hardenability
Here is a distinction that trips up almost every beginner. Hardness is how hard the steel gets at the surface. Hardenability is how DEEP the hardness reaches into a thick part. They sound alike but are different properties: a steel can reach very high surface hardness yet have poor hardenability, so its core stays soft. Hardenability answers the question: if I quench a fat bar, how far in does it actually harden?
When you quench a bar, the surface cools almost instantly but the center cools slowly, because heat has to crawl out through the metal. If the steel transforms to hard martensite only when cooling is very fast, then only the skin (which cooled fast) hardens, and the slow-cooling core turns to soft pearlite instead. High hardenability means the steel forms martensite even at the slower cooling rates found deeper in, so it hardens all the way through. What buys hardenability is not more carbon (carbon sets the maximum hardness) but alloying elements (chromium, molybdenum, nickel, manganese, boron) which slow the competing soft transformations so martensite forms even on a lazy quench.
Hardenability is central to real design because most parts are not razor-thin. A cheap plain-carbon steel might harden only a couple of millimeters deep, leaving a soft interior; a low-alloy steel like 4140 hardens through much thicker sections, which is why gears, shafts, and bolts are made from alloy steels. It also lets you quench more gently (oil instead of water), reducing cracking and distortion. Hardenability is measured, not guessed, using the Jominy end-quench test.
Two bars quenched identically: a plain 1040 steel hardens perhaps 3 to 5 mm deep and stays soft inside, while a 4140 (chromium-molybdenum) bar of the same size hardens right through. Same maximum hardness (set by about 0.4 percent carbon), very different depth (set by the alloy).
Carbon sets HOW hard; alloying sets HOW DEEP. That is the whole idea of hardenability.
The classic trap: adding carbon raises maximum hardness but does relatively little for hardenability, depth of hardening comes mostly from alloying elements. Hardness and hardenability are not the same measurement.