Seawater Density Calculator (EOS-80)

Find the in-situ density, sigma-t and freezing point of seawater from practical salinity, temperature and pressure using the UNESCO EOS-80 equation.

🌊 Seawater Density Calculator (EOS-80)
Practical salinity (S)
PSU
042
Temperature (T)
°C
-240
Sea pressure (p), about equal to depth in metres
dbar
010000
In-situ density
—
Sigma-t
—
Specific volume
—
Pressure compression
—
Freezing point
—

🌊 What is Seawater Density (EOS-80)?

Seawater density is the mass of a cubic metre of ocean water, typically about 1020 to 1070 kg/m3, and it depends on three measurable quantities: salinity, temperature and pressure. The relationship is not a simple formula but an empirical equation of state. The standard used for decades is the UNESCO 1980 International Equation of State, known as EOS-80, published by Fofonoff and Millard in 1983 and built on laboratory measurements by Millero and Poisson (atmospheric pressure density) and Bryden and Millero (the secant bulk modulus that handles compression).

Oceanographers use density everywhere. It controls whether a water mass sinks or floats, so it drives deep-water formation in the North Atlantic and around Antarctica, the stratification that limits vertical mixing and nutrient supply, the buoyancy and stability of the upper ocean, and the pressure gradients that set geostrophic currents. Density is also needed to convert pressure to depth, to design moorings and submersibles, to calibrate CTD (conductivity, temperature, depth) profiles and to interpret sea-level change from thermal expansion.

A few distinctions matter. The salinity input is practical salinity on the PSS-78 scale, derived from conductivity, which is unitless even though it is often quoted as PSU. Pressure is sea pressure (gauge), not absolute pressure, so the sea surface is 0 dbar. In-situ density includes compression by the water above, so it rises with depth even in a perfectly mixed column. Sigma-t removes that effect by evaluating density at zero pressure and subtracting 1000. For stability questions in deep water, oceanographers prefer potential density referenced to a chosen pressure.

This calculator implements the full EOS-80 coefficient set exactly and reproduces the published UNESCO check values to better than 0.00001 kg/m3. It reports in-situ density, sigma-t, specific volume, the percentage density gain due to pressure, and the freezing point, and it plots density against temperature for your salinity and for 5 units either side, so you can see how sensitive density is to each variable.

📐 Formula

ρ(S,T,p)  =  ρ(S,T,0) ÷ (1 − p ÷ K(S,T,p))
S = practical salinity (PSS-78, valid 0 to 42)
T = temperature (°C, IPTS-68, valid −2 to 40)
p = sea pressure in bars (1 bar = 10 dbar), valid 0 to 1000 bar
ρ(S,T,0) = ρw(T) + A(T)·S + B(T)·S3/2 + C·S2, with ρw(T) = 999.842594 + 6.793952×10−2T − 9.095290×10−3T2 + 1.001685×10−4T3 − 1.120083×10−6T4 + 6.536332×10−9T5
K(S,T,p) = secant bulk modulus (bar), a polynomial in S1/2, T and p from Bryden and Millero (as given in Fofonoff and Millard 1983)
Sigma-t = ρ(S,T,0) − 1000, and freezing point Tf = −0.0575S + 1.710523×10−3S3/2 − 2.154996×10−4S2 − 7.53×10−4pdbar
Example: S = 35, T = 5 °C, p = 0 gives ρ = 1027.675 kg/m3 and sigma-t = 27.675.

📖 How to Use This Calculator

Steps

1
Enter salinity and temperature. Type the practical salinity (0 to 42) and the in-situ temperature in degrees Celsius, or drag the sliders.
2
Enter the sea pressure. Type the pressure in decibars, which is about the same number as the depth in metres, or leave it at 0 for the sea surface.
3
Read density, sigma-t and freezing point. The calculator reports in-situ density, sigma-t, specific volume, pressure compression and freezing point, and charts density against temperature with your point marked.

💡 Example Calculations

Example 1 — Standard Cold Seawater (UNESCO Check Value)

S = 35, T = 5 °C, p = 0 dbar

1
Pure-water term ρw(5) = 999.9668 kg/m3, and the salt terms add the rest to give ρ(35,5,0) = 1027.675 kg/m3
2
Sigma-t = 1027.675 − 1000 = 27.675, and specific volume = 1000 / 1027.675 = 0.973070 ×10−3 m3/kg
Density = 1027.675 kg/m3, freezing point = −1.9223 °C
Try this example →

Example 2 — Warm Tropical Surface Water

S = 35, T = 25 °C, p = 0 dbar

1
Pure-water term ρw(25) = 997.0480 kg/m3, and the salt terms give ρ(35,25,0) = 1023.343 kg/m3
2
Sigma-t = 23.343. Warming by 20 °C lowered density by 4.33 kg/m3 compared with Example 1
Density = 1023.343 kg/m3, specific volume = 0.977189 ×10−3 m3/kg
Try this example →

Example 3 — Deep Water at 4000 dbar

S = 34.7, T = 2 °C, p = 4000 dbar

1
Density at zero pressure ρ(34.7,2,0) = 1027.731 kg/m3, so sigma-t = 27.731
2
With p = 400 bar the secant bulk modulus is K = 23169.88 bar, so ρ = 1027.731 / (1 − 400/23169.88) = 1045.786 kg/m3, a gain of 1.757% from compression
Density = 1045.786 kg/m3, freezing point = −4.9171 °C
Try this example →

Example 4 — Polar Surface Water Near Freezing

S = 34.5, T = −1.8 °C, p = 0 dbar

1
Pure-water term ρw(−1.8) = 999.6902 kg/m3, and the salt terms give ρ(34.5,−1.8,0) = 1027.775 kg/m3
2
Freezing point Tf = −0.0575(34.5) + 1.710523×10−3(34.5)1.5 − 2.154996×10−4(34.5)2 = −1.8936 °C, so the sample sits just 0.09 °C above freezing
Density = 1027.775 kg/m3, sigma-t = 27.775
Try this example →

❓ Frequently Asked Questions

What is the EOS-80 equation of state for seawater?+
EOS-80 is the UNESCO 1980 International Equation of State, published by Fofonoff and Millard in 1983. It gives seawater density as a polynomial function of practical salinity, temperature and pressure, built on Millero and Poisson's atmospheric-pressure density and a secant bulk modulus fitted to laboratory measurements. It is valid for salinity 0 to 42 and pressure up to 1000 bar.
What is the density of seawater at 35 PSU and 5 degrees Celsius?+
At salinity 35, temperature 5 degrees Celsius and zero pressure, the EOS-80 density is 1027.67547 kg/m3. This is one of the official UNESCO check values. At 25 degrees Celsius the same salinity gives 1023.34306 kg/m3, and at 5 degrees Celsius under 10000 dbar it rises to 1069.48914 kg/m3.
What is sigma-t in oceanography?+
Sigma-t is the density of a seawater sample at its measured salinity and temperature but at atmospheric (zero sea) pressure, minus 1000 kg/m3. A seawater density of 1027.675 kg/m3 corresponds to a sigma-t of 27.675. It is used to compare water masses without quoting the leading 1000.
How does temperature affect seawater density?+
Warming lowers density because water expands. At 35 PSU, density falls from about 1027.68 kg/m3 at 5 degrees Celsius to about 1023.34 kg/m3 at 25 degrees Celsius. Unlike fresh water, seawater above salinity 24.7 has no density maximum above its freezing point, so it keeps getting denser as it cools.
How does salinity affect seawater density?+
Adding salt raises density. Each additional practical salinity unit adds roughly 0.75 to 0.8 kg/m3 near the surface. Brackish water at 7 PSU and 10 degrees Celsius has a density near 1005.17 kg/m3, compared with about 1027 kg/m3 for open-ocean water.
How does pressure change seawater density?+
Seawater is slightly compressible. At 35 PSU and 5 degrees Celsius the density increases from 1027.675 kg/m3 at the surface to 1032.259 kg/m3 at 1000 dbar and 1069.489 kg/m3 at 10000 dbar, which is about 0.45 percent for the first kilometre of depth.
What is the freezing point of seawater?+
At 35 PSU and atmospheric pressure, seawater freezes at about -1.922 degrees Celsius. The UNESCO 1978 formula lowers the freezing point by about 0.0575 degrees Celsius per unit of salinity and by 0.00075 degrees Celsius per decibar of pressure, so deep brine can stay liquid well below -2 degrees Celsius.
What is the difference between in-situ density and potential density?+
In-situ density is the actual density at the sample's pressure, so it grows with depth even in a perfectly mixed column. Potential density is the density the parcel would have if brought adiabatically to a reference pressure, so it removes compression and is the right variable for stability. This calculator reports in-situ density and sigma-t.
What units does this seawater density calculator use?+
Salinity is practical salinity (PSS-78, dimensionless, shown as PSU), temperature is in degrees Celsius, and pressure is sea pressure in decibars. Density and sigma-t are in kg/m3, specific volume is in 10^-3 m3/kg, and the freezing point is in degrees Celsius.
Is EOS-80 still used, and how does it compare with TEOS-10?+
EOS-80 is still used for historical data and many models, but oceanographers now recommend TEOS-10, which uses absolute salinity and conservative temperature. For typical open-ocean water the two densities differ only slightly, with the difference depending mainly on regional salinity composition.
Tags: Seawater Density Calculator EOS-80 Calculator UNESCO Equation of State Sigma-T Calculator Ocean Density Calculator Formula Free Online

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What is the EOS-80 equation of state for seawater?

EOS-80 is the UNESCO 1980 International Equation of State, published by Fofonoff and Millard in 1983. It gives seawater density as a polynomial function of practical salinity, temperature and pressure, built on Millero and Poisson's atmospheric-pressure density and a secant bulk modulus fitted to laboratory measurements. It is valid for salinity 0 to 42 and pressure up to 1000 bar.

What is the density of seawater at 35 PSU and 5 degrees Celsius?

At salinity 35, temperature 5 degrees Celsius and zero pressure, the EOS-80 density is 1027.67547 kg/m3. This is one of the official UNESCO check values. At 25 degrees Celsius the same salinity gives 1023.34306 kg/m3, and at 5 degrees Celsius under 10000 dbar it rises to 1069.48914 kg/m3.

What is sigma-t in oceanography?

Sigma-t is the density of a seawater sample at its measured salinity and temperature but at atmospheric (zero sea) pressure, minus 1000 kg/m3. A seawater density of 1027.675 kg/m3 corresponds to a sigma-t of 27.675. It is used to compare water masses without quoting the leading 1000.

How does temperature affect seawater density?

Warming lowers density because water expands. At 35 PSU, density falls from about 1027.68 kg/m3 at 5 degrees Celsius to about 1023.34 kg/m3 at 25 degrees Celsius. Unlike fresh water, seawater above salinity 24.7 has no density maximum above its freezing point, so it keeps getting denser as it cools.

How does salinity affect seawater density?

Adding salt raises density. Each additional practical salinity unit adds roughly 0.75 to 0.8 kg/m3 near the surface. Brackish water at 7 PSU and 10 degrees Celsius has a density near 1005.17 kg/m3, compared with about 1027 kg/m3 for open-ocean water.

How does pressure change seawater density?

Seawater is slightly compressible. At 35 PSU and 5 degrees Celsius the density increases from 1027.675 kg/m3 at the surface to 1032.259 kg/m3 at 1000 dbar and 1069.489 kg/m3 at 10000 dbar, about 0.45 percent for the first kilometre of depth.

What is the freezing point of seawater?

At 35 PSU and atmospheric pressure, seawater freezes at about -1.922 degrees Celsius. The UNESCO 1978 formula lowers the freezing point by about 0.0575 degrees Celsius per unit of salinity and by 0.00075 degrees Celsius per decibar of pressure, so deep brine can stay liquid well below -2 degrees Celsius.

What is the difference between in-situ density and potential density?

In-situ density is the actual density at the sample's pressure, so it grows with depth even in a perfectly mixed column. Potential density is the density the parcel would have if brought adiabatically to a reference pressure, so it removes compression and is the right variable for stability. This calculator reports in-situ density and sigma-t.

What units does this seawater density calculator use?

Salinity is practical salinity (PSS-78, dimensionless, shown as PSU), temperature is in degrees Celsius, and pressure is sea pressure in decibars. Density and sigma-t are in kg/m3, specific volume is in 10^-3 m3/kg, and the freezing point is in degrees Celsius.

Is EOS-80 still used, and how does it compare with TEOS-10?

EOS-80 is still used for historical data and many models, but oceanographers now recommend TEOS-10, which uses absolute salinity and conservative temperature. For typical open-ocean water the two densities differ only slightly, with the difference depending mainly on regional salinity composition.

📌 Quick Tips

💡Use practical salinity (PSS-78, unitless, often written in PSU) as the salinity input. It is a conductivity-based quantity, not grams of salt per kilogram, so it differs slightly from absolute salinity.
💡Pressure here is gauge (sea pressure) in decibars, which is zero at the sea surface. One decibar is very nearly one metre of depth, so 4000 dbar is roughly 3960 m depth in typical ocean water.
💡Sigma-t is the density at the measured salinity and temperature but with the pressure set to zero, minus 1000 kg/m3. It is the classic quantity used to judge static stability of surface layers.
💡Do not compare in-situ densities at different depths to judge stability, because pressure compression dominates. Compare potential density instead, which refers all parcels to one reference pressure.
💡EOS-80 is valid for salinity 0 to 42, temperature -2 to 40 degrees Celsius and pressure up to 1000 bar (10000 dbar). TEOS-10 is the newer standard, but EOS-80 remains in vast numbers of historical datasets.