LD50 Dose-Response Curve Calculator
Estimate response probability at any dose using the log-logistic model.
Enter LD50 and Hill slope to plot the sigmoid dose-response curve for any compound.
The log-logistic (Hill) dose-response model is the standard curve fit for most pharmacological and toxicological data. The response at a given dose D is:
E = D^n / (ED50^n + D^n)
where ED50 (or LD50 for lethal effects) is the dose producing 50% response, and n is the Hill coefficient controlling curve steepness.
Hill coefficient n. n = 1 gives a shallow, symmetric sigmoid. n = 2 means the curve climbs steeply. n close to 0.5 is a wide, gradual curve. Most drugs and toxins have n between 0.5 and 3. When n is exactly 1, this reduces to the standard hyperbolic Michaelis-Menten equation.
LD50 vs ED50. LD50 is the median lethal dose — the dose that kills 50% of a test population. ED50 is the median effective dose, giving a therapeutic response in 50% of subjects. The therapeutic index = LD50 / ED50. A ratio above 10 is generally considered safe; below 3 is worrying.
Dose units. LD50 is typically expressed in mg/kg body weight. Common reference values: aspirin LD50 is about 200 mg/kg in rats; caffeine is about 192 mg/kg; table salt (NaCl) is around 3000 mg/kg; botulinum toxin is about 0.001 mg/kg.
Reading the curve. The chart shows predicted response from 1% to 100 times the LD50 on a log scale. The 50% intercept always falls at exactly the LD50. The steeper the curve, the smaller the dose range between 10% and 90% response.
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This calculator runs entirely in your browser, so the numbers you enter stay on your device. The math behind it is written by hand and tested against worked examples and standard references before the page goes live.
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