Sea-Level Rise (Thermal Expansion)
Rise in sea level as ocean water warms and expands.
Formula
Variables
Example
Warming water expands, raising seas even before any ice melts
How it works
When ocean water warms, each parcel of water occupies a slightly larger volume because its molecules move farther apart. If a surface layer of thickness h expands upward, that extra volume shows up as a rise in sea level, Δh, and the increase is proportional to both the depth of the warmed layer and the temperature change. The factor β tells you how strongly the water expands per degree, so the formula is a simple linear approximation for small to moderate warming.
When to use it
Use this formula when estimating sea-level rise caused only by thermal expansion of seawater, such as in climate studies or simple ocean-warming models. It is useful when you know the average warming of a mixed ocean layer and want a quick estimate before considering ice melt or other effects.
Worked example, step by step
Suppose the top h = 700 m of the ocean warms by ΔT = 1.5 °C, and seawater has a thermal expansion coefficient β = 2.1 × 10^-4 °C^-1. Δh = h β ΔT Δh = 700 × (2.1 × 10^-4) × 1.5 Δh = 700 × 3.15 × 10^-4 Δh = 0.2205 m Δh ≈ 0.22 m So the sea level would rise by about 22 cm from thermal expansion alone.
Common mistakes to avoid
- Using the total ocean depth instead of the warmed layer depth
- Forgetting that β must match the temperature units, usually per °C
- Treating this as the total sea-level rise from climate change and ignoring ice melt and other contributions
Did You Know?
Thermal expansion causes roughly a third to a half of observed sea-level rise.
Share this formula
More in Weather & Calamities
View allSaturation Vapour Pressure
IntermediateThe maximum water-vapour pressure air can hold at a given temperature (Tetens formula).
Apparent Temperature (Heat Index)
IntermediateHow hot the air actually feels once humidity and wind are taken into account.
Beaufort Wind Scale
IntermediateConverts a Beaufort force number into an approximate wind speed.
Wind Pressure (Dynamic)
IntermediateThe pressure a moving airmass exerts on a surface such as a wall or roof.
Radiative Forcing from CO₂
AdvancedExtra energy trapped by the atmosphere as carbon-dioxide concentration rises.
Planetary Equilibrium Temperature
AdvancedThe temperature a planet would settle at from sunlight alone, before greenhouse warming.