Tsunami Travel Time Calculator
Calculate tsunami wave speed and travel time across ocean basins using the shallow water wave equation v = √(g×d). Covers deep ocean, continental shelf shoaling, and major Pacific routes with historical examples.
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Wave Speed (km/h)
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Travel Time (hours) —
Travel Time (minutes) —
Arrival estimate —
Extended More scenarios, charts & detailed breakdown ▾
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Speed (km/h)
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Travel time (hours) —
Reference —
Professional Full parameters & maximum detail ▾
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Deep ocean speed (km/h)
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Shelf speed (km/h) —
Time in deep ocean (h) —
Time on shelf (h) —
Total travel time (h) —
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How to Use This Calculator
- Enter distance from epicenter and average ocean depth.
- Results show wave speed (km/h) and estimated travel time.
- Use Pacific Routes tab for preset major ocean crossings with historical references.
- Use Continental Shelf tab to see how the wave slows and amplifies near shore.
- Professional mode splits the path into deep ocean and shelf segments for a combined arrival estimate.
Formula
v = √(g × depth) (shallow water wave equation)
g = 9.81 m/s² | depth in meters → v in m/s × 3.6 = km/h
Travel time = distance / speed
Shoaling (Green's Law): height ∝ depth^(−1/4)
Example
Example: Japan → Hawaii, 6200 km, depth 4000 m → speed ≈ 713 km/h, travel time ≈ 8.7 hours. (2011 Tōhoku tsunami observed ~8h, confirming the formula.)
Frequently Asked Questions
- In the deep ocean, a tsunami travels at speeds determined by the shallow water wave equation: v = √(g × depth), where g = 9.81 m/s² and depth is ocean depth in meters. At an average ocean depth of 4,000 meters, this gives v = √(9.81 × 4000) ≈ 198 m/s ≈ 713 km/h — comparable to a commercial jet aircraft. This extraordinarily high speed is possible because tsunami wavelengths (typically 100–500 km) are far greater than ocean depth (~4 km), placing them in the 'shallow water wave' regime regardless of actual water depth. In open ocean the wave height is less than 1 meter and the wave is undetectable to ships. As the tsunami approaches shore and depth decreases to 200 m, speed drops to about 159 km/h; at 50 m depth it slows to about 79 km/h. This speed reduction concentrates energy and dramatically increases wave height — the phenomenon called shoaling.
- The energy of a tsunami wave is proportional to the square of its amplitude (height) and travels at speed v = √(g×d). As depth decreases approaching shore, wave speed decreases. Since energy must be conserved (ignoring friction), and since the wave is simultaneously being compressed in wavelength, the amplitude must increase — this is called Green's Law, which predicts that wave height scales as depth^(-1/4). So if depth decreases by a factor of 16 (from 4000 m to 250 m), wave height doubles. In practice, a barely perceptible 0.5 m ocean swell can become a 10+ meter wall of water at the coast. The process also depends on coastal geometry: funnel-shaped bays concentrate energy further (Hilo Bay, Hawaii is notoriously vulnerable), while offshore barriers and wide continental shelves dissipate energy. Numerical models used by NOAA's Pacific Tsunami Warning Center (PTWC) simulate these effects in near-real-time after major earthquakes.
- Modern tsunami arrival time prediction combines real-time seismic data, ocean bathymetry databases, and numerical wave propagation models. Within minutes of a major earthquake, the NOAA Pacific Tsunami Warning Center (PTWC) and ITIC estimate the epicenter location and magnitude. Pre-computed propagation databases (such as NOAA's ComMIT/MOST model) allow rapid generation of arrival time maps across entire ocean basins. DART (Deep-ocean Assessment and Reporting of Tsunamis) buoys anchored at strategic Pacific locations detect tsunami passage and transmit real-time water pressure data that confirms wave generation and measures amplitude. These buoy readings are assimilated into running models to improve forecasts within 15–20 minutes of the earthquake. The simple formula used in this calculator — travel time = distance / √(g×depth) — gives a useful first estimate but real-time models account for variable bathymetry along the entire wave path, which can alter arrival times by tens of minutes.
- Tsunamis have nothing to do with tides — 'tidal wave' is a colloquial misnomer that scientific and emergency management communities actively discourage. True tidal waves are the predictable daily rise and fall of sea level driven by the gravitational pull of the Moon and Sun. Tsunamis are generated by sudden displacement of a large volume of water, most commonly by submarine earthquakes (the fault floor suddenly moves up or down, displacing the water column above it), but also by undersea landslides, volcanic eruptions, and rarely by meteorite impacts. The 2004 Indian Ocean tsunami was triggered by a Mw 9.1 rupture that lifted the seafloor by up to 10 meters along a 1,200 km fault, displacing an estimated 30 cubic kilometers of water. Unlike wind-driven waves (which involve circular motion of surface water), tsunami particles move in horizontal ellipses extending to the seafloor — the entire water column moves, which is why tsunamis carry so much more energy and destructive power than ordinary storm waves.
- The Pacific Rim is lined by the world's most seismically active subduction zones — the Cascadia, Japan, Aleutian, Peru-Chile, and Tonga trenches among others — where oceanic plates dive beneath continental plates and periodically release centuries of accumulated stress in megathrust earthquakes (Mw 8.5+). These events are the most efficient tsunami generators because they displace vast areas of seafloor vertically. The Pacific Ocean's breadth (up to 17,000 km) means tsunamis can travel to almost any Pacific coastline given enough time. Communities in Hawaii, Japan, Alaska, British Columbia, Washington, Oregon, California, Peru, Chile, New Zealand, and many Pacific island nations all face recurring tsunami risk from both local and distant sources. Local sources are most dangerous because warning time may be only minutes — the earthquake shaking itself IS the warning. The Indian Ocean tsunami of 2004 demonstrated that historically tsunami-naive regions can also face catastrophic events when appropriate warning infrastructure is absent.
Related Calculators
Sources & References (5) ▾
- NOAA Pacific Tsunami Warning Center (PTWC) — NOAA National Weather Service
- USGS – Tsunamis and Earthquake Hazards — U.S. Geological Survey
- ITIC – International Tsunami Information Center — IOC/UNESCO
- IOC/UNESCO Tsunami Programme — Intergovernmental Oceanographic Commission UNESCO
- Bryant E – Tsunami: The Underrated Hazard (3rd ed.) — Springer 2014