Trophic State Index Calculator

Introduction: what the Carlson TSI measures

Limnologists use trophic state to describe the overall biological productivity of a lake. At one end of the spectrum, clear oligotrophic lakes typically have low algal biomass, low nutrient concentrations, and high water clarity. At the other end, nutrient-rich eutrophic and hypereutrophic lakes may experience frequent algal blooms, reduced transparency, surface scums, and oxygen stress that can affect fish and invertebrates.

The Carlson Trophic State Index (TSI) is a widely used numeric scale that translates common field and laboratory measurements into comparable values. It is especially useful when you want a single, easy-to-communicate number for reporting, trend tracking, or comparing sites sampled with similar methods.

This calculator estimates TSI from three inputs: Secchi disk depth (a measure of water clarity), chlorophyll‑a (a proxy for algal biomass), and total phosphorus (a key nutrient that often limits algal growth in freshwater). Each measurement is converted using a natural-log transformation so the resulting indices are on a similar scale and can be averaged.

How to use this calculator

1. Enter Secchi depth in meters (m).
2. Enter chlorophyll‑a in micrograms per liter (µg/L).
3. Enter total phosphorus in micrograms per liter (µg/L).
4. Select Compute TSI to calculate each component (TSI-SD, TSI-Chl, TSI-TP) and the average TSI.

Inputs must be positive numbers. If you have measurements in different units (for example, Secchi depth in feet or phosphorus in mg/L), convert them first so the formulas remain valid.

Units and quick conversions (optional)

The equations on this page assume the standard Carlson units. If your dataset uses other units, convert before calculating. The following quick conversions are commonly needed in lake monitoring programs:

• Secchi depth: feet to meters: m = ft × 0.3048. Example: 10 ft ≈ 3.05 m.
• Total phosphorus: mg/L to µg/L: µg/L = mg/L × 1000. Example: 0.025 mg/L = 25 µg/L.
• Chlorophyll‑a: mg/m³ is numerically equivalent to µg/L in water (because 1 mg/m³ = 1 µg/L).

If you are unsure about units, check the lab report carefully. Confusing mg/L and µg/L is a common source of unrealistic TSI values.

Formula (Carlson 1977) and assumptions

This calculator uses the classic Carlson TSI equations with the natural logarithm (ln, implemented as Math.log() in JavaScript). The equations are:

• Secchi depth: TSI based on Secchi depth equals 60 minus 14.41 times natural log of SD. ${\mathrm{TSI}}_{\mathrm{SD}}=60-14.41\ln (\mathrm{SD})$
• Chlorophyll‑a: TSI based on chlorophyll equals 9.81 times natural log of chlorophyll plus 30.6. ${\mathrm{TSI}}_{\mathrm{Chl}}=9.81\ln (\mathrm{Chl})+30.6$
• Total phosphorus: TSI based on total phosphorus equals 14.42 times natural log of TP plus 4.15. ${\mathrm{TSI}}_{\mathrm{TP}}=14.42\ln (\mathrm{TP})+4.15$

Where SD is Secchi depth in meters, Chl is chlorophyll‑a in µg/L, and TP is total phosphorus in µg/L. The calculator then computes: Average TSI = (TSI_SD + TSI_Chl + TSI_TP) / 3.

Interpretation is most meaningful when the three measurements are collected from the same lake and season (often mid-summer) using consistent methods. Because the equations are logarithmic, very small values close to zero are not valid; that is why the calculator requires positive inputs.

Worked example (step-by-step)

Example inputs: SD = 5 m, Chl‑a = 4 µg/L, TP = 10 µg/L.

• TSI(SD) = 60 − 14.41 × ln(5) ≈ 60 − 14.41 × 1.609 ≈ 36.8
• TSI(Chl) = 9.81 × ln(4) + 30.6 ≈ 9.81 × 1.386 + 30.6 ≈ 44.2
• TSI(TP) = 14.42 × ln(10) + 4.15 ≈ 14.42 × 2.303 + 4.15 ≈ 37.3
• Average TSI ≈ (36.8 + 44.2 + 37.3) / 3 ≈ 39.4 → typically interpreted as oligotrophic to low mesotrophic.

Your results may differ slightly due to rounding. If your three component TSIs disagree strongly, that can be a useful diagnostic rather than an “error.” For example, stained water (high dissolved organic matter) can reduce Secchi depth without a proportional increase in chlorophyll, while wind-driven sediment resuspension can reduce clarity even when nutrients are moderate.

Second example: a bloom-prone lake

Consider a more nutrient-rich system with SD = 0.5 m, Chl‑a = 40 µg/L, and TP = 80 µg/L. The component indices will typically fall in the 70+ range, and the mean will often classify the lake as hypereutrophic. In practical terms, that category is associated with frequent nuisance blooms, poor recreational aesthetics, and a higher risk of low dissolved oxygen events.

This kind of comparison is one reason TSI is popular in communication: it helps translate three different measurements into a single scale that is easier to discuss with stakeholders, lake associations, and decision-makers.

TSI interpretation table (common ranges)

Limitations and interpretation notes

Carlson’s TSI is widely used, but it is not a complete lake-health assessment. It was developed primarily for temperate, phosphorus-limited systems and assumes a typical relationship among phosphorus, chlorophyll, and transparency. In real lakes, those relationships can vary.

• Colored dissolved organic matter (brown/stained water) and inorganic turbidity (suspended sediments) can reduce Secchi depth without a matching increase in algae.
• Shallow, frequently mixed lakes may show different dynamics than deeper stratified lakes because sediments can be resuspended and nutrients can recycle quickly.
• Nitrogen limitation, grazing pressure by zooplankton, or unusual algal communities can decouple chlorophyll from phosphorus.
• Sampling timing matters: a single summer sample may not represent seasonal variability; consider multiple dates and locations.

For management decisions, pair TSI with other indicators such as dissolved oxygen profiles, nutrient loading estimates, cyanobacteria monitoring, and aquatic vegetation surveys. TSI is best viewed as a screening and communication tool rather than a stand-alone regulatory endpoint.

Why the equations use logarithms

Lake nutrient and algae concentrations span orders of magnitude. The logarithmic transformation compresses that range so changes are easier to compare on a single scale. It also reflects that the relationship between nutrients and clarity is not linear: at higher nutrient levels, additional inputs can cause disproportionately large declines in transparency.

Another practical benefit is that the log-based scale tends to produce values that align with intuitive categories (clear/low algae vs. turbid/high algae) across many lakes. That said, the index is still an empirical model; it summarizes typical patterns rather than guaranteeing a perfect prediction for every lake.

Data tips (to get meaningful results)

Use consistent methods. For Secchi depth, measure on the shaded side of the boat, avoid glare, and record the average of the disappearance and reappearance depths. For chlorophyll‑a and total phosphorus, use comparable lab methods and note whether results are surface grabs, integrated samples, or depth-specific.

If you are comparing lakes, try to compare similar seasons (for example, mid-summer) and similar sampling depths. This helps ensure differences in TSI reflect real trophic differences rather than sampling artifacts. If you are tracking a single lake over time, keep the sampling station and protocol as consistent as possible.

How managers and lake groups use TSI

TSI is often used for trend analysis (is the lake getting more eutrophic over time?), communication (summarizing monitoring results in a single number), and prioritization (identifying lakes or basins that may benefit from nutrient reduction). Because the index is easy to compute, it is also common in citizen science programs that collect Secchi depth and occasional nutrient samples.

When the three component indices are similar, it suggests the lake behaves like the “typical” Carlson relationships. When they differ, the pattern can hint at what else is happening. A relatively high TSI based on Secchi depth compared with chlorophyll can indicate non-algal turbidity or stained water. A relatively high chlorophyll TSI compared with phosphorus can suggest efficient nutrient use, internal loading, or a period of rapid algal growth.

Common questions

Can I compute TSI with only one measurement? Carlson defined separate indices for SD, chlorophyll, and phosphorus. This page reports all three and their mean. If you only have one metric, you can still interpret that component, but the “average TSI” concept assumes all three are available.

What does “ln” mean? It is the natural logarithm (base e). In this calculator, it is computed with JavaScript’s Math.log().

Why does the calculator reject zero or negative values? The equations use a logarithm, and ln(0) and ln(negative) are undefined. If you have a lab report showing “below detection,” consider using an appropriate substituted value recommended by your monitoring program rather than entering zero.

Is a higher TSI always “bad”? Not necessarily. Some lakes are naturally productive due to geology, shallow depth, or watershed characteristics. However, rapid increases in TSI over time can indicate cultural eutrophication from human-driven nutrient inputs.