The cost per square foot will be very high, and the result would be substandard space. If it's at all possible, adding the equivalent amount of floor area above ground would be less expensive, and would give you much better space quality.
To extend a crawl space to become a basement requires underpinning of all three crawl space walls, and hand excavating the entire space and carrying the soil out almost bucket by bucket. You may have a center girder supported by posts, and the posts would have to be replaced and new footings for them constructed, while the girder is somehow temporarily supported. All of this is very labor-intensive and therefore costly.
There are also some building code issues that need to be addressed for a basement which didn't apply to a crawl space, such as insulation and egress. Depending on your proposed use, there may be others, such as natural light and ventilation.
Without knowing many factors such as the size of the area, your location, your soil conditions, the depth of the excavation, etc., it isn't possible to make any statements about costs, other than to say it won't be cheap, and the result would still only be a basement.
Architect (NY) and Home Designer (PA)