Snigs,
I'm not aware of any quick formulae, but someone else might know one. But a quick Google search suggests that what you need is a "Psychometric Chart". Another Google search turns up quite a few of these, but the best one I can find is
here .
Unfortunately, it's all in Farenheit, but once you've done the necessary conversions, start by finding the outside air temperature on the bottom scale. Then locate the relative humidity on the top scale. Follow the curved line for the relative humidity down and to the left until it meets the vertical line for the temperature. From this point, locate the nearest diagonal line, and follow this line up and to the left, from where you can read the dew point. Then, use this dew point together with the temperature to work out the cloud base using the rules of thumb you already know.
FFF
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[Edit, because after reading the instructions on the website I've linked to, I discover that I've made a mistake in describing how to use the chart. It is the horizontal lines which represent equal dew point, not the diagonal lines. If you use the diagonal lines, you will get the wet-bulb temperature, not the dew point, and the whole thing stops working! So, once you've found where your vertical line and your curved line meet, you then follow the
horizontal line to the left hand side and read off the dew point.]