Absolute Salinity and Conservative Temperature Calculator (TEOS-10)

Convert Practical Salinity to Absolute Salinity and potential temperature to Conservative Temperature using the TEOS-10 definitions.

🌊 Absolute Salinity and Conservative Temperature Calculator (TEOS-10)
Practical Salinity (SP)
PSU
042
Potential temperature (θ, 0 dbar)
°C
-240
Conservative Temperature (CT)
—
Absolute Salinity (SA)
—
θ − CT
—
Potential enthalpy (h0)
—

🌊 What are Absolute Salinity and Conservative Temperature?

Absolute Salinity (SA) and Conservative Temperature (CT) are the two primary state variables of TEOS-10, the Thermodynamic Equation of Seawater 2010 adopted by UNESCO's Intergovernmental Oceanographic Commission in 2009. They replace the older Practical Salinity (SP, defined by conductivity ratios on the PSS-78 scale) and potential temperature (θ) in modern oceanography. Absolute Salinity is a mass fraction in g/kg, and Conservative Temperature is a rescaled form of potential enthalpy, expressed in degrees Celsius.

The conversion from SP to SA starts with the Reference Composition. Reference Salinity is SR = (35.16504 / 35) × SP, so a standard ocean sample with SP = 35 has SR = 35.16504 g/kg. The full Absolute Salinity adds a small regional correction δSA that accounts for real variations in dissolved silicate, nitrate and carbonate. That correction is about 0.0 to 0.03 g/kg in most of the ocean, and this calculator ignores it, so it returns the Reference Salinity.

Conservative Temperature solves a different problem. Potential temperature is not conserved when water masses mix, because the specific heat of seawater depends on salinity and temperature. Potential enthalpy h0 is conserved far more closely, and CT = h0 / cp0 simply scales it to temperature units using the constant cp0 = 3991.86795711963 J/(kg K). Researchers use CT to compute ocean heat content, heat fluxes, water mass mixing, and as the temperature input to TEOS-10 density and sound speed routines. For typical ocean water the difference θ − CT is under about 0.1 °C, but in fresh water it can exceed 1 °C.

Important accuracy note: the official GSW toolbox evaluates CT with a fitted polynomial for potential enthalpy. This calculator instead numerically integrates the UNESCO seawater specific heat polynomial at 0 dbar from 0 °C up to θ, then divides by cp0. That is a documented approximation with an accuracy of an estimated few thousandths of a °C for ocean water (not validated against the official GSW check values), not the exact GSW result. It also sets h0 to zero at 0 °C at every salinity, which neglects a small salinity-dependent offset (about 0.01 °C at the lowest salinities, near zero at SP = 35).

📐 Formula

SA = (35.16504 / 35) × SP    CT = h0 / cp0 = (1 / cp0) ∫0θ cp(SP, T) dT
SP = Practical Salinity (PSS-78, dimensionless)
SA = Absolute Salinity (g/kg), Reference Composition, with δSA taken as zero
θ = potential temperature referenced to 0 dbar (°C)
cp(S, T) = specific heat of seawater at 0 dbar, cp = c0(T) + A(T) S + B(T) S1.5 (UNESCO polynomial, J/(kg K))
h0 = potential enthalpy at 0 dbar relative to 0 °C (J/kg)
cp0 = 3991.86795711963 J/(kg K), the TEOS-10 constant
Example: SP = 35 and θ = 20 °C give SA = 35.1650 g/kg and CT = 19.9786 °C.

📖 How to Use This Calculator

Steps

1
Enter the practical salinity. Type the Practical Salinity SP from a CTD or bottle sample, typically 30 to 38 in the open ocean.
2
Enter the potential temperature. Type the potential temperature θ in degrees Celsius, referenced to the sea surface (0 dbar).
3
Read SA, CT and the difference. The calculator shows Absolute Salinity, Conservative Temperature, potential enthalpy and the θ − CT gap, and plots the gap against temperature.

💡 Example Calculations

Example 1 — Warm Subtropical Surface Water

SP = 35, θ = 20 °C

1
SA = (35.16504 / 35) × 35 = 35.1650 g/kg
2
h0 = ∫ cp dT from 0 to 20 °C = 79.752 kJ/kg
3
CT = 79752 / 3991.868 = 19.9786 °C
θ − CT = 0.0214 °C
Try this example →

Example 2 — Fresher Coastal Water

SP = 30, θ = 15 °C

1
SA = (35.16504 / 35) × 30 = 30.1415 g/kg
2
h0 = ∫ cp dT from 0 to 15 °C = 60.217 kJ/kg
3
CT = 60217 / 3991.868 = 15.0850 °C
θ − CT = −0.0850 °C (CT is warmer than θ)
Try this example →

Example 3 — Hot Saline Red Sea Water

SP = 38, θ = 35 °C

1
SA = (35.16504 / 35) × 38 = 38.1792 g/kg
2
h0 = ∫ cp dT from 0 to 35 °C = 139.192 kJ/kg
3
CT = 139192 / 3991.868 = 34.8688 °C
θ − CT = 0.1312 °C
Try this example →

Example 4 — Fresh Water Limit

SP = 0, θ = 25 °C

1
SA = (35.16504 / 35) × 0 = 0.0000 g/kg
2
h0 = ∫ cp dT from 0 to 25 °C = 104.790 kJ/kg
3
CT = 104790 / 3991.868 = 26.2509 °C
θ − CT = −1.2509 °C (fresh water has a larger specific heat than cp0)
Try this example →

❓ Frequently Asked Questions

What is Absolute Salinity in TEOS-10?+
Absolute Salinity SA is the mass fraction of dissolved material in seawater, expressed in g/kg. TEOS-10 uses it instead of Practical Salinity because SA is a true thermodynamic variable, while SP is a dimensionless conductivity-based scale. For standard seawater SA = 35.16504 g/kg when SP = 35.
How do you convert Practical Salinity to Absolute Salinity?+
For the Reference Composition, SA = SR = (35.16504 / 35) × SP, which is about 1.004715 × SP. The full conversion adds a regional correction δSA, which is about 0.0 to 0.03 g/kg in most of the ocean and is not included here.
What is Conservative Temperature?+
Conservative Temperature CT is potential enthalpy h0 divided by the fixed constant cp0 = 3991.86795711963 J/(kg K). It is expressed in degrees Celsius and is a far better measure of the heat content of seawater than potential temperature.
What is the difference between potential temperature and Conservative Temperature?+
Potential temperature θ is the temperature a water parcel would have if moved adiabatically to the surface. Conservative Temperature is proportional to the parcel's potential enthalpy. They differ by up to about 0.1 °C for ocean water and by 1 °C or more in very fresh water.
Why did oceanographers replace potential temperature with Conservative Temperature?+
Potential temperature is not conserved when water masses mix, because the specific heat of seawater varies with salinity and temperature. Potential enthalpy is conserved to a much better approximation, so Conservative Temperature became the recommended heat variable in TEOS-10 for ocean heat content and mixing studies.
How accurate is this Conservative Temperature calculator?+
The method integrates the UNESCO seawater specific heat polynomial from 0 °C to θ and divides by cp0. For ocean salinities this should agree with the official GSW result to an estimated few thousandths of a °C. At very low salinity the neglected h0 offset at 0 °C can add about 0.01 °C. It is not the exact GSW polynomial.
What is the Reference Composition of seawater?+
The Reference Composition is a defined mix of the major sea salt constituents, determined by Millero and colleagues in 2008, that is used to define Reference Salinity SR. It represents standard seawater, and SR is exactly 35.16504 g/kg at SP = 35.
What is the density anomaly δSA?+
δSA is the difference between Absolute Salinity and Reference Salinity caused by real regional variations in the ratios of dissolved silicate, nitrate and carbonate. It is about 0.0 to 0.03 g/kg in most of the ocean, reaching larger values only in the deep North Pacific and some coastal seas.
Is Conservative Temperature the same as in situ temperature?+
No. In situ temperature is what a thermometer reads at depth. Potential temperature removes the effect of pressure, and Conservative Temperature then rescales potential enthalpy. This calculator takes potential temperature referenced to 0 dbar as input, not in situ temperature.
What range of inputs does the calculator accept?+
Practical Salinity from 0 to 42 and potential temperature from -2 to 40 °C. The UNESCO specific heat polynomial was fitted to salinities of 0 to 40 and temperatures of 0 to 35 °C, so values beyond that are extrapolated and less reliable.
Tags: Absolute Salinity Calculator Conservative Temperature Calculator TEOS-10 Calculator Practical Salinity to Absolute Salinity Potential Temperature to Conservative Temperature Oceanography Calculator Calculator Formula Free Online

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What is Absolute Salinity in TEOS-10?

Absolute Salinity SA is the mass fraction of dissolved material in seawater, expressed in g/kg. TEOS-10 uses it instead of Practical Salinity because SA is a true thermodynamic variable, while SP is a dimensionless conductivity-based scale. For standard seawater SA = 35.16504 g/kg when SP = 35.

How do you convert Practical Salinity to Absolute Salinity?

For the Reference Composition, SA = SR = (35.16504 / 35) x SP, which is about 1.004715 x SP. The full conversion adds a regional correction delta SA, which is about 0.0 to 0.03 g/kg in most of the ocean and is not included here.

What is Conservative Temperature?

Conservative Temperature CT is potential enthalpy h0 divided by the fixed constant cp0 = 3991.86795711963 J/(kg K). It is expressed in degrees Celsius and is a far better measure of the heat content of seawater than potential temperature.

What is the difference between potential temperature and Conservative Temperature?

Potential temperature theta is the temperature a water parcel would have if moved adiabatically to the surface. Conservative Temperature is proportional to the parcel's potential enthalpy. They differ by up to about 0.1 C for ocean water and by 1 C or more in very fresh water.

Why did oceanographers replace potential temperature with Conservative Temperature?

Potential temperature is not conserved when water masses mix, because the specific heat of seawater varies with salinity and temperature. Potential enthalpy is conserved to a much better approximation, so TEOS-10 adopted Conservative Temperature as the recommended heat variable.

How accurate is this Conservative Temperature calculator?

The method integrates the UNESCO seawater specific heat polynomial from 0 C to theta and divides by cp0. For ocean salinities this agrees with the official GSW result to an estimated few thousandths of a degree Celsius. At very low salinity the neglected h0 offset at 0 C can add about 0.01 C.

What is the Reference Composition of seawater?

The Reference Composition is a defined mix of the major sea salt constituents, determined by Millero and colleagues in 2008, that is used to define Reference Salinity SR. It represents standard seawater, and SR is exactly 35.16504 g/kg at SP = 35.

What is the density anomaly delta SA?

Delta SA is the difference between Absolute Salinity and Reference Salinity caused by real regional variations in the ratios of dissolved silicate, nitrate and carbonate. It is about 0.0 to 0.03 g/kg in most of the ocean, reaching larger values only in the deep North Pacific and some coastal seas.

Is Conservative Temperature the same as in situ temperature?

No. In situ temperature is what a thermometer reads at depth. Potential temperature removes the effect of pressure, and Conservative Temperature then rescales potential enthalpy. This calculator takes potential temperature referenced to 0 dbar as input, not in situ temperature.

What range of inputs does the calculator accept?

Practical Salinity from 0 to 42 and potential temperature from -2 to 40 C. The UNESCO specific heat polynomial was fitted to 0 to 40 in salinity and 0 to 35 C, so values beyond that are extrapolated and less reliable.

📌 Quick Tips

💡Absolute Salinity SA is in g/kg and is numerically about 0.5 percent larger than Practical Salinity SP, so a typical open ocean SP of 35 becomes SA of about 35.165 g/kg.
💡This tool uses the Reference Composition and ignores the regional density anomaly delta SA, which is roughly 0.0 to 0.03 g/kg across most of the ocean. For high accuracy work in the North Pacific or near the coast, use the full GSW toolbox with a latitude and longitude.
💡Conservative Temperature is proportional to potential enthalpy, so it tracks heat content far better than potential temperature. Mixing two water masses conserves CT, but does not exactly conserve theta.
💡For typical ocean salinities the gap between theta and CT stays within about 0.1 C, but in very fresh water it can reach 1 C or more. Check the chart before assuming the two are interchangeable.
💡CT here comes from numerically integrating the UNESCO seawater specific heat polynomial, with an accuracy of an estimated few thousandths of a degree Celsius for ocean water (not validated against the official GSW check values). It is not the exact GSW polynomial, so use the official toolbox when you need publication grade values.