So cameras work in **Stops** and composite packages use **Gain.** To convert between the two we need to do a bit of log maths. Heres how.

To convert from Stops (f) to Gain

Gain = 2^{f}

To convert from Gain to stops (f)

f = log_{2 }Gain

This is equivalent to:

f = ( log_{10 }Gain ) / ( log_{10 }2 )

If you want to see why then we’ll need to look a little deeper at log maths

### The three basic Laws of logarithms.

These three *identities* give us all the maths we need to know.

log_{a }X + log_{a }Y = log_{a }X * Y

log_{a }X – log_{a }Y = log_{a} ( X / Y )

log_{a}X^{Y} = Y log_{a} X

So if we’re dividing by the a **Gain** value then:

( log_{2 }1 ) – ( log_{2 }Gain ) = log_{2 }(1 / Gain)

And since: log 1 = 0

– log_{2 }Gain = log_{2 }(1 / Gain)

This means that **dividing** by a **Gain** value will give a **negative f-Stop** value.

### Converting the base of the Log.

If your calculator can’t do Log_{2} you can use this formula to convert to Log_{10.}

log_{a }X = ( log_{b }X ) / ( log_{b }a )

So to convert a value from **Gain** to **Stops** ( f ) using log_{10} rather than log_{2}

f = ( log_{10 }Gain ) / ( log_{10 }2 )