Tsunami Engineering Calculator
Six calculators on one page. Change any value and its result updates instantly. No tabs, no buttons.
c = √(g · h)t = d / cH₂ = H₁ · (c₁/c₂)½Educational estimates only. These are simplified models. They are not a substitute for official warnings (NOAA, PTWC, national authorities). In a real event, follow local emergency services. If you feel a strong earthquake near the coast, move to high ground without waiting.
How a tsunami travels
How to use this tool
Pick the questionEach numbered card answers one question. Use only the ones you need, or all six in order.
Change a valueType in any field or choose from a list. Results update immediately and the diagram redraws.
Read the resultThe big number is the answer, the badge is a quick severity cue and the dark line shows the working.
Chain the cardsUse Wave Height → Shoaling → Impact for the size of the wave, and Arrival Time → Evacuation for the time you have.
What you can achieve
Understand tsunami physicsSee why waves cross oceans at jet speed and why they pile up near shore.
Estimate warning timeFind how long a wave takes to reach a coast from a given distance and depth.
Gauge scale of an eventRelate earthquake magnitude and fault type to an indicative wave height and runup.
Assess exposureCompare wave height with ground elevation and terrain to judge flooding severity.
Plan evacuationCheck whether your leave time fits inside the warning window, with a safety buffer.
Teach and learnUse it for classes, drills, community planning and exam practice.
Reference tables
Depth, speed and crossing time (computed from c = √(g·h))
| Depth | Speed (m/s) | Speed (km/h) | Speed (mph) | Time for 1,000 km |
|---|
Earthquake magnitude and tsunami potential (rule of thumb)
| Magnitude | Typical tsunami potential |
|---|---|
| Below 6.5 | Rarely damaging. Small local waves only if shallow and offshore. |
| 6.5 to 7.5 | Local to regional tsunami possible, mainly for thrust or underwater landslide events. |
| 7.5 to 8.5 | Destructive locally, damaging regionally. |
| 8.5 and above | Basin-wide tsunami possible. Great subduction earthquakes. |
Fault mechanism and tsunami generation (factors used in Card 3)
| Mechanism | Factor | Why |
|---|---|---|
| Thrust / reverse | 1.00 | Large vertical seafloor displacement, typical of subduction zones. |
| Normal | 0.50 | Some vertical motion, smaller rupture areas. |
| Strike-slip | 0.15 | Mostly horizontal motion, little water displaced. |
Impact severity scale (excess = wave height − ground elevation, Card 5)
| Excess water | Level | Typical effects |
|---|---|---|
| 0 m or less | Low | Splash-over only at this location. |
| Under 1 m | Moderate | Ground-level flooding, vehicles and light structures at risk. |
| 1 to 3 m | High | Wood-frame buildings damaged, strong currents. |
| 3 m or more | Severe | Catastrophic damage, including to concrete structures. |
| Terrain | Inland km per metre of excess |
|---|---|
| Steep coast / cliffs | 0.02 |
| Moderate slope | 0.10 |
| Gentle slope / beach | 0.40 |
| Flat plain / delta | 1.20 |
Notable tsunamis (approximate figures)
| Event | Cause | Notes |
|---|---|---|
| Chile 1960 | M9.5 earthquake | Largest quake recorded. Waves crossed the Pacific to Hawaii and Japan. |
| Alaska 1964 | M9.2 earthquake | Damaging waves along the US and Canadian west coast. |
| Indian Ocean 2004 | M9.1 earthquake | About 230,000 deaths across 14 countries. Hours of travel time to distant coasts. |
| Tohoku, Japan 2011 | M9.0 earthquake | Runup near 40 m locally, about 18,000 dead or missing. |
| Lituya Bay 1958 | Landslide | Runup about 524 m, the highest ever recorded. |
Evacuation time margin (Card 6)
| Remaining time | Status | Action |
|---|---|---|
| More than 5 min | Safe | Leave promptly. Do not wait for the wave to be seen. |
| 0 to 5 min | Tight | Go now to the highest reachable ground. |
| Negative | Too late | Vertical evacuation: upper floors of a strong reinforced building. |
Key points
Speed depends on depthIn deep ocean a tsunami travels at jet-airliner speed, and slows sharply in shallow water.
Slower but tallerAs depth falls the wave slows, and its height grows roughly with the inverse fourth root of depth (Green's law).
Go high, go earlyEven a 1 m wave floods low ground. Time to leave matters more than the exact wave height.
What it means
The Tsunami Calculator is an advanced, physics-based tool that helps you estimate key tsunami parameters: how fast a wave travels through the ocean, how long it takes to reach the coast, its likely height based on earthquake magnitude and fault type, how it grows as it enters shallow water (shoaling), the severity of coastal impact, and whether there's enough time to evacuate safely. Built on real oceanographic formulas and calibrated against historical events like the 2004 Indian Ocean and 2011 Tōhoku tsunamis, it's designed for students, researchers, and coastal communities worldwide. For educational purposes only — not a substitute for official tsunami warning systems.
Variables Reference — Tsunami Calculator
Symbols & Units
All variables used across the six tsunami calculator modules. Each symbol is defined with its corresponding quantity and SI unit for quick reference during calculations.
| Symbol | Quantity | Unit | Module |
|---|---|---|---|
| c | Wave Speed | m/s, km/h | Wave Speed |
| h | Ocean Depth | meters | Wave Speed |
| g | Gravitational Acceleration | 9.80665 m/s² | Wave Speed |
| t | Arrival Time | hours, minutes | Arrival Time |
| d | Distance from Epicenter | km | Arrival Time |
| havg | Average Depth Along Path | meters | Arrival Time |
| H | Offshore Wave Height | meters | Wave Height |
| M | Earthquake Magnitude | Mw | Wave Height |
| Deq | Earthquake Depth | km | Wave Height |
| R | Runup (Max Onshore Height) | meters | Wave Height |
| Hdeep | Deep‑Water Wave Height | meters | Shoaling |
| Hshallow | Shallow‑Water Wave Height | meters | Shoaling |
| cdeep | Deep‑Water Wave Speed | m/s, km/h | Shoaling |
| cshallow | Shallow‑Water Wave Speed | m/s, km/h | Shoaling |
| PF | Shoaling Amplification Factor | dimensionless | Shoaling |
| hdeep | Deep Water Depth | meters | Shoaling |
| hshallow | Shallow Water Depth | meters | Shoaling |
| S | Severity Level | Low / Moderate / High / Severe | Impact |
| I | Inland Flooding Distance | km | Impact |
| E | Coastal Elevation | meters above sea level | Impact |
| Tarr | Tsunami Arrival Time | minutes | Evacuation |
| Tevac | Evacuation Duration | minutes | Evacuation |
| Trem | Remaining Safe Time | minutes | Evacuation |
| K | Machine Constant (X‑ray) | mGy·m²/(kVp²·mAs) | Dosimetry |
| kVp | Peak Tube Voltage | kVp | Dosimetry |
| mAs | Tube Current × Exposure Time | mAs | Dosimetry |
| d | Source‑to‑Image Distance (SID) | meters | Dosimetry |
Total Variables
26
Covers all tsunami calculations: Wave Speed, Arrival Time, Wave Height, Shoaling, Impact, Evacuation, and Dosimetry.
Worked example
Tsunami Wave Speed (c = √(g × h))
Deep‑Water Propagation
Scenario: A major undersea earthquake occurs in the Pacific Ocean, generating a tsunami that travels across deep water. The average ocean depth along the propagation path is 4,200 meters. Calculate the tsunami's wave speed in both m/s and km/h to estimate how quickly it will reach distant coastlines.
| Parameter | Value |
|---|---|
| Ocean Depth (h) | 4,200 m |
| Gravity (g) | 9.80665 m/s² |
| Wave Speed (c) | 202.9 m/s (computed below) |
| Wave Speed (c) | 730.4 km/h (computed below) |
1Identify the average ocean depth along the tsunami's propagation path — for deep‑ocean tsunamis, this is typically 3,000–5,000 m.
2Use the shallow‑water wave formula: c = √(g × h), where g = 9.80665 m/s² is gravitational acceleration.
3Substitute values: c = √(9.80665 × 4,200) = √(41,187.93) = 202.9 m/s.
4Convert to km/h: multiply by 3.6 → 202.9 × 3.6 = 730.4 km/h — faster than a commercial jet!
Wave Speed
c = 202.9 m/s = 730.4 km/h
At this speed, the tsunami can travel from Japan to Hawaii (≈6,000 km) in about 8.2 hours, giving coastal communities critical time to prepare.
Tsunami Arrival Time (t = d / c)
Early Warning
Scenario: A magnitude 8.2 earthquake occurs off the coast of Chile, generating a tsunami that travels toward New Zealand. The distance from the epicenter to Auckland is approximately 9,500 km. The average ocean depth along the path is 3,800 m. How long will it take for the tsunami to reach Auckland?
| Parameter | Value |
|---|---|
| Distance (d) | 9,500 km |
| Avg. Depth (h) | 3,800 m |
| Wave Speed (c) | 193.0 m/s = 694.8 km/h |
| Arrival Time (t) | 13.7 hours (computed below) |
| Arrival Time (t) | 13 hours 40 minutes |
1Calculate the wave speed using c = √(g × h) = √(9.80665 × 3,800) = 193.0 m/s.
2Convert speed to km/h: 193.0 × 3.6 = 694.8 km/h.
3Calculate travel time: t = d / c = 9,500 / 694.8 = 13.67 hours.
4Convert to hours & minutes: 0.67 × 60 = 40 minutes → 13 hours 40 minutes.
Estimated Arrival
t = 13.7 hours (13h 40min)
This provides nearly 14 hours of lead time — enough for evacuation and emergency response. Official warnings from PTWC should be taken seriously.
Tsunami Wave Height Estimation (Empirical)
Magnitude‑Based
Scenario: A Mw 8.5 earthquake occurs at a depth of 25 km in the Sunda Trench, generating a tsunami that threatens coastal communities in Indonesia. Estimate the offshore wave height and the potential runup at the coast using empirical relationships.
| Parameter | Value |
|---|---|
| Earthquake Magnitude (M) | 8.5 Mw |
| Earthquake Depth (D) | 25 km |
| Offshore Wave Height (H) | 3.87 m (computed below) |
| Estimated Runup (R) | 7.74 – 11.6 m (computed below) |
1Use the empirical model: H ≈ 10^(M/2.3) × 0.01 ÷ (1 + D/100).
2Calculate base height: 10^(8.5/2.3) = 10^(3.6957) = 4,962. The base height is 4,962 × 0.01 = 49.62 m.
3Apply depth factor: 1 + 25/100 = 1.25 → 49.62 / 1.25 = 3.87 m offshore wave height.
4Estimate runup: R ≈ H × (2.0 – 3.0) = 3.87 × 2.5 = 9.7 m (typical).
Wave Height & Runup
H = 3.87 m offshore · R ≈ 9.7 m runup
A 3.87 m offshore wave can produce a 9.7 m runup at the coast — this is a High severity event requiring immediate evacuation of coastal areas.
Wave Shoaling & Slowdown (H₂ = H₁ × √(c₁/c₂))
Near‑Shore Transformation
Scenario: A tsunami with an offshore wave height of 2.0 m travels across a 3,500 m deep ocean. As it approaches a continental shelf, the water depth decreases to 150 m. Calculate the new wave height and speed near the shore, and determine the amplification factor due to shoaling.
| Parameter | Value |
|---|---|
| Deep Depth (h₁) | 3,500 m |
| Shallow Depth (h₂) | 150 m |
| Initial Height (H₁) | 2.0 m |
| Deep Speed (c₁) | 185.2 m/s = 666.7 km/h |
| Shallow Speed (c₂) | 38.3 m/s = 137.9 km/h |
| Amplification Factor (PF) | 2.20× (computed below) |
| Shallow Height (H₂) | 4.40 m (computed below) |
1Calculate deep speed: c₁ = √(g × h₁) = √(9.80665 × 3,500) = 185.2 m/s = 666.7 km/h.
2Calculate shallow speed: c₂ = √(g × h₂) = √(9.80665 × 150) = 38.3 m/s = 137.9 km/h.
3Compute shoaling factor: PF = √(c₁/c₂) = √(666.7/137.9) = √(4.83) = 2.20.
4Calculate shallow height: H₂ = H₁ × PF = 2.0 × 2.20 = 4.40 m.
Shoaling Effect
Speed: 666.7 → 137.9 km/h · Height: 2.0 → 4.40 m
The wave slows down by 79% while growing 2.2× taller. This dramatic transformation explains why tsunamis that are barely noticeable in deep water become destructive walls of water near the coast.
Evacuation Time Helper (T_rem = T_arr − T_evac)
Life‑Saving Decision
Scenario: A tsunami warning is issued for a coastal town. The estimated arrival time is 25 minutes. The town's evacuation plan estimates that residents can reach higher ground in 18 minutes. Determine whether there is enough time for a safe evacuation and what action should be taken.
| Parameter | Value |
|---|---|
| Tsunami Arrival (T_arr) | 25 minutes |
| Evacuation Duration (T_evac) | 18 minutes |
| Remaining Time (T_rem) | 7 minutes (computed below) |
| Status | ⚠️ Tight — Move Quickly! |
1Determine the estimated tsunami arrival time from official warning systems (T_arr = 25 min).
2Calculate the time needed to evacuate based on distance to safety and walking speed (T_evac = 18 min).
3Compute remaining time: T_rem = T_arr − T_evac = 25 − 18 = 7 minutes.
4Assess the situation: With only 7 minutes of buffer, evacuation is possible but urgent. Do not delay — start moving immediately.
Evacuation Status
✅ Safe to Evacuate — 7 min buffer
You have 7 minutes of spare time. Evacuate immediately using the fastest route to high ground. Every second counts — if you feel an earthquake, do not wait for the warning.
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