That's a lot of joe!
The symptoms of caffeine intoxication are quite extraordinary. They may include restlessness, fidgeting, anxiety, increased urination, excitement, insomnia, flushing of the face, gastrointestinal disturbance, muscle twitching, a rambling flow of thought and speech, irregular or rapid heart beat, irritability, and psycho-motor agitation. In cases of excessive overdoses, mania, depression, lapses in judgment, disorientation, disinhibition, delusions, hallucinations, or psychosis may occur.
Caffeine overdose in humans is dependent on individual sensitivity. It is estimated that 150 to 200 milligrams of caffeine per kilogram of body mass is needed to be fatal. This would be around 75–100 cups of coffee for a 70 kilogram adult, consumed all at once! Over the years a number of fatalities have been caused by overdoses of readily available powdered caffeine supplements. According to science and wiki the estimated lethal amount is around half a tablespoon.
So according to science and wiki the lethal dose of caffeine is roughly 100 cups of coffee.
After some extensive research I found actual video proof of what really happens! In the below video Fry clearly demonstrates what happens if you get to 100 cup's.
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