On October 17, 2011, Shigeru Kondo concluded 371 days of computing 10,000,000,000,000 decimal places of π. Roughly 44 TB of disk were needed to perform the computation, and 7.6 TB of disk space was needed to store the compressed output of decimal and hexadecimal digits.
The advent of digital computers in the 20th century led to an increased rate of new π calculation records. John von Neumann (et al.) used ENIAC to compute 2,037 digits of π in 1949, a calculation that took 70 hours. Additional thousands of decimal places were obtained in the following decades, with the million-digit milestone passed in 1973.
Practically, one needs only 39 digits of π to make a circle the size of the observable universe accurate to the size of a hydrogen atom.
Assuming a total world population of roughly 7 billion people, everyone would have to memorize 1,428 digits in order to preserve all known digits of π in our collective heads. The Guinness-recognized record for remembered digits of π is 67,890 digits, held by Lu Chao, a 24-year-old graduate student from China. It took him 24 hours and 4 minutes to recite to the 67,890th decimal place of π without an error.
An average person can read out approximately 120 digits/min. Keeping this pace it would take more than 158,000 years to recite the 10 trillion digits discovered this year and roughly 3 weeks to read out the 4 million digits visualized here.