See how to calculate ld50 from your own dose-response table. Enter doses and percent mortality to get the log-dose curve, the substituted interpolation arithmetic, the EPA toxicity category, and how far the naive linear reading is off.
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The Dose-Response Curve & LD50 Interpolator plots the dose/percent-response table you enter and interpolates the LD50, ED50, LD90 or any other LDx directly on a log-dose axis — the way toxicity data is actually read.
Every line of arithmetic is shown with your own numbers: the bracketing pair, the fraction f = (T − r₁)/(r₂ − r₁), the log-dose interpolation, and the back-transform. The result is reported beside the naive linear-in-dose reading with its percent divergence, plus the EPA acute-oral toxicity category and signal word.
Find the two doses whose percent responses straddle 50%, take log10 of both doses, work out how far up the response gap 50% sits (f = (50 − r₁)/(r₂ − r₁)), move that same fraction along the log-dose axis, then raise 10 to that power.
Toxicity doses span orders of magnitude, and dose-response curves are only S-shaped when dose is plotted logarithmically. Reading straight across raw doses always overestimates the LD50, which is why this tool shows both readings side by side.
LD50 is the dose that kills 50% of the test population; ED50 is the dose that produces a defined non-lethal effect in 50% of it. The arithmetic is identical — only the response column and the label change.
For acute oral exposure the EPA uses four bands by LD50 in mg/kg: Category I is 50 mg/kg or less (DANGER), Category II is over 50 up to 500 mg/kg (WARNING), Category III is over 500 up to 5000 mg/kg (CAUTION), and Category IV is over 5000 mg/kg (CAUTION).
Yes. Set the target response to any value strictly between 0 and 100 and the label updates to match. The EPA toxicity category is only reported for an LD50 in mg/kg, because that is how the bands are defined.
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