Tsunami Arrival Time Calculator
Find how long a tsunami takes to cross an ocean path with changing depth, when it arrives on the clock, and how much warning time you have.
🌊 What is Tsunami Arrival Time?
Tsunami arrival time is the time a tsunami takes to travel from its source, usually an undersea earthquake, to a particular coast, and the clock time at which its first wave reaches that coast. Because a tsunami is a very long wave, its speed in the ocean depends only on the water depth: the deeper the water, the faster it moves. In the open ocean it travels at jet-aircraft speed, around 700 to 800 km/h, and then slows to the speed of a car as it climbs onto a continental shelf. Adding up the time spent in each depth zone gives the arrival time.
Emergency planners, coastal engineers, students and journalists use arrival times to answer practical questions. How many hours does a distant-source tsunami give a harbour before the first wave? Is there enough time for vertical or inland evacuation? Which stretch of a path adds the most delay? Warning centres use detailed numerical models for official forecasts, but a segment-by-segment estimate such as this one is how the basic travel-time maps and rules of thumb are built, and it is an excellent way to understand why a wave from Chile takes about 15 hours to reach Hawaii while a wave from a shelf-edge earthquake can arrive in minutes.
This page adds the multi-depth path, the cumulative time and the arrival clock time to the single-depth speed formula. In Depth path mode you enter up to 5 segments, each with a length in kilometres and a mean depth in metres. In Great-circle mode you enter source and receiver coordinates and one mean depth, and the distance is found with the haversine formula. In both modes you can enter an alert delay and an evacuation time to see the warning time left and the margin. For the speed on its own see the tsunami wave speed calculator, and for the height of the wave at the shore see the tsunami run-up height estimator.
Two misconceptions are worth avoiding. A tsunami is not a single wave but a train of waves, and the first wave is often not the largest, so the arrival time here marks the start of the danger, not its end. And the estimate is an approximation: the real wave front bends toward shallower water (refraction), the source is a long rupture rather than a point, and the seabed is far more complicated than five straight segments. Use the result to understand the scale of the time available, never as the only basis for a safety decision. Follow official warnings.
📐 Formula
📖 How to Use This Calculator
Steps
💡 Example Calculations
Example 1 — Pacific Crossing, Chile to Hawaii (Great-circle)
Source 38.2°S 73.05°W (off Chile), receiver 19.73°N 155.09°W (Hilo, Hawaii), mean depth 4000 m, origin 19:11 UTC
Example 2 — Japan 2011 to Hawaii (Depth path)
Five segments, 6300 km in total, mostly 5400 m deep, origin 05:46 UTC, alert delay 20 min, evacuation 60 min
Example 3 — Short Continental Shelf Path (Depth path)
A 200 km path from the shelf edge to the coast, origin 03:30 UTC, alert delay 10 min, evacuation 30 min
Example 4 — Shallow Segments Near the Coast (Depth path)
2030 km path, deep ocean then a shelf that shallows to 20 m, origin 12:00 UTC, alert delay 10 min, evacuation 45 min
❓ Frequently Asked Questions
🔗 Related Calculators
How do you calculate tsunami arrival time?
Divide the path into segments of roughly constant depth. For each, the wave speed is c = sqrt(g h) with g = 9.80665 m/s squared, and the time is length divided by speed. Add the segment times to get the total, then add it to the origin time to get the arrival clock time.
How fast does a tsunami travel in the deep ocean?
In 4000 m of water the speed is sqrt(9.80665 x 4000) = 198 m/s, about 713 km/h, close to a passenger jet. In 5000 m it is about 221 m/s or 797 km/h. NOAA describes deep-ocean tsunami speeds as comparable to a jet plane.
Why does a tsunami slow down near the coast?
Speed depends on depth, c = sqrt(g h). When the water shoals from 4000 m to 10 m the speed drops from about 198 m/s to about 10 m/s, roughly the speed of a car. The wave height grows as the speed falls because the energy is compressed.
Is the shallow-water formula valid for a tsunami in deep ocean?
Yes. A tsunami wavelength is tens to hundreds of kilometres, far longer than even the deepest ocean, so the water is shallow relative to the wave. That is why c = sqrt(g h) works, unlike for wind waves, whose speed depends on wavelength.
How long does a tsunami take to cross the Pacific?
Roughly 15 hours from Chile to Hawaii, about 10,700 km at an average depth near 4000 m. Crossing the full ocean from east to west takes about a day. Observed arrivals differ from simple estimates because of real bathymetry and the path taken.
What is tsunami warning time?
It is the time between an official alert and the arrival of the first wave. Here it equals total travel time minus the alert delay. Comparing it with the time needed to evacuate shows whether people at a given coast can reach safety in time.
How accurate is this tsunami travel time estimate?
Within about 5 to 10 percent for open-ocean paths when you choose representative depths. Errors grow near the coast, where depth changes quickly, and from the source region, which is not a point. Operational centres use full bathymetric models for official forecasts.
Why use a great-circle distance?
The shortest route over a sphere is the great circle, computed here with the haversine formula and Earth radius 6371 km. A real tsunami bends toward shallower water and around islands, so the actual path is usually a little longer than the great circle.
What mean depth should I use for the open ocean?
Use about 4000 m for a typical Pacific or Atlantic crossing, since average ocean depth is about 3700 m and abyssal plains are 4000 to 6000 m. Over a continental shelf use 50 to 200 m, and in a trench region use the local chart depth.
What does +1 day mean in the arrival time?
It means the tsunami arrives on the calendar day after the origin time in UTC. For example, an origin at 19:11 UTC with a 15 hour travel time arrives at 10:10 UTC the next day, shown as 10:10 UTC (+1 day). Convert to local time yourself.