There is no magic number that your car will be worth after an accident. It is, of course, variable depending on the age, make and model of your car, how severe the accident was and what kind of shape your car was in before the accident happened. You will also need to know the details of your insurance policy, if you have one. Plus, if the accident was not your fault and you don't live in an area with "no fault" insurance, you will need the insurance information from the other party.
Have your car appraised. Most times, the insurance company will send out an appraiser to look at your car and take some pictures of the damage soon after you report the accident. Then, within a few days' time, you will get an estimate of how much it will cost to have it fixed. A rudimentary way to calculate your car's value is to subtract this number from the car's value before the accident. (Not sure? Look in the Kelley Blue Book. See Step 2.) There are two caveats, however. First of all, if you still have a lien on your car, you will most likely be required to get it fixed even if you don't want to. Secondly, your insurance company may declare your vehicle to be a "total loss" if its value is deemed to be lower than the cost necessary to fix it. If this is the case, the company will give you a check. The sum offered is what it deems your car is worth.
Check the Kelley Blue Book. This is another good way to find out the amount you may be able to sell your car for after your accident. You can consult the actual paper book or go to the website. (There are also similar sites, such as NADA Guides, you can use.) When you look up your vehicle's make, model and year, you will then have the option of choosing the car's condition. Use your better judgment as to whether your car has minor or major damage. It shouldn't be too hard to determine. Basically any car that's not drivable or has more than a few hours of body work and painting needed to fix it falls into the major category.
Take your car to a used car dealer, like CarMax, and see what kind of offer you get. No matter what number you determine for the value of your car, it is only worth as much as someone is willing to pay for it. If your car is rare or historic, you may be able to garner a good price on it--even if it's only good for spare parts. On the other hand, if your car has fire or water damage from the accident, you may have a hard time even giving it away, since this could lead to severe mechanical problems down the road.
