If you want to get very technical and scientific, a pinch is generally defined as 1/16 teaspoon. While there’s some debate about this, The New Food Lover’s Companion considers a pinch to be 1/16 tsp, while a dash is “somewhere between 1/16 and a scant 1/8 teaspoon.” Not all cookbooks agree.
So there’s your answer. Satisfied? We didn’t think so.
While that’s a lovely intellectual exercise, the fundamental problem, of course, is that practically nobody has a 1/16 tsp measuring spoon in their kitchen drawer. Most standard measuring spoon sets include sizes down to 1/4 tsp; if you’re lucky, you may have a 1/8 tsp measure. In that case, fill it halfway for your 1/16 tsp pinch.
In practice, a pinch of a fine ingredient (like salt, pepper, cayenne, etc.) is the amount you can pick up between your thumb and your index finger. This amount is different for everyone, and there are extremes. You can get quite a bit of salt between your thumb and index fingers if you try really hard. Further confusing matters, some chefs have been known to dip three or four fingers into the salt dish for their “pinch,” which yields an even greater quantity.
If you’re not sure what a pinch looks like, try this. On a dark coloured plate, place a 1/4 tsp mound of salt. Divide it in half, then divide it in half again. That should help you guesstimate the quantity for future reference. It’s not an exact measure, but it’s in the ballpark.
As long as you use your thumb and index finger to pick up a “pinch” of a fine dry ingredient from a dish, you’ll likely be getting the amount your recipe calls for. More precision than this is rarely required.