance to Coast = 1000 = 2 input(s) provided
- Calculate Tsunami SpeedTsunami Speed713.1 = 713.1
- Calculate Travel TimeTravel Time1.4 = 1.4
- Calculate SpeedSpeed385 = 385
- Calculate Travel TimeTravel Time84.1 = 84.1
Engine last updated . Checked against 4 independently-derived tests — how we verify calculators. Built by Paul Gunder, a software engineer, not a licensed financial, medical, or legal professional.
Frequently Asked Questions
Why do tsunamis speed up in the deep ocean and slow down near shore?
Wave speed in this shallow-water model depends only on water depth: v = √(g·d). Deeper water produces a higher speed, so a tsunami crossing a deep ocean basin travels fastest there and progressively slows as the seafloor rises toward the coast. That slowdown is also what concentrates the wave's energy into a taller wave near shore, which is why the deep-ocean wave height (often under a meter) is a poor indicator of the wave height that eventually reaches the coastline.
Does a longer distance to the coast always mean more warning time?
Generally yes for a fixed average depth, since travel time is distance divided by wave speed, but the relationship is not purely proportional to distance alone -- the average depth along that specific path matters just as much. A source that is farther away but crosses consistently deep water can arrive sooner than a closer source whose path crosses a shallow shelf, because the deep-water path supports a much faster wave speed.
What does the shoaling amplification factor represent?
It is Green's Law applied between the average ocean depth you entered and a representative 10 m coastal shelf depth: amplification equals (ocean depth / shelf depth) raised to the one-quarter power. It estimates how much a tsunami's height grows as it shoals from deep water onto a shallow shelf, assuming the wave's energy flux is conserved. Real coastal amplification also depends on shoreline shape, harbor resonance, and seafloor features this simplified factor does not capture.
Why does the calculator use a 10 m shelf depth for every calculation?
The 10 m value is a fixed representative nearshore depth used only to illustrate typical shoaling amplification, not a measurement of any specific coastal location. Actual nearshore bathymetry varies from steep drop-offs to gently sloping shelves extending kilometers offshore, and that local shape is one of the biggest factors in how large a tsunami's runup becomes at a particular beach.
Is this calculator accurate enough for real tsunami warning decisions?
No -- it is an educational approximation using a single average depth and a fixed assumed wave period, not the detailed bathymetric and seismic modeling that real tsunami warning centers use. For actual coastal safety, always follow guidance from an official tsunami warning system such as NOAA's National Tsunami Warning Center rather than any simplified calculator.
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