Practical Salinity Calculator

Convert a conductivity reading into practical salinity (PSS-78) or work backwards from salinity to the conductivity a sensor should read.

🌊 Practical Salinity Calculator (PSS-78)
Measured conductivity (C)42.914 mS/cm
mS/cm
190
Practical salinity (S)35
(no unit)
242
Temperature (T)15 °C
°C
-235
Temperature scale
Pressure (p, above atmosphere)0 dbar
dbar
010000
Practical salinity (S)
—
Conductivity ratio R
—
Ratio Rt (T, p removed)
—
Reference salinity (approx.)
—

Expected conductivity
—
Conductivity in S/m
—
Conductivity ratio R
—
Ratio Rt (T, p removed)
—

🌊 What is Practical Salinity?

Practical salinity is the standard way oceanographers report how salty seawater is. Instead of weighing dissolved salt, which is slow and difficult, the Practical Salinity Scale 1978 (PSS-78) infers salinity from how well a water sample conducts electricity. Dissolved ions carry current, so saltier water conducts better. By comparing the sample with a reference solution of potassium chloride, and correcting for temperature and pressure, the scale produces a single number, S, that is about 35 for typical open-ocean water, 38 or more in the Red Sea and Mediterranean, and 30 to 33 in coastal and polar surface waters diluted by rivers and ice melt.

Practical salinity underlies almost all modern ocean data. Every CTD (conductivity, temperature, depth) cast on a research ship, every Argo float profile, and every moored sensor measures conductivity and converts it with the algorithm on this page. Salinity, together with temperature and pressure, sets seawater density, which drives ocean circulation, stratification and the formation of deep water. Oceanographers, coastal engineers, aquaculture operators, desalination plant designers and students all need to move between a raw conductivity reading and a defensible salinity value.

Several points are often misunderstood. Practical salinity has no unit: it is a ratio of conductivities, so the common label PSU is informal and not part of the SI. It is also not exactly grams of salt per kilogram of water. The newer TEOS-10 standard defines absolute salinity in g/kg, which for standard seawater is about 0.47 percent larger than practical salinity (35.165 g/kg for S = 35). Finally, conductivity depends strongly on temperature, roughly 2 percent per degree Celsius, so a conductivity number means nothing until the temperature and pressure of the measurement are known.

This calculator implements the full PSS-78 algorithm in two directions. The first mode converts a measured conductivity, temperature and pressure into practical salinity. The second mode runs the algorithm backwards, using bisection, to tell you what conductivity a sensor should read for a chosen salinity, which is useful for checking calibration with standard seawater or planning a sensor range. The chart shows the full salinity to conductivity relationship at your temperature and pressure, with your current point marked.

📐 Formula

Rt  =  R ÷ (rp × rt)   →   S  =  Σ ai Rti/2  +  [(T − 15) ÷ (1 + k(T − 15))] Σ bi Rti/2
R = C ÷ 42.914 mS/cm, the conductivity ratio to standard seawater (S = 35, T = 15 °C, p = 0)
rt(T) = c0 + c1T + c2T² + c3T³ + c4T4, with c = 0.6766097, 2.00564×10−2, 1.104259×10−4, −6.9698×10−7, 1.0031×10−9
rp = 1 + p(e1 + e2p + e3p²) ÷ (1 + d1T + d2T² + (d3 + d4T)R), with p in dbar, e = 2.070×10−5, −6.370×10−10, 3.989×10−15 and d = 3.426×10−2, 4.464×10−4, 0.4215, −3.107×10−3
ai = 0.0080, −0.1692, 25.3851, 14.0941, −7.0261, 2.7081 (sum to exactly 35 at Rt = 1)
bi = 0.0005, −0.0056, −0.0066, −0.0375, 0.0636, −0.0144 (sum to zero at Rt = 1) and k = 0.0162
T = temperature on IPTS-68 in °C, from T68 = 1.00024 × T90 when you enter an ITS-90 value
Example: C = 42.914 mS/cm, T = 15 °C (IPTS-68), p = 0 gives R = Rt = 1 and S = 35.000.

The coefficients are those of Lewis (1980) and UNESCO Technical Papers in Marine Science 44 (1983). The reverse mode solves S(R) = Starget for R by bisection, because the PSS-78 equation is monotonic in R, and then returns C = R × 42.914 mS/cm.

📖 How to Use This Calculator

Steps

1
Choose a direction. Pick Conductivity to Salinity to convert a sensor reading, or Salinity to Conductivity to find what a sensor should read.
2
Enter temperature, scale and pressure. Type the in-situ temperature, say whether it is ITS-90 or IPTS-68, and enter the pressure in decibars (0 at the surface, about 1 dbar per metre of depth).
3
Enter the conductivity or salinity. Type the measured conductivity in mS/cm (multiply S/m by 10), or the target practical salinity between 2 and 42.
4
Read the result and chart. The calculator shows the answer with the conductivity ratios, and plots salinity against conductivity with your current point marked.

💡 Example Calculations

Example 1 — Standard Seawater

C = 42.914 mS/cm, T = 15 °C (IPTS-68), p = 0 dbar

1
R = 42.914 ÷ 42.914 = 1.00000, and at 15 °C and 0 dbar rt and rp are 1, so Rt = 1.00000.
2
Sum of ai = 0.0080 − 0.1692 + 25.3851 + 14.0941 − 7.0261 + 2.7081 = 35.0000, and the temperature term is zero at 15 °C.
Practical salinity S = 35.000 (reference salinity about 35.165 g/kg)
Try this example →

Example 2 — Warm Tropical Surface Water

C = 53 mS/cm, T = 25 °C (ITS-90), p = 0 dbar

1
T68 = 1.00024 × 25 = 25.006 °C and R = 53 ÷ 42.914 = 1.23503.
2
Removing the temperature effect with rt(25.006) gives Rt = 0.99866.
Practical salinity S = 34.947
Try this example →

Example 3 — Cold Deep Water at 4000 dbar

C = 32 mS/cm, T = 2 °C (ITS-90), p = 4000 dbar

1
R = 32 ÷ 42.914 = 0.74568 at T68 = 2.000 °C.
2
The pressure term rp raises the in-situ conductivity, and removing it together with rt gives Rt = 0.98761.
Practical salinity S = 34.520 (reference salinity about 34.683 g/kg)
Try this example →

Example 4 — Expected Conductivity of S = 35 at 20 °C

S = 35, T = 20 °C (ITS-90), p = 0 dbar, reverse mode

1
T68 = 1.00024 × 20 = 20.005 °C. Bisection on the forward function finds R = 1.11661, where Rt = 1.00000.
2
C = 1.11661 × 42.914 = 47.918 mS/cm.
Expected conductivity = 47.9180 mS/cm = 4.79180 S/m
Try this example →

Example 5 — UNESCO Check Value at 40 °C and 10000 dbar

C = 81.0255 mS/cm (R = 1.888091), T = 40 °C (IPTS-68), p = 10000 dbar

1
R = 81.0255 ÷ 42.914 = 1.88809. At 40 °C and 10000 dbar, Rt = 1.12474.
2
Evaluating both polynomials gives the value published in the UNESCO 1983 check table, S = 40 (here 39.99999 before rounding).
Practical salinity S = 40.000
Try this example →

❓ Frequently Asked Questions

How do you calculate practical salinity from conductivity?+
Divide the measured conductivity by 42.914 mS/cm to get the ratio R, correct R for pressure and temperature to get Rt = R / (rp * rt), then evaluate S = sum of a_i * Rt^(i/2) plus the temperature term. The result is a unitless number, and conductivity of 42.914 mS/cm at 15 degrees Celsius and 0 dbar gives exactly S = 35.
What is the Practical Salinity Scale 1978 (PSS-78)?+
PSS-78 is the international definition of salinity from conductivity, adopted by UNESCO in 1981 from the work of Lewis and Perkin. It defines S = 35 as seawater whose conductivity ratio to a standard potassium chloride solution is exactly 1 at 15 degrees Celsius and one atmosphere, and gives polynomials for other temperatures, pressures and salinities from 2 to 42.
What units does practical salinity have?+
None. Practical salinity is a ratio of conductivities and therefore dimensionless. The label PSU (practical salinity unit) is common but is not an SI unit and is discouraged by the Joint Panel on Oceanographic Tables and Standards. Write salinity as a plain number such as S = 35.000 or S = 35.
What conductivity corresponds to a salinity of 35?+
At 15 degrees Celsius and the sea surface the conductivity of S = 35 seawater is 42.914 mS/cm, which is 4.2914 S/m. At 25 degrees Celsius the same water conducts about 53.0 mS/cm, and at 0 degrees Celsius about 29.0 mS/cm, so a conductivity number is meaningless without its temperature.
Why does the calculator need temperature and pressure?+
Conductivity rises about 2 percent per degree Celsius and about 1 percent per 1000 dbar of pressure, so the same salinity gives very different readings in warm surface water and cold deep water. PSS-78 removes both effects with the rt(T) polynomial and the Rp pressure correction before converting to salinity.
What is the difference between ITS-90 and IPTS-68 temperature?+
IPTS-68 and ITS-90 are two versions of the international temperature scale. PSS-78 was defined using IPTS-68, and T68 = 1.00024 * T90 near ocean temperatures. At 15 degrees Celsius the scales differ by 0.004 degrees, which changes computed salinity by a few thousandths at most.
What is the valid range of PSS-78?+
PSS-78 is defined for practical salinity 2 to 42, temperature -2 to 35 degrees Celsius and pressure 0 to about 10000 dbar. This calculator accepts temperatures up to 40 degrees Celsius so the UNESCO check value at 40 degrees can be reproduced, and warns when the computed salinity falls outside 2 to 42.
How accurate is salinity from a CTD conductivity sensor?+
The PSS-78 equations themselves are accurate to about 0.001 in salinity. Real accuracy is set by the sensor: a well calibrated CTD reaches 0.002 to 0.005 in salinity, while a handheld meter may only reach 0.1 to 0.3. Calibration against IAPSO Standard Seawater with a laboratory salinometer is the reference method.
How is practical salinity different from absolute salinity?+
Practical salinity comes from conductivity alone. Absolute salinity, used in TEOS-10, is the mass fraction of dissolved material in g/kg and is about 1.00472 times practical salinity for standard seawater, plus a regional correction. This calculator shows the reference salinity estimate S * 35.16504/35 in g/kg for comparison.
Can I use this for freshwater or lakes?+
Not reliably. PSS-78 is built for ocean-type water with the sea-salt composition ratios, and below S = 2 the equation is outside its definition. Lakes and rivers with a different ionic mix need conductivity or total dissolved solids methods instead, so treat any result below 2 as a rough extrapolation.
What does the reverse mode do?+
Reverse mode takes a target salinity, temperature and pressure and finds the conductivity a sensor should read. PSS-78 has no closed-form inverse, so the calculator bisects the forward function until it matches your salinity. It is handy for checking a sensor against standard seawater or sizing a conductivity range.
Tags: Practical Salinity Calculator PSS-78 Calculator Salinity From Conductivity Conductivity to Salinity Seawater Salinity Calculator CTD Salinity Oceanography Calculator Calculator Formula Free

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How do you calculate practical salinity from conductivity?

Divide the measured conductivity by 42.914 mS/cm to get the ratio R, correct R for pressure and temperature to get Rt = R / (rp * rt), then evaluate S = sum of a_i * Rt^(i/2) plus the temperature term. The result is a unitless number, and conductivity of 42.914 mS/cm at 15 degrees Celsius and 0 dbar gives exactly S = 35.

What is the Practical Salinity Scale 1978 (PSS-78)?

PSS-78 is the international definition of salinity from conductivity, adopted by UNESCO in 1981 from the work of Lewis and Perkin. It defines S = 35 as seawater whose conductivity ratio to a standard potassium chloride solution is exactly 1 at 15 degrees Celsius and one atmosphere, and gives polynomials for other temperatures, pressures and salinities from 2 to 42.

What units does practical salinity have?

None. Practical salinity is a ratio of conductivities and therefore dimensionless. The label PSU (practical salinity unit) is common but is not an SI unit and is discouraged by the Joint Panel on Oceanographic Tables and Standards. Write salinity as a plain number such as S = 35.000 or S = 35.

What conductivity corresponds to a salinity of 35?

At 15 degrees Celsius and the sea surface the conductivity of S = 35 seawater is 42.914 mS/cm, which is 4.2914 S/m. At 25 degrees Celsius the same water conducts about 53.0 mS/cm, and at 0 degrees Celsius about 29.0 mS/cm, so a conductivity number is meaningless without its temperature.

Why does the calculator need temperature and pressure?

Conductivity rises about 2 percent per degree Celsius and about 1 percent per 1000 dbar of pressure, so the same salinity gives very different readings in warm surface water and cold deep water. PSS-78 removes both effects with the rt(T) polynomial and the Rp pressure correction before converting to salinity.

What is the difference between ITS-90 and IPTS-68 temperature?

IPTS-68 and ITS-90 are two versions of the international temperature scale. PSS-78 was defined using IPTS-68, and T68 = 1.00024 * T90 near ocean temperatures. At 15 degrees Celsius the scales differ by 0.004 degrees, which changes computed salinity by a few thousandths at most.

What is the valid range of PSS-78?

PSS-78 is defined for practical salinity 2 to 42, temperature -2 to 35 degrees Celsius and pressure 0 to about 10000 dbar. This calculator accepts temperatures up to 40 degrees Celsius so the UNESCO check value at 40 degrees can be reproduced, and warns when the computed salinity falls outside 2 to 42.

How accurate is salinity from a CTD conductivity sensor?

The PSS-78 equations themselves are accurate to about 0.001 in salinity. Real accuracy is set by the sensor: a well calibrated CTD reaches 0.002 to 0.005 in salinity, while a handheld meter may only reach 0.1 to 0.3. Calibration against IAPSO Standard Seawater with a laboratory salinometer is the reference method.

How is practical salinity different from absolute salinity?

Practical salinity comes from conductivity alone. Absolute salinity, used in TEOS-10, is the mass fraction of dissolved material in g/kg and is about 1.00472 times practical salinity for standard seawater, plus a regional correction. This calculator shows the reference salinity estimate S * 35.16504/35 in g/kg for comparison.

Can I use this for freshwater or lakes?

Not reliably. PSS-78 is built for ocean-type water with the sea-salt composition ratios, and below S = 2 the equation is outside its definition. Lakes and rivers with a different ionic mix need conductivity or total dissolved solids methods instead, so treat any result below 2 as a rough extrapolation.

📌 Quick Tips

💡Practical salinity is a ratio of conductivities, so it has no unit. The label PSU is informal and not an SI unit, and a value of 35.000 simply means seawater that conducts exactly as much as the standard solution of 32.4356 g of KCl per kg of solution at 15 degrees Celsius.
💡Always tell the calculator which temperature scale your sensor reports. PSS-78 was defined on IPTS-68, and a modern ITS-90 reading is about 0.0004 times larger at 15 degrees Celsius. Ignoring the difference shifts salinity by only a few thousandths, but it matters for high-accuracy work.
💡Conductivity must be the in-situ value at the measured temperature and pressure, not a value already corrected to 25 degrees Celsius. If your meter reports specific conductance at 25 degrees Celsius, use that temperature in the calculator.
💡PSS-78 is formally defined for salinities from 2 to 42 and temperatures from -2 to 35 degrees Celsius. Estuary and brackish samples below 2 need the Hill et al. (1986) extension, which this calculator does not include.
💡Practical salinity is not the same as the mass fraction of dissolved salt. TEOS-10 absolute salinity in g/kg is about 0.47 percent larger than practical salinity for standard seawater, and regional composition anomalies add small further differences.