Value of Pi

NASA has been asked how many decimals of the mathematical constant pi (π) NASA-JPL scientists and engineers use when making calculations:

Does JPL only use 3.14 for its pi calculations? Or do you use more decimals like say:

3.141592653589793238462643383279502884197169399375105

82097494459230781640628620899862803482

534211706798214808651328230664709384460

9550582231725359408128481117450

2841027019385211055596

446229489549303819644288109756659334

4612847564823378678316527120190914564856692346034861045

4326648213393607260249141273724

5870066063155881748815209209628292

54091715364367892590360

We posed this question to the director and chief engineer for NASA’s Dawn mission, Marc Rayman. Here’s what he said:

Thank you for your question! This isn’t the first time I’ve heard a question like this. In fact, it was posed many years ago by a sixth-grade science and space enthusiast who was later fortunate enough to earn a doctorate in physics and become involved in space exploration. His name was Marc Rayman.

To start, let me answer your question directly. For JPL’s highest accuracy calculations, which are for interplanetary navigation, we use 3.141592653589793. Let’s look at this a little more closely to understand why we don’t use more decimal places. I think we can even see that there are no physically realistic calculations scientists ever perform for which it is necessary to include nearly as many decimal points as you present.

Consider these examples:

  1. The most distant spacecraft from Earth is Voyager 1It is about 12.5 billion miles away. Let’s say we have a circle with a radius of exactly that size (or 25 billion miles in diameter) and we want to calculate the circumference, which is pi times the radius times 2. Using pi rounded to the 15th decimal, as I gave above, that comes out to a little more than 78 billion miles. We don’t need to be concerned here with exactly what the value is (you can multiply it out if you like) but rather what the error in the value is by not using more digits of pi. In other words, by cutting pi off at the 15th decimal point, we would calculate a circumference for that circle that is very slightly off. It turns out that our calculated circumference of the 25 billion mile diameter circle would be wrong by 1.5 inches. Think about that. We have a circle more than 78 billion miles around, and our calculation of that distance would be off by perhaps less than the length of your little finger.

Read More from NASA’s Jet Propulsion Lab

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