Pharmacology
Emax Model Calculator
Predicts the effect of a drug at a given concentration with the sigmoid Emax (Hill) equation, and plots the full concentration–effect curve.
Effect at test concentration
66.7% of maximum
Therapeutic range – between 50% and 80% of Emax.
Inputs
Largest effect the drug can produce, often 100%.
Concentration giving half of Emax. Must be above 0.
Steepness; typically 0.5–3. n = 1 is the simple hyperbola.
Effect with no drug present, usually 0.
Concentration at which to predict the effect.
Try an example drug
Examples set Emax, EC₅₀ and n, and reset the baseline to 0. The test concentration is kept.
Working
E = 0 + (100 × 10^1) ÷ (5^1 + 10^1)
Concentration–effect curve (linear scale)
Effect against concentration from 0 to 25 nM. The red line marks EC₅₀, the grey line 50% effect.
Log-concentration curve
The same model on a log₁₀ axis, from EC₅₀ ÷ 100 to EC₅₀ × 100 — the classic sigmoid shape.
E = E₀ + (Emax × Cⁿ) ÷ (EC₅₀ⁿ + Cⁿ)
E is the predicted effect, E₀ the baseline effect with no drug, Emax the maximal drug effect, C the concentration, EC₅₀ the concentration producing half of Emax, and n the Hill coefficient.
With n = 1 the equation is a simple hyperbola. A Hill coefficient above 1 makes the curve steeper (often read as positive cooperativity); below 1 makes it shallower.
Keep learning
References
- Rowland and Tozer's Clinical Pharmacokinetics and Pharmacodynamics: Concepts and Applications. 5th ed. Philadelphia: Wolters Kluwer; 2019.
Common questions
EC₅₀ measures potency — how much drug is needed for half the maximal effect. Emax measures efficacy — how big the effect can get at all. A drug can be very potent (low EC₅₀) yet have a low Emax, like a partial agonist.
On a linear axis the curve rises quickly and then flattens, which hides the low-concentration region. On a log₁₀ axis the same curve becomes a symmetric S-shape centred on EC₅₀, which is how dose–response curves are normally presented.
It sets the steepness of the curve. With n > 1 the effect switches from low to high over a narrow concentration range; with n < 1 the change is spread over many-fold concentrations.
The interpretation bands compare the absolute effect with fixed cut-offs of 50% and 80%, rather than with half of your own Emax. With Emax below 100% (or a non-zero baseline) read the number itself rather than the band.
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