Education News & Blogs – NASA Jet Propulsion Laboratory

Learn how pi is used by NASA and how many of its infinite digits have been calculated, then explore the science and engineering that makes the Pi Day Challenge possible.

Update: March 15, 2023 – The answers are here! Visit the NASA Pi Day Challenge page to view the illustrated answer keys for each problem.

This year marks the 10th installment of the NASA Pi Day Challenge. Celebrated on March 14, Pi Day is the annual holiday that pays tribute to the mathematical constant pi – the number that results from dividing any circle's circumference by its diameter.

Every year, Pi Day gives us a reason to celebrate the mathematical wonder that helps NASA explore the universe and enjoy our favorite sweet and savory pies. Students can join in the fun once again by using pi to explore Earth and space themselves in the NASA Pi Day Challenge.

Read on to learn more about the science behind this year's challenge and find out how students can put their math mettle to the test to solve real problems faced by NASA scientists and engineers as we explore Earth, Mars, asteroids, and beyond!

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How It Works
The Science Behind the 2023 NASA Pi Day Challenge
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Infographic of all of the Pi in the Sky 10 graphics and problems

Visit the Pi in the Sky 10 lesson page to explore classroom resources and downloads for the 2023 NASA Pi Day Challenge. Image credit: NASA/JPL-Caltech | + Expand image

The Perseverance rover approaches a lander on the surface of Mars. A small rocket flies toward an orbiter overhead while a Mars helicopter flies in the background. A partially illuminated Earth appears in the distnace.

This illustration shows a concept for multiple robots that would team up to ferry to Earth samples of rocks and soil being collected from the Martian surface by NASA's Mars Perseverance rover. Image credit: NASA/JPL-Caltech | › Full image and caption

An illustration shows the 18 hexagonal pieces that make up the primary mirror of the James Webb Space Telescope next to the primary mirror of the Hubble Space Telescope. The James Webb Mirror stands taller with a label that reads 6.5 meters in height, while the Hubble mirror is labled with a diameter of 2.4 meters. Two human figures are shown smaller than the Hubble mirror for comparison.

Image from animation comparing the relative sizes of James Webb's primary mirror to Hubble's primary mirror. Credit: NASA/Goddard Space Flight Center . | › Full animation

An illustration shows the Psyche asteroid in a star field. The asteroid ranges in color from light grey to dark grey to brown and is covered with a rocky, cratered surface.

This illustration depicts the metal-rich asteroid Psyche, which is located in the main asteroid belt between Mars and Jupiter. Credits: NASA/JPL-Caltech/ASU | + Full image and caption

A composite of four images of the sun, each being covered by progressively more of the sun. The final image shows the sun eclipsed by the moon with a ring of light showing behind the moon that is too small to cover the entire disk of the sun.

This image sequence shows an annular solar eclipse from May 2012. The bottom right frame illustrates the distinctive ring, or "annulus," of such eclipses. A similar eclipse will be visible from the South Pacific on May 10, 2013. Credits: Brocken Inaglory, CC BY-SA 3.0, via Wikimedia Commons | + Expand image

How It Works

Dividing any circle’s circumference by its diameter gives you an answer of pi, which is usually rounded to 3.14. Because pi is an irrational number, its decimal representation goes on forever and never repeats. In 2022, mathematician Simon Plouffe discovered the formula to calculate any single digit of pi. In the same year, teams around the world used cloud computing technology to calculate pi to 100 trillion digits. But you might be surprised to learn that for space exploration, NASA uses far fewer digits of pi.

Here at NASA, we use pi to measure the area of telescope mirrors, determine the composition of asteroids, and calculate the volume of rock samples. But pi isn’t just used for exploring the cosmos. Since pi can be used to find the area or circumference of round objects and the volume or surface area of shapes like cylinders, cones, and spheres, it is useful in all sorts of ways. Transportation teams use pi when determining the size of new subway tunnels. Electricians can use pi when calculating the current or voltage passing through circuits. And you might even use pi to figure out how much fencing is needed around a circular school garden bed.

In the United States, March 14 can be written as 3.14, which is why that date was chosen for celebrating all things pi. In 2009, the U.S. House of Representatives passed a resolution officially designating March 14 as Pi Day and encouraging teachers and students to celebrate the day with activities that teach students about pi. And that's precisely what the NASA Pi Day Challenge is all about!

The Science Behind the 2023 NASA Pi Day Challenge

This 10th installment of the NASA Pi Day Challenge includes four noodle-nudgers that get students using pi to calculate the amount of rock sampled by the Perseverance Mars rover, the light-collecting power of the James Webb Space Telescope, the composition of asteroid (16) Psyche, and the type of solar eclipse we can expect in October.

Read on to learn more about the science and engineering behind each problem or click the link below to jump right into the challenge.

› Take the NASA Pi Day Challenge

› Educators, get the lesson here!

Tubular Tally

NASA’s Mars rover, Perseverance, was designed to collect rock samples that will eventually be brought to Earth by a future mission. Sending objects from Mars to Earth is very difficult and something we've never done before. To keep the rock cores pristine on the journey to Earth, the rover hermetically seals them inside a specially designed sample tube. Once the samples are brought to Earth, scientists will be able to study them more closely with equipment that is too large to make the trip to Mars. In Tubular Tally, students use pi to determine the volume of a rock sample collected in a single tube.

Rad Reflection

When NASA launched the Hubble Space Telescope in 1990, scientists hoped that the telescope, with its large mirror and sensitivity to ultraviolet, visible, and near-infrared light, would unlock secrets of the universe from an orbit high above the atmosphere. Indeed, their hope became reality. Hubble’s discoveries, which are made possible in part by its mirror, rewrote astronomy textbooks. In 2022, the next great observatory, the James Webb Space Telescope, began exploring the infrared universe with an even larger mirror from a location beyond the orbit of the Moon. In Rad Reflection, students use pi to gain a new understanding of our ability to peer deep into the cosmos by comparing the area of Hubble’s primary mirror with the one on Webb .

Metal Math

Orbiting the Sun between Mars and Jupiter, the asteroid (16) Psyche is of particular interest to scientists because its surface may be metallic. Earth and other terrestrial planets have metal cores, but they are buried deep inside the planets, so they are difficult to study. By sending a spacecraft to study Psyche up close, scientists hope to learn more about terrestrial planet cores and our solar system’s history. That's where NASA's Psyche comes in. The mission will use specialized tools to study Psyche's composition from orbit. Determining how much metal exists on the asteroid is one of the key objectives of the mission. In Metal Math, students will do their own investigation of the asteroid's makeup, using pi to calculate the approximate density of Psyche and compare that to the density of known terrestrial materials.

Eclipsing Enigma

On Oct. 14, 2023, a solar eclipse will be visible across North and South America, as the Moon passes between Earth and the Sun, blocking the Sun's light from our perspective. Because Earth’s orbit around the Sun and the Moon’s orbit around Earth are not perfect circles, the distances between them change throughout their orbits. Depending on those distances, the Sun's disk area might be fully or only partially blocked during a solar eclipse. In Eclipsing Enigma, students get a sneak peek at what to expect in October by using pi to determine how much of the Sun’s disk will be eclipsed by the Moon and whether to expect a total or annular eclipse.

Teach It

Celebrate Pi Day by getting students thinking like NASA scientists and engineers to solve real-world problems in the NASA Pi Day Challenge. In addition to solving this year’s challenge, you can also dig into the more than 30 puzzlers from previous challenges available in our Pi Day collection. Completing the problem set and reading about other ways NASA uses pi is a great way for students to see the importance of the M in STEM.

Pi Day Resources

Pi in the Sky Lessons

Here's everything you need to bring the NASA Pi Day Challenge into the classroom.

Grades 4-12

Time Varies
NASA Pi Day Challenge

The entire NASA Pi Day Challenge collection can be found in one, handy slideshow for students.

Grades 4-12

Time Varies
How Many Decimals of Pi Do We Really Need?

While you may have memorized more than 70,000 digits of pi, world record holders, a JPL engineer explains why you really only need a tiny fraction of that for most calculations.
18 Ways NASA Uses Pi

Whether it's sending spacecraft to other planets, driving rovers on Mars, finding out what planets are made of or how deep alien oceans are, pi takes us far at NASA. Find out how pi helps us explore space.
10 Ways to Celebrate Pi Day With NASA on March 14

Find out what makes pi so special, how it’s used to explore space, and how you can join the celebration with resources from NASA.
Infographic: Planet Pi

This poster shows some of the ways NASA scientists and engineers use the mathematical constant pi (3.14) and includes common pi formulas.
Downloads

Can't get enough pi? Download this year's NASA Pi Day Challenge graphics, including mobile phone and desktop backgrounds:
- Pi in the Sky 10 Poster (PDF, 11.3 MB)
- Perseverance Mars Rover Background: Phone | Desktop
- James Webb Space Telescope Background: Phone | Desktop
- Psyche Mission Background: Phone | Desktop
- 2023 Eclipse Background: Phone | Desktop
National Council of Teachers of Mathematics: Notice and Wonder

Creative brainstorming through noticing and wondering encourages student participation, engagement, and students' understanding of the NASA Pi Day Challenge.

Subject Mathematics
Pi Day: What's Going 'Round

Tell us what you're up to this Pi Day and share your stories and photos on our showcase page.

Plus, join the conversation using the hashtag #NASAPiDayChallenge on Facebook, Twitter, and Instagram.

Related Lessons for Educators

Related Activities for Students

Recursos en español

18 Maneras en Que la NASA Usa Pi

Pi nos lleva lejos en la NASA. Estas son solo algunas de las formas en que pi nos ayuda a explorar el espacio.

Facts and Figures

Websites

ABOUT THE AUTHOR

Lyle Tavernier, Educational Technology Specialist, NASA-JPL Education Office

Lyle Tavernier is an educational technology specialist at NASA's Jet Propulsion Laboratory. When he’s not busy working in the areas of distance learning and instructional technology, you might find him running with his dog, cooking or planning his next trip.

While world record holders may have memorized more than 70,000 digits of pi, a JPL engineer explains why you really only need a tiny fraction of that for most calculations – even at NASA.

Update: October 24, 2022 – This article, originally written in 2016, has been updated to reflect the latest values for NASA’s Voyager 1 spacecraft, which continues to venture farther into interstellar space. The author, Marc Rayman, has ventured on too, from the chief engineer for NASA’s Dawn mission, which concluded successfully in 2018, to the chief engineer for mission operations and science at NASA’s Jet Propulsion Laboratory.

The decimals of pi are listed out on an orange background with a large pi symbol in the background.

This graphic shows more than 500 of the infinite number of decimals in pi. Image credit: NASA/JPL-Caltech | + Expand image

We received this question from a fan on Facebook who wondered how many decimals of the never-ending 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 [360 or even more]?”

Here’s JPL’s Chief Engineer for Mission Operations and Science, Marc Rayman, with the answer:

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 asked about. Consider these examples:

The most distant spacecraft from Earth is Voyager 1. As of this writing, it’s about 14.7 billion miles (23.6 billion kilometers) away. Let’s be generous and call that 15 billion miles (24 billion kilometers). Now say we have a circle with a radius of exactly that size, 30 billion miles (48 billion kilometers) 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 94 billion miles (more than 150 billion kilometers). 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 30-billion-mile (48-billion-kilometer) diameter circle would be wrong by less than half an inch (about one centimeter). Think about that. We have a circle more than 94 billion miles (more than 150 billion kilometers) around, and our calculation of that distance would be off by no more than the width of your little finger.

Put your pi math skills to the test with this problem from NASA's Pi Day Challenge. Can you use pi to determine what fraction of a signal from Voyager 1 reaches Earth? Image credit: NASA/JPL-Caltech | + Expand image | › View lesson page
We can bring this closer to home by looking at our planet, Earth. It is more than 7,900 miles (12,700 kilometers) in diameter at the equator. The circumference is roughly 24,900 miles (40,100 kilometers). That's how far you would travel if you circumnavigated the globe – and didn't worry about hills, valleys, and obstacles like buildings, ocean waves, etc. How far off would your odometer be if you used the limited version of pi above? The discrepancy would be the size of a molecule. There are many different kinds of molecules, of course, so they span a wide range of sizes, but I hope this gives you an idea. Another way to view this is that your error by not using more digits of pi would be more than 30,000 times thinner than a hair!

Image credit: NASA | + Expand image
Let's go to the largest size there is: the known universe. The radius of the universe is about 46 billion light years. Now let me ask (and answer!) a different question: How many digits of pi would we need 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, the simplest atom? It turns out that 37 decimal places (38 digits, including the number 3 to the left of the decimal point) would be quite sufficient. Think about how fantastically vast the universe is. It’s certainly far beyond what you can see with your eyes even on the darkest, most beautiful night of sparkling stars. It’s yet farther beyond the extraordinary vision of the James Webb Space Telescope. And the vastness of the universe is truly far, far, far beyond what we can even conceive. Now think about how incredibly tiny a single atom is. Isn’t it amazing that we wouldn’t need to use many digits of pi at all to cover that entire unbelievable range?

If you were to hold a single grain of sand at arm's length, you could cover the entire area of space taken up by this image, which was captured by the James Webb Space Telescope and contains thousands of galaxies. The oldest-known galaxy identified in the image is 13.1 billion years old. Image credit: NASA, ESA, CSA, STScI | + Expand image | › More about the image | Text description (PDF)
Pi is an intriguing number with interesting mathematical properties. It’s fun to think about its truly endless sequence of digits, and it may be surprising how often it appears in the equations scientists and engineers use. But there are no questions – prosaic or esoteric – in humankind’s noble efforts to explore or comprehend the marvels of the cosmos, from the unimaginably smallest scales to the inconceivably largest, that could require very many of those digits.

Hear more from Marc in his inspiring TEDx talk, “If It Isn’t Impossible, It Isn’t Worth Trying” and in his Dawn Journal, where he wrote frequent updates about the Dawn mission’s extraordinary extraterrestrial expedition to the protoplanet Vesta and dwarf planet Ceres.

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Educator Resources

Articles

Multimedia & Downloads

Infographic: Planet Pi

This poster shows some of the ways NASA scientists and engineers use the mathematical constant pi (3.14) and includes common pi formulas.

Recursos en español

18 Maneras en Que la NASA Usa Pi

Pi nos lleva lejos en la NASA. Estas son solo algunas de las formas en que pi nos ayuda a explorar el espacio.

TAGS: Pi, Pi Day, Dawn, Voyager, Engineering, Science, Mathematics

ABOUT THE AUTHOR

NASA/JPL Edu

NASA/JPL Edu supports science, technology, engineering and mathematics (STEM) education by providing NASA and JPL activities, resources and materials to educators and students in grades K-12 as well as STEM internships and research opportunities to higher education students and faculty.

Learn about pi and some of the ways the number is used at NASA. Then, dig into the science behind the Pi Day Challenge.

Update: March 15, 2022 – The answers are here! Visit the NASA Pi Day Challenge slideshow to view the illustrated answer keys for each of the problems in the 2022 challenge.

Jump To

In the News
How It Works
The Science Behind the 2022 NASA Pi Day Challenge
Teach It
Explore More

In the News

No matter what Punxsutawney Phil saw on Groundhog Day, a sure sign that spring approaches is Pi Day. Celebrated on March 14, it’s the annual holiday that pays tribute to the mathematical constant pi – the number that results from dividing any circle's circumference by its diameter.

Every year, Pi Day gives us a reason to not only celebrate the mathematical wonder that helps NASA explore the universe, but also to enjoy our favorite sweet and savory pies. Students can join in the fun by using pi to explore Earth and space themselves in our ninth annual NASA Pi Day Challenge.

Read on to learn more about the science behind this year's challenge and find out how students can put their math mettle to the test to solve real problems faced by NASA scientists and engineers as we explore Earth, the Moon, Mars, and beyond!

Infographic of all of the Pi in the Sky 9 graphics and problems

Visit the Pi in the Sky 9 lesson page to explore classroom resources and downloads for the 2022 NASA Pi Day Challenge. Image credit: NASA/JPL-Caltech | + Expand image

An spacecraft orbiting the Moon shines a laser into a dark crater.

This artist's concept shows the Lunar Flashlight spacecraft, a six-unit CubeSat designed to search for ice on the Moon's surface using special lasers. Image credit: NASA/JPL-Caltech | › Full image details

Dome-covered seismometer sits on the surface of Mars while clouds pass overhead.

Clouds drift over the dome-covered seismometer, known as SEIS, belonging to NASA's InSight lander, on Mars. Credit: NASA/JPL-Caltech. | › Full image and caption

The SWOT spacecraft passes over Florida, sending signals and collecting data.

This animation shows the collection of data over the state of Florida, which is rich with rivers, lakes and wetlands. Credits: NASA/JPL-Caltech | + Expand image

A spacecraft points to a star that has three planets orbiting it.

Illustration of NASA’s Transiting Exoplanet Survey Satellite (TESS). Credits: NASA | + Expand image