Sea Level Rise from Thermal Expansion Calculator
Estimate thermosteric sea level rise from ocean warming and layer depth using the simplified thermal expansion formula.
🌊 What is Sea Level Rise from Thermal Expansion?
Thermal expansion sea level rise, also called thermosteric sea level rise, is the rise in global sea level caused by seawater expanding as it absorbs heat and warms, with no water added to the ocean at all. It happens because the density of water decreases as its temperature increases, so a column of warmer seawater physically occupies more volume than the same mass of colder seawater, pushing the surface higher. This is a purely physical volume effect, distinct from any melting ice adding new mass to the ocean.
Oceanographers and climate scientists use thermosteric sea level rise estimates constantly, to attribute how much of the observed rise in global mean sea level over the last century comes from ocean warming rather than ice melt, to project future sea level under different warming scenarios using ocean heat content projections, to explain regional differences in sea level trends since warming and expansion are not uniform across ocean basins, and to sanity-check climate model output against tide gauge and satellite altimetry records.
A common misconception is that all sea level rise comes from melting ice. In reality, thermal expansion has historically contributed roughly a third to a half of observed global mean sea level rise, and it is entirely separate from the eustatic (mass-based) contribution of melting glaciers and ice sheets. Another misconception is that the ocean warms uniformly with depth. It does not. Most of the heat absorbed by the ocean so far is concentrated in the upper few hundred meters, which is why the depth of the layer being considered matters enormously to the result.
This calculator applies a simplified thermal expansion formula so you can quickly estimate the thermosteric sea level rise contribution for any combination of expansion coefficient, ocean warming, and layer depth, and compare how sensitive the result is to the depth assumption you choose.
📐 Formula
This is a simplified linear approximation. IPCC assessments (per IPCC AR6 Working Group I, Chapter 9) use full ocean temperature and salinity profiles rather than a single average coefficient, depth, and warming value, but this formula captures the correct order of magnitude and the key alpha-times-depth relationship.
📖 How to Use This Calculator
Steps
💡 Example Calculations
Example 1 — Near-term Mixed-Layer Warming
α = 2.1 × 10⁻⁴ /°C, ΔT = 0.6°C, D = 700 m (mixed layer)
Example 2 — Upper 2000 m Ocean Warming
α = 2.1 × 10⁻⁴ /°C, ΔT = 0.15°C, D = 2000 m (upper ocean, Argo-monitored layer)
Example 3 — Upper-Bound Future Warming Scenario
α = 3.0 × 10⁻⁴ /°C, ΔT = 2.0°C, D = 700 m (mixed layer under strong future warming)
❓ Frequently Asked Questions
🔗 Related Calculators
What is thermosteric sea level rise?
Thermosteric sea level rise is the portion of sea level rise caused by seawater expanding as it warms, with no change in ocean mass. It happens because water density decreases as temperature rises, so a warmer column of seawater occupies more volume and its surface sits higher, even though no water was added to the ocean.
What formula does this calculator use for thermal expansion sea level rise?
It uses the simplified expression delta SLR = alpha x delta T x D, where alpha is the thermal expansion coefficient of seawater (per degree C), delta T is the ocean warming being considered (degrees C), and D is the depth of the ocean layer being warmed (meters). The result is converted to millimeters for display.
What value should I use for the thermal expansion coefficient alpha?
A commonly used simplified value is about 2.1 x 10 to the -4 per degree C, within the broader accepted range of roughly 2 to 4 x 10 to the -4 per degree C. The true coefficient rises with temperature and pressure, so warmer, deeper water expands more per degree of warming than cold, shallow water.
Why does the ocean layer depth D matter so much in this formula?
Because thermal expansion is a volume effect that accumulates through the whole warmed water column. Doubling the depth of water that warms by the same amount roughly doubles the sea level rise, which is why a shallow mixed-layer estimate and a full-ocean-depth estimate for the same delta T can differ by a factor of five or more.
Should I use the mixed-layer depth or the full ocean depth?
Use the mixed layer (roughly 700 m) for near-term estimates, since most of the heat the ocean has absorbed so far is concentrated near the surface. Use the full average ocean depth (roughly 3700 m) only for very long-term or equilibrium scenarios, since it takes centuries for warming to mix all the way to the deep ocean.
How much has thermal expansion contributed to observed sea level rise so far?
IPCC assessments attribute roughly one third to one half of the observed global mean sea level rise since 1900 to thermal expansion, with the remainder coming mainly from land ice melt (glaciers, Greenland, and Antarctica) and smaller contributions from land water storage changes.
How does thermal expansion sea level rise compare to sea level rise from ice melt?
They are two separate physical mechanisms. Thermal expansion adds no water to the ocean, it just expands the water already there as it warms. Ice melt adds new water mass from land ice. See the companion Sea Level Rise from Ice Melt Calculator, which uses the mass-based formula delta SLR = ice mass lost (Gt) / 361.8, to estimate the eustatic contribution separately.
Is the alpha x delta T x D formula exact?
No, it is a simplified linear approximation. The true thermal expansion coefficient varies with temperature, pressure, and salinity, and real ocean warming is not distributed evenly with depth. Full climate models use temperature and salinity profiles at many depth levels rather than a single average delta T and D, but this simplified formula captures the right order of magnitude and the key physical relationship.
What is a realistic delta T value to enter for near-term estimates?
Upper-ocean (mixed layer) warming of roughly 0.5 to 1.0 degrees C since pre-industrial times is a commonly cited range for the surface and near-surface ocean. Full-ocean average warming is much smaller, often estimated well under 0.1 degrees C, because the deep ocean has warmed far less than the surface.
Can I use this calculator to estimate future sea level rise under a warming scenario?
Yes. Enter a projected delta T for the layer depth you are interested in, such as an IPCC scenario's upper-ocean warming projection for 2100, and the calculator returns the resulting thermosteric sea level rise contribution in millimeters and centimeters.
Why does the calculator also show a full-ocean depth comparison?
The full-ocean comparison box applies the same delta T you entered across the entire 3700 m average ocean depth, purely to illustrate how strongly the result depends on depth. It is a sensitivity comparison, not a realistic estimate, since the deep ocean has not actually warmed by the same amount as the mixed layer.
Does this calculator account for the total observed sea level rise, including ice melt?
No, this calculator isolates only the thermal expansion (thermosteric) contribution. To estimate total sea level rise, add the result from this calculator to the eustatic contribution from land ice melt, calculated separately with the companion Sea Level Rise from Ice Melt Calculator.