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
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    $\begingroup$ @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
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    $\begingroup$ Surprisingly, there's no answer in Cajori's History of Mathematical Notations. $\endgroup$
    – Chappers
    Feb 2, 2016 at 21:42
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    $\begingroup$ Because using $d$ for displacement would just look stupid.$$\int dd$$ $\endgroup$
    – John Joy
    Feb 2, 2016 at 23:40
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    $\begingroup$ 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

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