Orders of magnitude (force) explained

The following list shows different orders of magnitude of force.

Since weight under gravity is a force, several of these examples refer to the weight of various objects. Unless otherwise stated, these are weights under average Earth gravity at sea level.

Below 1 N

Factor (N)ValueItem
10
Gravitational attraction of the proton and the electron in hydrogen atom[1]
10
quectonewton (qN)		8.9 qNWeight of an electron
10
16 rN Weight of a hydrogen atom
10
yoctonewton (yN)		5 yNForce necessary to synchronize the motion of a single trapped ion with an external signal measured in a 2010 experiment[2] [3]
10170 yNForce measured in a 2010 experiment by perturbing 60 beryllium-9 ions[4] [5]
10
attonewton (aN)
1030 aNSmallest force of gravity measured[6] [7]
10
femtonewton (fN)		 
10~10 fNBrownian motion force on an E. coli bacterium averaged over 1 second[8]
~10 fNWeight of an E. coli bacterium[9] [10]
10~100 fNForce to stretch double-stranded DNA to 50% relative extension
10
piconewton (pN)		~4 pNForce to break a hydrogen bond
~5 pNMaximum force of a molecular motor
10 
10~160 pNForce to break a typical noncovalent bond
10
nanonewton (nN)		~1.6 nNForce to break a typical covalent bond
10
~82nNForce on an electron in a hydrogen atom
10
~200nNForce between two 1 meter long conductors, 1 meter apart by an outdated definition of one ampere
10
micronewton (μN)		1–150 μNOutput of FEEP ion thrusters used in NASA's Laser Interferometer Space Antenna[11] -1025 μN-->
10 
10
millinewton (mN)		2-4 mN
1019-92 mNThrust of the NSTAR ion engine tested on NASA's space probe Deep Space 1[12]
10  

1 N and above

MagnitudeValueItem
1 N1.4 NThe weight of a smartphone[13] [14]
2.5 NTypical thrust of a Dual-Stage 4-Grid ion thruster.
9.8 NOne kilogram-force, nominal weight of a 1kg (02lb) object at sea level on Earth[15]
10 N50 NAverage force to break the shell of a chicken egg from a young hen[16]
10 N720 NAverage force of human bite, measured at molars[17]
10 N
kilonewton (kN)		5 kNThe force applied by the engine of a small car during peak acceleration
8 kNThe maximum force achieved by weight lifters during a 'clean and jerk' lift[18] (During the clean part)
9 kNThe bite force of one adult American alligator[19]
10 N16.5 kNThe bite force of a 5.2m (17.1feet) saltwater crocodile[20]
18 kNThe estimated bite force of a 6.1m (20feet) adult great white shark[21]
25 kNApproximate force applied by the motors of a Tesla Model S during maximal acceleration[22]
25.5 to 34.5 kNThe estimated bite force of a large 6.7m (22feet) adult saltwater crocodile[23]
10 N100 kNThe average force applied by seatbelt and airbag to a restrained passenger in a car which hits a stationary barrier at 100 km/h[24]
569 kNMaximum thrust of a large turbofan engine (General Electric GE90)
890 kNMaximum pulling force (tractive effort) of a single large diesel-electric locomotive
10 N
meganewton (MN)		1.8 MNThrust of Space Shuttle Main Engine at lift-off[25] [26] [27]
1.9 MNWeight of the largest Blue Whale
10 N35 MNThrust of Saturn V rocket at lift-off[28]
10 N570 MNSimplistic estimate of force of sunlight on Earth[29]
10 N
giganewton (GN)
10 N200 ENGravitational attraction between Earth and Moon[30]
10 N35 ZNGravitational attraction between Earth and Sun[31]
10 N≈450 RNGravitational attraction between our Galaxy and Andromeda Galaxy[32]
10 NPlanck force

Notes and References

  1. Hugh D. Young, University Physics 4th Ed, 1992, Addison-Wesley Publishing Co, Inc.
  2. Knünz . S. . Herrmann . M. . Batteiger . V. . Saathoff . G. . Hänsch . T. . Vahala . K. . Udem . T. . Injection Locking of a Trapped-Ion Phonon Laser . Physical Review Letters . 105 . 1 . 013004 . 2010 . 20867440 . 10.1103/PhysRevLett.105.013004 . 2010PhRvL.105a3004K.
  3. Web site: Single atoms for detecting extremely weak forces. Max Planck Institute of Quantum Optics. 2010-09-02. https://web.archive.org/web/20100826073110/http://www.mpq.mpg.de/cms/mpq/en/news/press/10_08_04.html. 2010-08-26. dead.
  4. 10.1038/news.2010.187. Brumfiel . G.. Scientists measure atomic nudge. 2010. Nature.
  5. 1004.0780. Ultrasensitive detection of force and displacement using trapped ions. M. J. Biercuk . H. Uys . J. W. Britton . A. P. VanDevender . J. J. Bollinger . Nature Nanotechnology. 9 Apr 2010. 5. 9. 646–650. 10.1038/NNANO.2010.165. 20729835. 2010NatNa...5..646B. 119244588 . detection of forces as small as 174 yN.
  6. Fuchs . Tim M. . Uitenbroek . Dennis G. . Plugge . Jaimy . van Halteren . Noud . van Soest . Jean-Paul . Vinante . Andrea . Ulbricht . Hendrik . Oosterkamp . Tjerk H. . 2024-02-23 . Measuring gravity with milligram levitated masses . Science Advances . en . 10 . 8 . 10.1126/sciadv.adk2949 . 2375-2548 . 10889343 . 38394194.
  7. Web site: 2024-02-25 . Scientists measure gravity in Attonewton — up to one billionth of a billionth of a Newton . live . http://web.archive.org/web/20240906184119/https://www.wionews.com/science/scientists-measure-gravity-in-attonewton-up-to-one-billionth-of-a-billionth-of-a-newton-693577 . 2024-09-06 . 2024-09-06 . WION . en-us.
  8. Web site: Forces involved at the biological level. PicoTwist. 30 December 2011.
  9. Web site: E. coli Statistics . The CyberCell Database . 2011-09-11 . dead . https://web.archive.org/web/20111027220034/http://www.ccdb.ualberta.ca/CCDB/cgi-bin/STAT_NEW.cgi . 2011-10-27 .
  10. Calculated: weight = mass * g = 1e-15 kg * 9.81 m/s^2 = 1e-14 N
  11. Web site: Archived copy . 2009-01-09 . dead . https://web.archive.org/web/20120212124006/http://www.lisa-science.org/list/list_meetings/potsdam_2006/lpf-presentation.pdf . 2012-02-12 .
  12. Web site: NSTAR Ion Thruster. https://web.archive.org/web/20030111164356/http://www.grc.nasa.gov/WWW/ion/past/90s/nstar.htm. dead. 11 January 2003. NASA. 9 January 2012. thrust from 19 mN to 92 mN.
  13. Web site: How Much Does Your Smartphone Really Weigh?. 15 December 2016 .
  14. https://pubs.usgs.gov/fs/2006/3097/fs2006-3097.pdf
  15. Web site: Appendix B8—Factors for Units Listed Alphabetically. NIST Guide for the Use of the International System of Units (SI). 2 July 2009. NIST. 9 January 2012.
  16. Book: Damme, Klaus. Geflügeljahrbuch 2021. Eugen Ulmer KG. 2020. 978-3-8186-1186-6. Stuttgart, Germany. 262–281.
  17. Houston T E, Bite Force and Bite Pressure: Comparisons of Humans and Dogs, 2003 Web site: Archived copy . 2016-02-10 . dead . https://web.archive.org/web/20110124154459/http://www.glapbta.com/BFBP.pdf . 2011-01-24 .
  18. The Human Machine By R. McNeill Alexander, Mark Iley, Sally Alexander
  19. Erickson . G. M. . Lappin . A. K. . Vliet . K. A. . 10.1017/S0952836903003819 . The ontogeny of bite-force performance in American alligator (Alligator mississippiensis) . Journal of Zoology . 260 . 3 . 317 . 2003 . dead . https://web.archive.org/web/20110607102352/http://www.csupomona.edu/~aklappin/Alligator%20Bite%20Force%20Ontogeny.pdf . 2011-06-07 . 9452 N
  20. Web site: Crocodiles Have Strongest Bite Ever Measured, Hands-on Tests Show. 15 March 2012. The "winners"—saltwater crocodiles—slammed their jaws shut with 3,700 pounds per square inch (psi), or 16,460 newtons, of bite force..
  21. Web site: Great White Tops List of Hardest-Biting Sharks. Discovery News. Discovery Channel. 21 January 2012. a bite force of 9,320 Newton at the tip of its jaws and 18,216 N at the back of its jaws.
  22. Calculated from maximum acceleration of 1.22 g and kerb mass of 2050kg (4,520lb).
  23. Insights into the Ecology and Evolutionary Success of Crocodilians Revealed through Bite-Force and Tooth-Pressure Experimentation. 2012. 10.1371/journal.pone.0031781. scientifically documented 6.7-meter long Crocodylus porosus individuals were likely capable of molariform bite forces of approximately 27,531 N to 34,424 N (6,187 to 7,736 lbs).. free. Erickson. Gregory M.. Gignac. Paul M.. Steppan. Scott J.. Lappin. A. Kristopher. Vliet. Kent A.. Brueggen. John D.. Inouye. Brian D.. Kledzik. David. Webb. Grahame J. W.. PLOS ONE. 7. 3. e31781. 22431965. 3303775. 2012PLoSO...731781E.
  24. Lawrence Weinstein and John A. Adams, Guesstimation, 2008, Section 6.3.1
  25. Web site: Space Shuttle Main Engine. Pratt & Whitney Rocketdyne. 20 April 2013. 109% power level at sea level: 418,000 lb. https://web.archive.org/web/20121114175951/http://www.pratt-whitney.com/Space_Shuttle_Main_Engine. 14 November 2012. dead.
  26. Web site: SSME. https://web.archive.org/web/20020626223311/http://www.astronautix.com/engines/ssme.htm. dead. June 26, 2002. Mark. Wade. Encyclopedia Astronautica. 27 October 2011. Launches normally used 104% ... as a maximum.
  27. Calculated: 418000 lbf * 4.45 N/lbf * (104% launch power level / 109%) = 1.77e6 N.
  28. Web site: What Was the Saturn V?. NASA. 21 January 2012. The rocket generated 34.5 million newtons ... of thrust at launch. https://web.archive.org/web/20101110155517/http://www.nasa.gov/audience/foreducators/rocketry/home/what-was-the-saturn-v-58.html. 10 November 2010.
  29. 1.63 x 10−14 x gravitational attraction between Earth and Sun, assuming total absorption of sunlight Sunlight Exerts Pressure, NASA Glenn LTP Math & Science Resources
  30. Web site: The Earth-Moon Equations . 2009-01-09 . dead . https://web.archive.org/web/20120217010943/http://www.ridgecrest.ca.us/~do_while/sage/v5i5d.htm . 2012-02-17 .
  31. http://imagine.gsfc.nasa.gov/docs/ask_astro/answers/961029b.html NASA.gov
  32. Calculated from known masses (both kg) at a distance of 2.5 Mly.

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