Tsunami Speed and Arrival Time Calculator
How fast a tsunami crosses the ocean for a given depth, how long it takes to arrive, its wavelength and how much taller it grows as it slows near the coast.
Results
The dashed line marks the value you entered.
What this tool does
A tsunami is so long — a hundred kilometres or more from crest to crest — that the whole ocean is 'shallow' for it, and it travels at √(g d): about 700 km/h in 4000 m of water, the speed of a jet airliner. Near the coast it slows to a few tens of km/h, and because the energy has nowhere to go the wave grows taller, by Green's law as the fourth root of the depth ratio. In the open ocean it may be under a metre high and unnoticeable. The coast height here is only the shoaling effect; run-up on land can be much higher.
Formula
c = √(g d) · travel time = distance ÷ c · λ = c T · Green's law: H₂ = H₁ (d₁ ÷ d₂)^¼
Variables
| Symbol | Meaning | Unit |
|---|---|---|
dp | Depth | m |
ds | Distance the tsunami has to travel | km |
tp | Period of the wave (time between crests) | min |
hw | Wave height in the open ocean | m |
dc | Depth near the coast | m |
KH | Speed in the open ocean | km/h |
TT | Travel time | h |
WL | Wavelength in the open ocean | km |
CK | Speed near the coast | km/h |
CH | Wave height near the coast (Green's law) | m |
Worked example
- Depth4000 m
- Distance the tsunami has to travel5000 km
- Period of the wave (time between crests)20 min
- Wave height in the open ocean1 m
- Depth near the coast10 m
- Speed in the open ocean713 km/h
- Travel time7.01 h
- Wavelength in the open ocean238 km
- Speed near the coast36 km/h
- Wave height near the coast (Green's law)4.47 m
Limitations
- The result is an estimate based only on the values you type. Real situations often include factors this calculator does not know about.
- The formula assumes ideal conditions: no friction losses, no air resistance and no efficiency losses unless you enter them.