How fast do fingernails grow?

The short answer to this question is... about 0.1 mm per day. Roughly the speed at which the continents move, it is often said.

The more interesting answer:

Nail growth is fastest in our youths, and slows with age. It is critically dependent on the blood supply to the matrix (growth area of the nail). People who use their nails a lot (e.g. piano players, chronic 'nail biters') tend to 'massage' the area and increase blood flow locally. The result: their nails grow quicker. Perhaps for a similar reason, the nails of the right hand usually grow faster than the nails on the left hand. Amazingly, the nails of the third (middle) and fourth (ring) fingers usually grow faster than those on the first (thumb) or fifth (pinkie). (There is much debate as to why, but again this may be due to a 'massage' effect, as these two fingers protrude the most, and so are often subject to the greatest forces.)

Another example of the nails' response to blood flow is seen with the varying rate of growth in differing climates. The vessels of the skin (and hence hands and nails) usually dilate with heat, thus providing the area with more blood. This is an attempt to lose more heat from the blood to maintain a constant body temperature. However, the side-effect is quicker nail growth in warm climates!

Nail growth is also particularly sensitive to the body's general health status. It is slowed significantly by many chronic disease states, like malnutrition, liver disease, heart failure, chronic lung disease, chronic kidney disease, etc. Slower nail growth makes the nail look more opaque, and clinicians call this sign leukonychia (white nails). Leukonychia can also be a feature in a normal individual though.

And how fast do toenails grow? Slower - about one third to one quarter as quickly.