Tsunami Wave Speed Calculator
Find how fast a tsunami travels from ocean depth, then estimate travel time over a distance and wavelength from the wave period.
🌊 What is Tsunami Wave Speed?
Tsunami wave speed is how fast a tsunami crest moves across the ocean. Unlike wind waves, a tsunami is generated by the sudden displacement of the whole water column, usually by an undersea earthquake, a landslide or a volcanic eruption. That gives it a very long wavelength, often 100 to 500 kilometers, and a period of 5 to 60 minutes. Because this wavelength is so much greater than the ocean depth, the wave behaves as a shallow-water wave, and its speed depends only on the water depth and gravity: c = √(g × d).
The result is surprising to many people. In an average deep ocean depth of 4000 m a tsunami moves at about 198 m/s, or roughly 713 km/h, as fast as a passenger jet. Emergency planners use this to estimate arrival times, which is the basis of coastal warning systems. Oceanographers use it to work out wavelengths from observed periods, to check how the wave refracts around underwater ridges, and to explain why tsunami waves pile up and slow down as they reach the shallow shelf. Students use it as a clean example of how a physical law depends on a single variable.
A common misconception is that a faster tsunami must be a bigger one. In fact, the speed does not depend on the height or the energy of the wave. It depends only on depth. A tiny tsunami and a catastrophic one cross the same ocean at the same speed. The second misconception is that a tsunami is a towering wall of water at sea. In the open ocean it is often less than a meter high and goes unnoticed by ships, and only grows as the depth falls and the wave slows.
This calculator takes an average ocean depth, a travel distance and a wave period. It returns the speed in km/h and m/s, the travel time in hours, the wavelength in kilometers, and a shallow-water check that compares wavelength to depth. A chart shows speed against depth for the whole 0 to 11,000 m range with your chosen depth marked, so you can see how rapidly speed falls once the water becomes shallow.
📐 Formula
📖 How to Use This Calculator
Steps
💡 Example Calculations
Example 1 — Open Pacific Basin
Depth 4000 m, distance 5000 km, period 15 min
Example 2 — Continental Shelf
Depth 100 m, distance 50 km, period 10 min
Example 3 — Near the Shoreline
Depth 10 m, distance 10 km, period 10 min
Example 4 — Over a Deep Ocean Trench
Depth 10900 m, distance 8000 km, period 20 min
❓ Frequently Asked Questions
🔗 Related Calculators
How fast does a tsunami travel in the deep ocean?
In 4000 m of water a tsunami travels at c = sqrt(9.81 x 4000) = 198.09 m/s, which is about 713 km/h, close to the speed of a jet airliner. In the deepest trenches near 11,000 m the speed rises to about 1,180 km/h.
What is the formula for tsunami wave speed?
Tsunami speed is c = sqrt(g d), where g is 9.81 m/s squared and d is the water depth in meters. This is the shallow-water wave speed, valid because a tsunami wavelength is far larger than the ocean depth.
Why does a tsunami slow down near the coast?
Speed depends on the square root of depth, so as the seafloor rises the wave slows. In 10 m of water the speed is only 9.90 m/s (35.7 km/h). The energy is conserved, so the slowing wave bunches up and its height increases.
How long does a tsunami take to cross the Pacific Ocean?
At an average depth near 4000 m the speed is about 713 km/h, so a 5000 km trip takes about 7 hours. Crossing the whole Pacific, around 10,000 to 17,000 km depending on the path, takes roughly 14 to 24 hours.
Does tsunami speed depend on wave height or wavelength?
No. In the shallow-water limit the speed depends only on water depth and gravity. A small and a large tsunami in the same depth travel at the same speed, which is why arrival times can be forecast before the wave height is known.
What is the wavelength of a tsunami?
Wavelength equals speed times period, L = c x T. At 198.09 m/s and a 15 minute period the wavelength is 178.28 km, which is about 44.6 times the 4000 m depth. That large ratio is why the wave behaves as a shallow-water wave.
What is the difference between tsunami speed and wave height?
Speed is how quickly the wave crest moves, set by depth. Height is the amplitude of the water surface. In the deep ocean a tsunami may be under one meter high while moving at hundreds of kilometers per hour, then grows near shore.
Why does the calculator use g = 9.81 m/s squared?
9.81 m/s squared is the standard value for gravitational acceleration at Earth's surface. Actual gravity varies by about 0.5 percent between the equator and poles, which changes the speed by only about 0.25 percent, so 9.81 is accurate enough.
Is the shallow-water formula valid for ordinary wind waves?
No. Wind waves have wavelengths of tens to hundreds of meters, far shorter than the ocean depth, so they travel as deep-water waves whose speed depends on wavelength. The formula c = sqrt(g d) applies when wavelength is more than about 20 times depth.
How accurate is a tsunami travel time estimate from this calculator?
It gives a good first estimate using one average depth. Real tsunamis cross varying seafloor, refract around ridges and islands, and slow down in the final shallow approach, so operational warning centers use full numerical models along the actual path.