If you're drinking more than 4 cups of black tea a day, you're drinking too much. According to the Mayo Clinic, it is safe for most healthy adults to consume up to 400 milligrams of caffeine per day. Four cups of black tea contain about 400 milligrams of caffeine.
WebMD states that drinking more than 5 cups of black tea per day can cause side effects, such as headache, sleep problems, nervousness, irritability, ringing in the ears and heartburn. For some people, the recommended consumption is much less. Pregnant women should not drink more than 2 cups of black tea per day because of an increased risk of miscarriage. People with osteoporosis should not drink more than 3 cups because it causes calcium to flush out with the urine, thus weakening the bones.