Lake Trophic State Index (Carlson) Calculator

Understanding the Carlson trophic state index calculator — concept and principle

Lakes range from clear, nutrient-poor waters to green, algae-rich ones. Carlson's trophic state index (TSI) puts that range on a single 0–100 scale using three common measurements: Secchi disk transparency, chlorophyll-a and total phosphorus. This calculator computes each TSI, averages them and names the trophic state, for comparing lakes and tracking change over years.

Clearer water (deeper Secchi disk) lowers the index; more algae and phosphorus raise it.

How it is calculated

TSI(SD) = 60 − 14.41 · ln(SD), with Secchi depth SD in metres.
TSI(Chl) = 9.81 · ln(Chl) + 30.6, with chlorophyll-a in µg/L.
TSI(TP) = 14.42 · ln(TP) + 4.15, with total phosphorus in µg/L.
State from the average: below 40 oligotrophic, 40–50 mesotrophic, 50–70 eutrophic, 70 and above hypereutrophic.

ln is the natural logarithm.

The principle

Carlson built the index on Secchi depth: TSI 0 corresponds to a transparency of 64 m, and each 10-unit rise means the Secchi depth halves, so TSI 60 is 1 m and TSI 70 is 0.5 m. Because algae are the main cause of turbidity in many lakes, he used regression relationships between Secchi depth, chlorophyll and phosphorus to place the other two variables on the same scale. A given TSI value should therefore indicate roughly the same trophic condition whichever variable it came from.

Worked example

Inputs: SD = 2 m, Chl = 10 µg/L, TP = 30 µg/L.
TSI(SD) = 60 − 14.41 × ln 2 = 60 − 14.41 × 0.69315 = 50.01.
TSI(Chl) = 9.81 × ln 10 + 30.6 = 9.81 × 2.30259 + 30.6 = 53.19.
TSI(TP) = 14.42 × ln 30 + 4.15 = 14.42 × 3.40120 + 4.15 = 53.20.
Average = (50.01 + 53.19 + 53.20) / 3 = 52.13, which is in the 50–70 band: eutrophic.

Each point is the calculator re-run with only “Secchi depth (m)” changed; the gold point is the default example. Change the inputs above and this chart follows your numbers.

Secchi depth (m)	TSI (Secchi)
0.5	69.98825087
1	60
1.5	54.15724779
2	50.01174913
2.5	46.79625055
3	44.16899692
4	40.02349826

How to read the result

Low TSI means clear water with little algae; high TSI means frequent algal growth, low transparency and a greater chance of oxygen depletion in deep water. Look at the three indices separately as well as the average. If TSI(TP) is clearly above TSI(Chl), something other than phosphorus, such as light or nitrogen, may limit algae; if TSI(SD) is higher than TSI(Chl), non-algal turbidity like clay may be reducing transparency. In the example the three agree closely, which suggests phosphorus-driven algal growth.

Common mistakes

Entering chlorophyll or phosphorus in mg/L instead of µg/L.
Using a single sample instead of growing-season averages.
Applying the scale to coloured or very turbid lakes where Secchi depth is not set by algae.

Keep in mind: Carlson recommended treating chlorophyll as the most direct indicator of algal biomass rather than relying on a simple average. The index describes trophic condition, not whether the water is safe for drinking or swimming.

Frequently asked questions

What does a TSI of 50 mean in practice?

It corresponds to a Secchi depth of about 2 m and marks the boundary between mesotrophic and eutrophic conditions on this scale.

Why use logarithms?

Nutrients and algae vary over orders of magnitude between lakes, and the log scale turns those multiplicative differences into equal steps.

Can I use it for reservoirs?

It was developed for lakes; reservoirs with short retention or high inorganic turbidity may not fit.

Sources: R. E. Carlson, "A trophic state index for lakes", Limnology and Oceanography 22(2), 1977 · R. G. Wetzel, Limnology: Lake and River Ecosystems, Academic Press

Checked 8 Nov 2026. Standard textbook formulas in SI units, computed in your browser. For learning and estimates — real designs must follow your local codes and be checked by a qualified engineer.

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