The amount of calories burned doing sit-ups depends on how much energy you expend. As explained by NutriStrategy and the LiveStrong Foundation, how much energy you expend doing any exercise, not just sit-ups, depends on your height, weight, and the time it takes you to do it.
The NutriStrategy site outlines a table indicating that a person weighing 130 pounds burns 17 calories during 5 minutes of sit-ups, a 155-pound person burns 20 calories, a 180-pound person burns 24s, and a 205-pound person burns 27. These numbers are all derived from 5 minutes of sit-ups. With these numbers, it can be calculated than you can burn up to 5.4 calories per minute while doing sit-ups.
Doing the same number of sit-ups in half the time decreases the amount of calories burned. How much energy you use to complete sit-ups also depends on the specific type of sit-up you do.