For me I've always gone by the size of the shoots (above ground), plus once the carrots start to show above ground and measure over an inch in diameter they won't be far off. The longer you leave them the bigger they get. These were about an inch and a half in diameter.

If you notice there are 2 rows, running away from us.... On the left are the ones I planted 2 weeks before the row on the right. Given a bit of sunlight and lots of water, the ones on the right will really start to grow in the next day or so.