Why is $s$ used for arc length? I looked around online, but I can't find a definite answer.

Thank you!

  • 2
    $\begingroup$ I've always assumed $s$ to stand for "segment" (as in "line segment"). That said, I don't have any sources to back up my case. $\endgroup$ Feb 2, 2016 at 21:40
  • 8
    $\begingroup$ @Omnomnomnom I looked up displacement and it's spatium in latin if that helps. It was just a thought. $\endgroup$
    – Karl
    Feb 2, 2016 at 21:41
  • 3
    $\begingroup$ Surprisingly, there's no answer in Cajori's History of Mathematical Notations. $\endgroup$
    – Chappers
    Feb 2, 2016 at 21:42
  • 7
    $\begingroup$ Because using $d$ for displacement would just look stupid.$$\int dd$$ $\endgroup$
    – John Joy
    Feb 2, 2016 at 23:40
  • 2
    $\begingroup$ I bet it comes from German Strecke or Latin spatium meaning distance. $\endgroup$ Feb 3, 2016 at 8:44

1 Answer 1


I strongly agree with Karl's and Björn's comments regarding the Latin orgin: spatium.

See: Leonhard Euler, Mechanica sive motus scientia analytice exposita, Tomus I, Petropoli, 1736 :

Propositio 4 [ page 13 ] Sit spatium $AM$, sive sit linea recta sive curva, $=s$, et celeritas, quam corpus habet in M sit $c$, quae erit functio quaedam ipsius $s$. Ab $M$ accipiatur elementum $Mm$, quod igitur motu aequabili idque celeritate $c$ percurri concipiendum est. Vocato elemento $Mm$, $ds$; erit tempus quo hoc elementum pe[r]curritur $=\frac{ds}{c}$. Integrando ergo habebitur tempus, quo totus arcus $AM$ absolvitur $=\int\frac{ds}{c}$.

  • $\begingroup$ This, along with its relation to other languages, makes me feel like this is the correct answer! Thanks! $\endgroup$
    – Nisala
    Feb 12, 2016 at 21:11

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.