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.