Beyond 65 digits, π serves no practical purpose

For spatial engineers’ highest accuracy calculations, used in interplanetary navigation, 3.141592653589793 is more than sufficient. Let’s understand why more decimals aren’t needed.

Consider these examples:

• Voyager 1, the farthest spacecraft from Earth, is about 14.7 billion miles away. Using π rounded to the 15th decimal, the circumference of a circle with a radius of 30 billion miles would be off by less than half an inch.

• Earth’s circumference is roughly 24,900 miles. The discrepancy using limited π would be smaller than the size of a molecule, over 30,000 times thinner than a hair.

• The radius of the universe is about 46 billion light years. To calculate the circumference of a circle with a radius of 46 billion light years to an accuracy equal to the diameter of a hydrogen atom, only 37 decimal places are necessary.

• With just 65 decimal places, we could determine the size of the observable universe within a Planck length, the shortest measurable distance.

While π’s digits are endless, for microscopic, macroscopic or cosmic endeavors, very few are necessary.