Aquatic Toxicology Calculator
Estimate LC50 from two dose-response data points using probit approximation. Calculate toxic units, PNEC, and environmental risk quotient.
About this calculator
Aquatic toxicology testing exposes organisms to a substance at several concentrations and records what fraction die, then fits a dose-response curve to estimate benchmark concentrations like the LC50 -- the concentration lethal to half the test population. This calculator uses a simplified two-point version of that method: probit analysis converts each mortality percentage into a probit value (roughly, how many standard deviations from the mean the response sits), then interpolates linearly between the two points in log-concentration/probit space to find where the line crosses probit 5 (50% mortality). The interpolated LC50 is most sensitive to the mortality percentage recorded at your higher test concentration -- that point anchors the steeper, more information-dense end of a typical dose-response curve, so a change there swings the fitted line more than an equivalent change at the shallower low-concentration end -- except when the two mortality percentages sit too close together, where the interpolation line's slope becomes too shallow to support a reliable estimate. Two test points with nearly identical mortality readings genuinely cannot pin down a dose-response slope, so when your two mortality percentages differ by only a few points this calculator falls back to reporting your low test concentration itself rather than extrapolating through a near-zero slope -- enter dose-response data with mortality percentages that are meaningfully different from each other for a trustworthy estimate; a near-tied pair is a real limit of two-point interpolation, not an engine error.
Environmental concentration and the assessment factor never move the LC50, LC10, or LC90 estimates themselves -- they only enter downstream, when the LC50 is divided by the assessment factor to derive PNEC (Predicted No-Effect Concentration), and PNEC is then compared against environmental concentration to compute the risk quotient. A larger assessment factor produces a smaller, more conservative PNEC and therefore a larger risk quotient for the same environmental exposure. This two-point probit interpolation is a coarse approximation -- real regulatory LC50 determinations use multiple concentrations, replicate counts, and full probit or logistic regression with confidence intervals, so treat this calculator's output as an illustrative estimate, not a substitute for a validated toxicology study.
Inputs
Results
LC50 (mg/L)
3.16
How to Use This Calculator
- Enter two dose-response data points: a low test concentration (mg/L) with its observed mortality percent, and a high test concentration (mg/L) with its observed mortality percent.
- Enter the environmental concentration (mg/L) — the measured or predicted level of the substance in the environment.
- Set the assessment factor (typical: 1000 for a single acute LC50, 100 for chronic data, 10 for field data) used to derive PNEC.
- Review the estimated LC50, LC10, and LC90 — concentrations lethal to 50%, 10%, and 90% of test organisms, interpolated via probit analysis.
- Check the toxic units (TU) and risk quotient (RQ): TU > 1 or RQ > 1 indicates the environmental concentration poses a likely risk relative to the PNEC.
How the result changes with Mortality at high conc (%)
| Mortality at high conc (%) | LC50 (mg/L) |
|---|---|
| 40 | 26.9 |
| 60 | 5.87 |
| 99 | 1.84 |
What each input means
- Low concentration (mg/L)
- Lower test concentration in mg/L.
- Mortality at low conc (%)
- Percent mortality observed at the lower concentration.
- High concentration (mg/L)
- Higher test concentration in mg/L.
- Mortality at high conc (%)
- Percent mortality observed at the higher concentration.
- Environmental conc (mg/L)
- Measured or predicted concentration of the substance in the environment.
- Assessment factor
- Safety factor for PNEC derivation. Typical: 1000 for single acute LC50, 100 for chronic data, 10 for field data.
What each result means
- LC50 (mg/L)
- Estimated concentration lethal to 50% of test organisms.
- LC10 (mg/L)
- Concentration lethal to 10% of organisms (low-effect threshold).
- LC90 (mg/L)
- Concentration lethal to 90% of organisms.
- Toxic units (TU)
- Environmental concentration divided by LC50. TU > 1 indicates likely adverse effects.
- PNEC (mg/L)
- Predicted No-Effect Concentration: LC50 divided by assessment factor.
- Risk quotient (RQ)
- Environmental concentration / PNEC. RQ > 1 indicates unacceptable risk.
How this is calculated
Worked example, using the default values
- Identify Input Parameters6 parametersLow concentration (mg/L) = 1, Mortality at low conc (%) = 20, High concentration (mg/L) = 10, Mortality at high conc (%) = 80, Environmental conc (mg/L) = 0.5, Assessment factor = 1000 = 6 input(s) provided
- Calculate LC50LC50 = pow(10, logLC50)3.1623 = 3.1623
- Calculate LC10LC10 = pow(10, logLC10)0.5475 = 0.5475
- Calculate LC90LC90 = pow(10, logLC90)18.2647 = 18.2647
Engine last updated . Checked against 3 independently-derived tests — how we verify calculators. Built by Paul Gunder, a software engineer, not a licensed financial, medical, or legal professional.
Frequently Asked Questions
If I can only double-check one of my two mortality readings, which one matters most to get right?
Prioritize the higher-concentration reading. It typically sits closer to the steep, information-dense middle of a dose-response curve, where mortality shifts quickly with concentration, while the low-concentration point usually falls on the shallower tail. A measurement error at the higher-concentration point rotates the fitted probit-log line more than the same-sized error at the lower one, so it carries more weight in the estimated LC50, LC10, and LC90 than the low-concentration reading does.
Can I use published mortality data instead of running my own bioassay to fill in the two test points?
Yes, as long as both points come from comparable exposure conditions. Published figures from a source like EPA ECOTOX, an SDS aquatic toxicity section, or a peer-reviewed study testing the same species and substance work fine, but the two readings need to share the same exposure duration and similar water-quality parameters such as temperature and hardness -- mixing a 48-hour mortality reading with a 96-hour one, for example, will distort the fitted dose-response line since organisms accumulate more effect the longer they're exposed.
How does the assessment factor affect PNEC and the risk quotient?
PNEC equals LC50 divided by the assessment factor, so a larger factor produces a smaller, more conservative PNEC. Since the risk quotient is environmental concentration divided by PNEC, a smaller PNEC produces a larger risk quotient for the same environmental exposure -- a higher assessment factor makes the same measured concentration look riskier.
What does a toxic units (TU) value greater than 1 mean?
Toxic units equal environmental concentration divided by LC50 directly, with no safety margin applied. A TU above 1 means the environmental concentration already exceeds the concentration lethal to half the test population -- a severe acute-toxicity warning, distinct from the more conservative risk quotient, which compares against PNEC instead of the raw LC50.
Why is this two-point probit method less reliable than a full toxicology study?
Regulatory LC50 determinations typically use five or more concentrations with multiple replicates and fit a full probit or logistic regression with a reported confidence interval. Interpolating a straight line between just two data points ignores curve shape and measurement variability, so this calculator's LC50 should be treated as a rough estimate for screening, not a substitute for a validated laboratory study.
Related Calculators
The questions that sit next to this one — chosen by subject, including calculators filed under a different category.
Whale Migration Calculator
Estimate cetacean migration distance, travel time, and energy expenditure based on breeding/feeding ground coordinates, swim speed, and body mass.
Marine BiologyBycatch Rate Calculator
Calculate bycatch ratio, discard rate, BPUE, and fleet-wide bycatch estimates from fishing operation data for fisheries management.
Marine BiologySeagrass Restoration Calculator
Plan seagrass restoration projects: estimate shoot requirements, labor, costs, carbon sequestration, and ecosystem service value.
Forensic ScienceToxicology Dose Back-Calculator
Back-calculate an ingested dose from blood concentration using volume of distribution and elimination kinetics. Estimate peak concentration and elimination time.
Emergency MedicineToxicology Antidote Dosing Calculator
Antidote dosing for common poisonings: acetaminophen/NAC, opioid/naloxone, benzodiazepine/flumazenil, organophosphate/atropine, digoxin/DigiFab.
More in Science & Physics.