Assuming that the company tax rate is 30% and that the dividend is fully franked, the formula is:
Dividend Yield divided by 0.7.
So, if the dividend yield is 3.15%,
The grossed up yield is:
3.15 / 0.7 = 4.5%
If the dividend is partly franked, you have to allow for that in your formula. One easy way to do this is to split the dividend into two parts: The part that is unfranked and the part that is franked.
For example, if the dividend is only 50% franked, your calculation would be:
(3.15 x 0.5) + (3.15 X 0.5 /0.7) = 3.825%
What I have done here is to take the unfranked half and add the franked half after grossing it up.
In general terms, for any other percentage of the dividend that is franked:
(Dividend yield x unfranked percentage) + (Dividend yield x franked percentage /0.7) = Grossed up dividend yield.
For example, take a dividend yield of 4.45% which is only 35% franked:
(4.45 x .65) + (4.45 x .35 /0.7) = 5.12%
By the way, the Sydney Morning Herald (and I think The Age) publishes the grossed up yields of the top 150 companies each Monday.