What is the conversion between focal length and times zoom?

There is no "industry standard formal definition" of the term 20x etc BUT
Almost universal usage is that this is the ratio between the maximum and minimum focal lengths available from the lens.

So eg an 18mm - 90mm is 90/18 = 5:1 = 5x.

The extreme available DSLR DX lens so far (as fara as I know) is 18mm-300mm = 300/18 = 15.55:1 ~= 16x

"Ultrazoom" compact cameras and video cameras with small sensor areas need correspondingly less glass to achieve a given 35mm-equivalent focal length, and quality is less to far-less of an issue than with SLRs, so far larger max to min zoom ratios are possible and available with these cameras than with SLRs.

What is the conversion between focal length and times zoom?

There is no "industry standard formal definition" of the term 20x etc BUT
Almost universal usage is that this is the ratio between the maximum and minimum focal lengths available from the lens.

So eg an 18mm - 90mm is 90/18 = 5:1 = 5x.

The extreme available DSLR DX lens so far (as far as I know) is 18mm  -300mm = 300/18 = 15.55:1 ~= 16x

"Ultrazoom" compact cameras and video cameras with small sensor areas need correspondingly less glass to achieve a given 35mm-equivalent focal length*, and quality is less to far-less of an issue than with SLRs, so far larger max to min zoom ratios are possible and available with these cameras than with SLRs.

• "35-mm equivalent" means that if the image on the sensor is the same as would have been achieved with a "35mm" film camera on standard sized 35mm film with an xx mm lens then the lens is said to xx mm in 35mm-equivalent.
  eg If a point & shoot camera lens when set to 15mm focal length, produces on the P&S sensor an image with the same content as would be produced on a 35mm film camera sensor when a 50mm lens was used then the lens is said to be set to '50mm, '35mm equivalent' "