I made an Excel sheet many years ago when I was still in school that was a very detailed, highly accurate racing calculator. You had to input your actual dyno-obtained horsepower values every 100 rpm, your race weight, gear ratios (transmission & rear), automatic or manual transmission, and some aerodynamic information (coefficient of drag and frontal area).
From all that information, it basically calculated the acceleration, speed, and position of the vehicle for the entire race (minus the first 60', which had to be inputted, as that's a very difficult thing to calculate with a lot of variables).
Assuming all of those inputs were accurate, especially the dyno information, it was EXTREMELY accurate. I compared it with a lot of stock performance cars (older 2-valve 4.6 Mustang GTs, 03/04 Cobras, 2011+ Coyote Mustangs, Corvettes, LS1 Camaros / TAs, etc.), as there is an abundance of data out there regarding what they dyno stock, and what they run at the track stock. It was almost always within .2 seconds and 2 mph of what they actually run. On my own personal car (600+ rwhp supercharged Mustang), that I ran at the track hundreds of times, and dynoed it quite a bit as well, the ET was .2 off and the mph was exact.
It was very interesting to play around with, as it made clear some truisms related to racing that aren't always very obvious. Things like gearing, shift points, horsepower vs. torque, peak vs. average horsepower, etc.
To the OP, as you can imagine, the inputs / calculations / outputs can vary quite a bit depending on exactly what you're looking for. So if you'll explain what you're after, I'll see if I can help.
As for the simple calculators out there, horsepower = force * velocity. Force = mass * acceleration. So if you combine the two, and solve it for acceleration, you get: acceleration = horsepower / (mass * velocity). From there, you can either do some simple numerical calculus or some more complex analytical calculus to determine accelerations, velocities, and positions across any time or distance you want (1/4 mile, 1/8 mile, etc.). Those calculators are taking some liberties regarding peak vs. average horsepower, gearing / shift points, wind resistance, 60' times, etc., but that's the basic jist of how they work.