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.


Pi to the 15th decimal is shown in a speckled starry band as a silhouetted face looks out over colorful concentric circles and black and white images of an atom, molecules, Earth, and the Voyager spacecraft. The left side of the image fades to black with

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 decimals of the infinite number 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:

  1. 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.
  2. The illustration shows a cartoonish Voyager 1 flying in space with a conical signal eminating from its antenna. An inset shows a more distant view of Voyager with a line extending to Earth and a distance label between the Voyager and Earth marked ~131 AU.

    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

  3. 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!
  4. A view of Earth from space showing East Africa, the Middle East, and Asia with swirls and splotches of clouds across the planet.

    Image credit: NASA | + Expand image

  5. 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?
Link to text description available below

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

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We talked to a few JPL interns about what they've been working on, how they're taking NASA into the future, and what it all means to them.


Despite the challenges of the past two years, it’s been a busy time for NASA’s Jet Propulsion Laboratory. Among the Lab’s activities have been the launch and landing of a new Mars rover, preparations for sending a spacecraft to explore an ocean world beyond Earth, first light for missions studying our changing climate and the universe beyond, and the development of technology to help address the COVID pandemic.

All the while, JPL interns have continued supporting scientists, engineers, and technologists behind the scenes to make those missions and projects happen.

More than 600 summer interns are taking part in that crucial work – both in-person at the laboratory in Southern California as well as from their homes and dorms across the country. In May, JPL welcomed summer interns back on site for the first time since 2019 while continuing to offer remote internships as projects allow.

We wanted to hear what interns have been up to, how they're contributing to NASA missions and science, and what the experience has meant to them. So we caught up with three students who have helped see the lab through the last year or two – and in one case, seven years. Watch their stories in the video above.

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The laboratory’s STEM internship and fellowship programs are managed by the JPL Education Office. Extending the NASA Office of STEM Engagement’s reach, JPL Education seeks to create the next generation of scientists, engineers, technologists and space explorers by supporting educators and bringing the excitement of NASA missions and science to learners of all ages.

Career opportunities in STEM and beyond can be found online at jpl.jobs. Learn more about careers and life at JPL on LinkedIn and by following @nasajplcareers on Instagram.

TAGS: Interns, Internships, College Students, Science, Engineering, InSight, Mars, Europa, Ocean Worlds, Enceladus, Saturn, Cassini, Ceres

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Illustration of InSight landing on Mars

Tom Hoffman, InSight Project Manager, NASA JPL, left, and Sue Smrekar, InSight deputy principal investigator, NASA JPL, react after receiving confirmation InSight is safe on the surface of Mars

This is the first image taken by NASA's InSight lander on the surface of Mars.

The Instrument Deployment Camera (IDC), located on the robotic arm of NASA's InSight lander, took this picture of the Martian surface on Nov. 26

UPDATE: Nov. 27, 2018 – The InSight spacecraft successfully touched down on Mars just before noon on Nov. 26, 2018, marking the eighth time NASA has succeeded in landing a spacecraft on the Red Planet. This story has been updated to reflect the current mission status. For more mission updates, follow along on the InSight Mission Blog, JPL News, as well as Facebook and Twitter (@NASAInSight, @NASAJPL and @NASA).


NASA's newest Mars mission, the InSight lander, touched down on the Red Planet just before noon PST on Nov. 26. But there's more work ahead before the mission can get a look into the inner workings of Mars. Get your classroom ready to partake in all the excitement of NASA’s InSight mission with this educator game plan. We’ve got everything you need to engage students in NASA's ongoing exploration of Mars!

Day Before Landing

Landing Day (Nov. 26)

Next Day

  • Review the Teachable Moment to find out what needs to happen before InSight’s science operations can begin. Then create an instructional plan with these lessons, activities and resources that get students engaged in the science and engineering behind the mission.
  • Check out InSight’s first images from Mars, here. (This is also where you can find raw images from InSight throughout the life of the mission.)

Over the Next Month


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TAGS: InSight, Mars Landing, Educators, K-12, Elementary School, Middle School, High School, Lessons and Activities, Educator Resources, Mars

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Update – Sept. 13, 2018: Due to the number of requests we have received, this bulletin board registration is now closed. In the event more materials become available, an update will be posted here. All materials are also available to download at the links below.


Launch back into STEM with these back-to-school resources from NASA all about hurricanes, clouds, weather, Earth science – and the satellites that study them. For a limited time, the Educator Resource Center at NASA's Jet Propulsion Laboratory is offering free bulletin-board materials to educators for display in classrooms or other educational settings.

Register today to receive free materials mailed directly to you or download them at the links below.

Out of stock

  • Bulletin board mailers are limited to teachers at U.S.-based institutions.
  • Available while supplies last.
  • Requests will be fulfilled in the order they are received.

Download bulletin board materials:

Visit our educator resources page for more downloads and online resources.

TAGS: Bulletin Board, Educator Resources, Materials, Educator Resource Center, Downloads, Posters

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Moon Phases Calendar and Calculator Project from NASA/JPL Edu

Looking for a stellar 2018 calendar? Try this new Moon Phases Calendar and Calculator DIY from the Education Office at NASA’s Jet Propulsion Laboratory!

Download the free, decoder-ring style calendar and assemble it to see when and where to view the Moon every day of the year. The calendar features daily moon phases, moonrise, moonset and overhead viewing times, a listing of Moon events including supermoons and lunar eclipses, plus graphics depicting the relative positions of Earth and the Moon during various moon phases. Use it to teach students about the phases of the Moon, for sky-gazing or simply as a unique wall calendar.

In the classroom, it makes a great addition to this Teachable Moment and related lessons about supermoons – two of which will ring in the new year in January 2018.

Explore these and more Moon-related lessons and activities from NASA/JPL Edu at the links below:


For Students

Project: Moon Phases Calendar and Calculator

Like a decoder wheel for the Moon, this calendar will show you where and when to see the Moon and every moon phase throughout the year!


Project: Look at the Moon! Journaling Project

Draw what you see in a Moon Journal and see if you can predict the moon phase that comes next.


For Educators

Teachable Moment: What’s a Supermoon and Just How Super Is It?

What are supermoons, why do they occur and how can they be used as an educational tool?


Observing the Moon (Grades K-6)

Students identify the Moon’s location in the sky and record their observations over the course of the moon-phase cycle in a journal.


Whip Up a Moon-Like Crater (Grades 1-6)

Whip up a Moon-like crater with baking ingredients as a demonstration for students.


Moon Phases (Grades 1-6)

Students take measurements of the Moon during its full phases over multiple Moon cycles to compare and contrast results.


Modeling the Earth-Moon System (Grades 6-8)

Whip up a Moon-like crater with baking ingredients as a demonstration for students.


Measuring the Supermoon (Grades 5-12)

Students take measurements of the Moon during its full phase over multiple Moon cycles to compare and contrast results.

TAGS: Moon, Supermoon, Moon Phases, Moon Phases Calendar, Projects, DIY, For Students, Astronomy

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Space-Themed Halloween Supplies

When Halloween rolls around at NASA’s Jet Propulsion Laboratory, we really let our nerd flags fly. Pumpkin carving contests turn into serious engineering design challenges and costume inspiration runs the gamut from real science to science fiction.

This year, join us in all our geekdom with these spooky (and educational!) space activities from the Education Office at NASA/JPL:


Create a Halloween Pumpkin Like a NASA Engineer

Project: Create a Halloween Pumpkin Like a NASA Engineer

Get tips and inspiration for creating a stellar pumpkin from the same people who send spacecraft to other planets!


Mysteries of the Solar System and Beyond Slideshow

Slideshow: Mysteries of the Solar System and Beyond

Strange things are happening all around the solar system. See if you can solve these space mysteries before finding out how scientists did it.


 

TAGS: Halloween, Pumpkin, Mysteries, Stranger Things, Science, Engineering, STEM

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Update – Sept. 20, 2017: Due to the number of requests we have received, this bulletin board registration is now closed. In the event more materials become available, an update will be posted here. All materials are also available to download at the links below. 


This year has been full of exciting discoveries at NASA as we learn more about our solar system as well as star systems light years away.

Want a cool way to share these missions and discoveries with your classroom? Sign up online to receive the latest classroom bulletin board set from the Educator Resource Center at NASA’s Jet Propulsion Laboratory.

Note:

  • Bulletin board mailers are limited to teachers at U.S.-based institutions.
  • Available while supplies last.
  • Requests will be fulfilled in the order they are received.

Here’s what’s included:


Exoplanet Space Tourism Posters

Exoplanet Space Tourism Posters

NASA’s Kepler space telescope, which has already discovered more than 1,000 planets beyond our solar system, continues to identify more and more of these so-called exoplanets – some of which have features similar to Earth. (Learn more about these worlds on NASA's Exoplanet Exploration website.) This popular poster set imagines what life would be like on these distant worlds.

Note: The bulletin board materials will include a small sample of the full set, which can be downloaded here.


Reading, Writing and Rings Activities

Reading, Writing and Rings

Closer to home, September 15 will mark the end of the Cassini mission, which has spent nearly 13 years orbiting the ringed giant Saturn. Images and science from Cassini have shaped our understanding of Saturn and its mysterious moons, and continue to provide wonder to students. This collection of activities will get students using reading and writing to explore the Cassini mission’s science at Saturn.

Find out more about the Cassini mission and its Grand Finale on Sept. 15, 2017.


Saturn Postcards

Saturn Postcards

Take in some of Cassini’s best views of Saturn with these NASA postcards featuring images from the mission!

Explore more images from the Cassini mission at Saturn.


Visit our educator resources page for more downloads and online resources.

TAGS: materials, educator resources, educator resource center, classroom resources, bulletin board, teaching materials

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JPL engineering Michael Staab (standing) with the last class of interns for NASA's Cassini mission at Saturn

For more than 22 years, since before NASA's Cassini mission even launched, flight controllers have invited summer interns to NASA’s Jet Propulsion Laboratory to help make the mission at Saturn happen. But with the spacecraft's journey ending in September, the current summer interns will be Cassini’s last.

Meet the students and learn what role they're playing in the nearly 13-year mission at Saturn.
› See the full story and image gallery on the Cassini Mission website


Explore JPL’s summer and year-round internship programs and apply at: http://www.jpl.nasa.gov/edu/intern

The laboratory’s STEM internship and fellowship programs are managed by the JPL Education Office. Extending the NASA Office of Education’s reach, JPL Education seeks to create the next generation of scientists, engineers, technologists and space explorers by supporting educators and bringing the excitement of NASA missions and science to learners of all ages.

TAGS: Cassini Mission, Saturn, Intern

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This summer, while many of us were sleeping in and avoiding heavy school work, lots of exciting things were happening in and around our solar system! Here's a guide to launching the 2016 school year right and turning those stellar events into educational connections from NASA. 

Science on Fire

An image of the Soberanes fire, in northern California near Big Sur
This false-color image of the Soberanes fire in Northern California, near Big Sur, was captured by the Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) instrument on NASA's Terra spacecraft on July 28, 2016.

Here at home, on Earth, it is fire season in many places in the Northern Hemisphere. Fire season comes about with warmer temperatures, dry air, and dry brush. Once a fire gets started in these conditions, it can rapidly spread and become out of control, especially when high winds are involved. This summer has already witnessed some dangerous fires including the Sand Fire in Southern California and the Soberanes Fire near Big Sur on the Central California coast. Beyond the immediate threat from flames, smoke degrades air quality and burn scars leave hillsides vulnerable to rain-induced mudslides.

NASA satellites and airborne instruments are helping scientists better understand wildfires and their impacts on our changing climate. And in the immediate term, they are helping firefighters track wildfires and respond to people and structures in risk areas.

Check out JPL's latest Teachable Moment to find out more about how scientists are studying wildfires, what they're learning and why it's important. And get links to two new lessons for students in grades 3-12 that have students use NASA data, algebra and geometry to approximate burn areas, fire-spread rate and fire intensity. (You can also go straight to the new lessons at: Fired Up Over Math: Studying Wildfires from Space and Pixels on Fire)

And speaking of Earth science, find out how you can get a free bulletin board featuring posters and lithographs about NASA Earth science and missions for your classroom!

Greetings from Jupiter

Watch a recap of the July 4 excitement as NASA's Juno spacecraft entered orbit around Jupiter.

On July 4, just in time for a fireworks spectacle, the Juno spacecraft went into orbit around Jupiter. Juno launched from Earth aboard a huge rocket and had been hurtling toward Jupiter for nearly five years. Getting into orbit around Jupiter was a real nail-biter here at NASA's Jet Propulsion Laboratory (which helps manage the mission) and we are all very happy everything went as planned. Juno’s mission is to study the origin, core and magnetic fields of our solar system’s largest planet. Juno will orbit Jupiter for only about 20 months before Jupiter’s intense radiation environment takes a toll on the spacecraft.

Communicating with a spacecraft as far away as Juno is a challenge that involves a lot of planning and teamwork. Try out this new lesson for young learners that demonstrates this process and provides practice with number concepts, counting and geometry, and data collection in a concrete, active manner. 

Wish you had your very own Juno spacecraft you could use to uncover secrets beneath Jupiter? Check out this easy-to-build Juno model that uses household objects and can be used in a game with friends and family!

Explore more about Juno with these related lessons and videos: 


TAGS: Back-to-School, Juno, Wildfires, Bulletin Board, Lessons, Activities, DIY

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