Engineering CalculatorsBearing Life & Selection: How ISO 281 Rates a Rolling Bearing
A plain-language guide to rolling-bearing selection to ISO 281: where the L10 = (C/P)^p rating-life formula comes from, the equivalent load P = X·Fr + Y·Fa, the static safety check, and how speed and lubrication set the limits.
What a bearing rating actually promises
A rolling bearing doesn't have a single "load it can take". Roll the same load through it long enough and the races eventually fail by rolling-contact fatigue — tiny cracks under the surface that spall into a pit. The question is never "will it hold?" but "how long will it last?" — and because fatigue is statistical, even that has to be a probability. ISO 281 is the standard that turns a load and a speed into a life, and it's the number stamped implicitly into every bearing catalogue's dynamic load rating C.
L10 and the C/P law
The headline result is the basic rating life, written L10: the number of revolutions (in millions) that 90% of a large batch of identical bearings will reach before the first sign of fatigue. The 10 means 10% are allowed to have failed by then — it is a design target, not a guarantee for any single bearing. It comes from a simple power law:
L₁₀ = (C / P)ᵖ
C is the bearing's dynamic load rating (the load that would give exactly one million revolutions of L10 life — a catalogue number), P is the actual equivalent load the bearing sees, and the exponent p is 3 for ball bearingsand 10/3 for roller bearings. That exponent is why bearing life is so sensitive to load: halving the load on a ball bearing multiplies life by 2³ = 8. To get hours from revolutions you just divide by the speed: L₁₀ₕ = 10⁶·L₁₀ / (60·n), with n in rpm.
Equivalent load: P = X·Fr + Y·Fa
Real bearings rarely see pure radial load. A bearing carrying both a radial force Fr and an axial (thrust) force Fa is rated on an equivalent dynamic load — the pure radial load that would do the same fatigue damage:
P = X·Fr + Y·Fa
The factors X and Y depend on the bearing type and on how much thrust it's carrying relative to its capacity. Below a threshold ratio e, a small amount of thrust is essentially free (X = 1, Y = 0, so P = Fr); above it, the thrust starts to count and X drops while Y rises. A deep-groove ball bearing's e and Y even slide with the ratio f₀·Fa/C₀; an angular-contact bearing's factors depend on its contact angle. Bearing types that can't react thrust at all (plain cylindrical and needle rollers) simply take P = Fr and need a separate locating bearing for the axial load.
The other check: static safety
Fatigue life is about motion. A bearing also has to survive standing still under a peak or shock load without the rolling elements brinelling (denting) the races. That's a separate check against the static load rating C₀: the static safety factor s₀ = C₀ / P₀, where P₀ is the equivalent static load. Typical targets are around 1–2 for smooth running, higher for shock; roller bearings (line contact) are held to a higher target than ball bearings (point contact). A bearing can easily pass its life target and still fail this one under a rare peak.
Speed and lubrication set the real ceiling
L10 assumes the bearing is properly lubricated. In practice the speed is what caps a selection: every catalogue lists a limiting speed, and the speed factor n·dm(speed × mean diameter) has to sit inside the band the chosen lubrication method allows — grease for low-to-moderate, oil for higher, with cooling for the extreme end. Housing temperature limits the grease and the seals, and a shaft running much hotter than the housing eats into the bearing's internal clearance through differential expansion — enough to preload and cook a bearing that passes every load check on paper. These are the limits that usually decide the design, not the fatigue sum.