Thanks tom and gideon your answers are probably best. How would one see how many frames are in the movie they filmed? The pressure mat sounds interesting but 2 of them is probably still quite expensive (more than 200 once you include a stop watch with an external trigger)
Any half-decent video editor will display the time in hours:minuteseconds:frames. GoPro Studio (free) does, as does Adobe Premier Elements (fairly cheap), plenty of other software available.
I'm not aware of anything off the shelf that's less than a couple of grand. If you want a DIY solution I'd suggest a stopwatch with an external trigger and a pressure mat (from a burglar alarm).
An alternative if you want accuracy and don't mind some inconvenience is to use a video camera (or film it with your phone) and then count the number of frames between start and finish. At 30 frames per second the accuracy over 10 seconds would be around 1/300 (i.e. 0.33%).