soldier, warrior (mostly used in the plural קלגסים). [Latin caliga (= heavy military shoe), whence figurative 'military service'. Related to calx (=heel), calcar (=spur), calceus (=shoe).]
Klein, as well as most sources I checked, doesn't connect calx as "heel" to the Latin calx meaning "lime, pebble", which is the source of such words as calcium and calculation. However, this site suggests that perhaps
The Latin word for heel is calx, calcis. Here we must take another short digression, because the Latin word for lime is also calx. The Century tells us that the underlying Latin means "small stone," and perhaps that is the connection between "lime" and the "heel." Lime, or chalk, begins as a small stone that is eroded while the heel bone can appear, to the eye, as if stone-shaped. The Latin word for shoe is calceus, or something that goes over the heel.In any case, caliga - the Roman sandals, secured with nails (which made quite a bit of noise) - were apparently frightening enough to give their name to the Roman soldiers in general (pictures here). For example, the Mishna (Sota 8:1) interprets part of the verse of Devarim 20:3 - "Let not your heart faint; fear not, nor be alarmed" - as saying not to fear the noise of the (enemy) troops - שפעת הקלגסין. The notorious Roman emperor Caligula also got his name from those shoes - his name mean "little (soldier's) boot", because as a child he accompanied his father, a general, in military campaigns.
You may have noticed that we don't have many words from the Talmudic period that derive from Latin; far more come from Greek. On the face of it, that seems strange: at the time of the Mishna and later, the Romans were in control of the Land of Israel, not the Greeks. However, Hellenistic culture continued to have significant impact even in the Roman empire, and Greek remained the literary language and lingua franca in the region. The Romans did not enforce their language on conquered areas, so it should not be such a surprise that Latin did not enter Talmudic Hebrew. In fact, a large portion of the words that did enter Hebrew, are related to the military - such as gardom גרדום - "gallows", ligyon לגיון - "legion", pigyon פגיון - "dagger", and of course, kalgas.