Logistic 4PL (Hill)
The four-parameter logistic, or Hill, curve: an S-shaped step between two plateaus that is symmetric on a logarithmic x axis. Use it for dose–response, ligand-binding and immunoassay standard curves.
Fit the example dataStart with your own data
Example: a simulated inhibitor dose–response curve, 13 points with y uncertainties, opened as a new copy you can edit.
Parameters
- Plateau as x approaches 0, for positive B.
- Hill slope: how steep the step is. Its sign decides which plateau, A or D, is reached at small x.
- Midpoint: the x at which y is halfway between A and D, such as an EC₅₀ or IC₅₀.
- Plateau as x becomes large, for positive B.
Tips
- Enter the dose or concentration itself, not its logarithm. A zero-dose control at x = 0 is fine; otherwise x/C must stay positive when B can take non-integer values.
- Include points on both plateaus. If one plateau is not reached, fix it at a known value, such as 0 for complete inhibition.
- Show the x axis on a log scale to see the symmetric S shape. For a standard curve, Evaluate’s y → x reads an unknown concentration from a measured response.
- For an asymmetric step, use Logistic 5PL.