Shigeru Kondo, a 55-year-old systems engineer for a food company based in northern Japan, easily surpassed the previous record of 2.7 trillion digits, set late last year by a French engineer.
The calculation of the ratio of the circumference of a circle to its diameter - usually abbreviated to 3.14 - took 90 days and seven hours, according to the Kyodo news agency.
The mammoth calculation nearly came to grief on more than one occasion, Mr Kondo said, including one morning when his daughter tripped a circuit breaker when she turned a hair dryer on. The project was saved when the computer switched to an emergency 10-minute back-up power source.
Mr Kondo was also forced to remove casings from the computer and blow cool air onto the machine with fans as the temperature in his home rose to 40 degrees in the hottest Japanese summer since 1946.
Mr Kondo's computer cost Y1.5 million (£11,550) to build and has a hard-drive capacity of 32 terabytes. He plans to apply to the Guinness Book of Records for recognition of his achievement.
His interest in calculating the value of pi dates back to his college days, Kondo said, adding that as he only used an estimated 60 percent of the machine's capacity he intends to try to compute the value of Pi to 10 trillion digits.
Mr Kondo's wife, Yukiko, 53, complained that the computer used up a lot of energy during the three-month project and increased the electricity bill to Y20,000 (£154) a month.