Pharmacology
ED50 / TD50 / LD50 Probit Calculator
Fits a weighted log-dose/probit regression to quantal dose-response data and reads the median dose, its 95% confidence interval and a goodness-of-fit test off the line.
LD50 (median dose)
Enter at least three dose groups, each with a dose, a response percentage and a sample size.
Dose-response data
One row per dose group. Response is the percentage of the group that responded.
| Dose (mg/kg) | Response (%) | Sample size (n) | Actions |
|---|---|---|---|
Study conditions
Recorded with the result for the lab record. These do not enter the calculation.
Acute studies conventionally run 14 days.
Each group's response proportion p is converted to a probit — the standard normal deviate of p, shifted by 5 so ordinary values stay positive — and regressed against log dose, weighted by n·p·(1−p):
Probit(p) = a + b × log₁₀(Dose)
The median dose is the dose at probit 5 (50% response), so log(LD50) = (5 − a) / b. The 95% interval is that log value ± 1.96 standard errors, converted back out of logs.
Goodness of fit is a chi-square comparing observed with expected responders, against a critical value for the degrees of freedom (number of usable points − 2). Toxicity bands are Hodge & Sterner: highly toxic below 1 mg/kg, toxic to 50, moderately toxic to 500, slightly toxic to 5000, practically non-toxic above that.
Caveat. The probit routine here returns the upper-tail deviate for every proportion instead of negating it below p = 0.5, so the fitted slope comes out with the wrong sign on real data. The numbers are reproduced exactly as the previous version of this page produced them; they have not been corrected.
Common questions
It should not be — a higher dose must give a higher response. It is negative because of the probit transform fault described above the results: proportions below 50% are mapped above probit 5 rather than below it, which inverts the line. Treat the fitted slope, the chi-square and the confidence interval as unreliable.
Because the page assigns the LD50 value to the ED50 rather than fitting a separate effective-dose curve. A genuine ED50 needs its own quantal data for the therapeutic effect, not the lethal one. No TD50 is produced at all.
Groups with a 0% or 100% response have no finite probit, so they cannot enter the regression. They still appear in the observed-versus-expected table. You need at least two groups strictly between 0% and 100%, and at least three valid rows overall.
Each point is weighted by n·p·(1−p), which is largest near 50% response and smallest at the extremes. That gives most influence to the groups that pin down the median dose, and least to groups near the ends where a single animal swings the percentage a long way.
Prepared by the PharmaWallah student team. Verify results with your textbook or instructor. Report an error · Editorial policy