Skill 8 of 11
In Progress

The Newton unit

To talk about ‘how much force’ there is, we of course need a unit for force. Should that be a fundamental unit?

Nope. Force is not a fundamental property because it can be created from mass and acceleration via Newton’s 2nd law. We can thus also derive its unit directly from that.

Newton’s 2nd law, $\sum \vec F=m\vec a$, tells us that some force is some ‘mass times acceleration’, so ‘some grams times some metres-per-second-per-second’. If we stick to the usual SI base unit for mass, $\mathrm{kg}$ instead of the $\mathrm g$,1 then it is ‘some kilograms times some metres-per-second-per-second’:2

$$\mathrm{[kg]\cdot \left[\frac{m}{s^2}\right]}= \underbrace{\mathrm{ \left[ kg\cdot \frac{m}{s^2}\right]}}_\mathrm{[N]}$$

In honour of the discoverer, let’s give this chunk of units its own name: the Newton, symbolised $\mathrm N$:3

$$\mathrm{[N]}= \mathrm{ \left[ kg\cdot \frac{m}{s^2}\right]} $$

Now we can say that ‘it takes 1 Newton to hold up an apple’, or ‘he hit me with 2500 Newton’ and write it as $F=1\,\mathrm N$ and $F=2500\,\mathrm N$.

For a feeling of the Newton unit, here is an overview of the force magnitude scale:

Force scale
MeganewtonLifting a blue whale[6]
KilonewtonAlligator bite-force7
NewtonLifting an apple
MillinewtonA touch6
MicronewtonLifting an eyelash5
NanonewtonBreaking a chemical bond4


  1. Sears and Zemansky’s Univesity Physics with Modern Physics’ (book), Hugh D. Young & Roger A. Freedman, Pearson Education, 13th ed., 2012
  2. How Strong Is a Covalent Bond?’ (article), Michel Grandbois, Martin Beyer and others, Science, vol. 283, issue 5408, 1999,, DOI 10.1126/science.283.5408.1727, page 1727
  3. How to Weigh an Eyelash’ (web page), Elliot Williams, Hackaday, 2015, (accessed Sep. 27th, 2019)
  4. Tactile Sensitivity and Capability of Soft-Solid Texture Discrimination’ (article), Tugba Aktar, Jianshe Chen and others, Journal of Texture Studies, vol. 46, issue 6, 2015,, DOI 10.1111/jtxs.12142
  5. The ontogeny of bite-force performance in American alligator (Alligator mississippiensis)’ (article), Gregory M. Erickson, A. Kristopher Lappin and others, Journal of Zoology, vol. 260, issue 3, 2003,, DOI 10.1017/S0952836903003819
  6. Blue Whale’ (web page), National Geographic, 2018, (accessed Aug. 31st, 2019)