# S Curve shapes with flat middle

I was wondering if there is a simple formula to change an S-curve to have a flat area in the middle.

I am using the formula..

$$y=\frac{1}{1+e^{B-x}}$$

Where $B$ is the steepness of the curve.

This gives me a normal S-curve.

BUT i also want a curve to go up to a flat area then continue to go up. Eg..

I am not sure if this is still called a S-Curve but i am unsure of what to google.

Thanks

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## 1 Answer

You can do this by adding two of what you call an "S-curve":

$$y=\frac1{1+\mathrm e^{B_1-x}}+\frac1{1+\mathrm e^{B_2-x}}\;.$$

The coefficients $B$ in your expression and $B_1$ and $B_2$ in mine are not the steepness of the curve; they control where on the $x$-axis the rise occurs. You can introduce variable steepnesses $A_1$ and $A_2$ and variable total increases $C_1$ and $C_2$ like this:

$$y=\frac{C_1}{1+\mathrm e^{A_1(B_1-x)}}+\frac{C_2}{1+\mathrm e^{A_2(B_2-x)}}\;.$$

Here $B_1$ and $B_2$ are still the midpoints of the two rising flanks.

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Thank you that worked really well. – Sprouts Aug 9 '11 at 9:27