1. A bearing does not break — it wears out statistically

Almost every other component in this collection has a strength you check against: a stress, a limit, a safety factor. A rolling bearing does not work that way. Under a load it can perfectly well carry, it will still eventually fail by rolling contact fatigue — and two identical bearings, in identical machines, will fail at wildly different times.

So the rating is not "will it hold" but "how long". L₁₀ is the life that 90 % of a population reaches: one in ten will have spalled before it, and the median life is roughly five times longer.

• C — the basic dynamic load rating, off the catalogue page. It is defined as the load that gives exactly one million revolutions of L₁₀ life, so the equation is really just a scaling from that definition.
• P — the equivalent dynamic load, which is chapter 3.
• p — 3 for ball bearings, 10/3 for roller bearings.

Why the exponent differs

A ball touches its race at a point, a roller along a line. The line spreads the same force over more material, so the stress rises more slowly with load — which comes out as the gentler exponent. It is the same reason a roller bearing of the same size carries more.