How to use it
- Copy the concentration and response columns straight out of your spreadsheet and paste them in. A header row is fine.
- Use whatever concentration units you like — the IC50 comes back in the same ones. Just do not mix units within a column.
- Look at whether the points follow the line, and especially whether there are points on both plateaus. Without them, that plateau is extrapolation rather than estimation.
- Read the Hill slope, R² and the standard error together before deciding what the fit is worth.
💡 A zero-concentration control can be included. It counts in the fit and is only left out of the log-axis drawing.
Formula and cautions
A dose–response usually has an S shape, and writing that shape down as four numbers is the four-parameter logistic.
The four parameters
Two plateaus, the concentration half way between them, and how steeply it gets there.
- Curve
- y = y∞ + (y₀ − y∞) / (1 + (x / mid)^hill)
- Half-way point
- y(mid) = (y₀ + y∞) / 2
IC50 or EC50
The same number. It is called the IC50 when the response falls as concentration rises and the EC50 when it rises. The tool reads the direction off the fitted curve, so there is nothing to choose.
Why the Hill slope is always positive
Left free, a rising curve fits equally well with a negative slope and the two plateaus exchanged. The residuals are identical, so the data cannot say which it was — only the labels change, and they change to the opposite of what happened. So the slope is held positive and the direction is read from which plateau is larger.
Cautions
- ⛔ With no points on a plateau, the IC50 comes from outside the data rather than inside it — however handsome the curve looks. Check the plot.
- When the curve does not converge, no IC50 is reported. A half-way concentration forced onto scattered points looks exactly like a real one and means nothing.
- R² says how close, not whether the model is right. A wrong model fitted to dense points still reaches 0.99. Whether the points scatter evenly along the line matters more.
- The standard error says how tightly your points pin this curve down. How reproducible the assay is, is a different question, and only replicates answer it.
- The log axis is for looking at. The fit itself is done on the concentrations as you entered them.
Frequently asked questions
Often used together
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