It's hard to predict just how many credit score points you'll lose because of a late payment. That's because FICO and other companies who've developed credit scoring calculations have not made the details of the calculations available for the public.
FICO did release FICO score loss information based on two hypothetical situations. In the scenario, the person with 680 credit score (who already had one other late payment on their credit history) would lose between 60 and 80 points for a 30-day late credit card payment, while the person with the 780 credit score (with no other late payments) would lose between 90 and 110 points.
Your credit score might experience a similar drop if you have a credit profile similar to these scenarios. See How Credit Mistakes Hurt Your FICO Score for more information.
You can better predict the impact of a late payment on your credit score using the FICO Score Simulator, available when you purchase the FICO Standard product from myFICO.com. FICO Standard includes your Equifax or TransUnion credit report and credit score.