Open any rolling-bearing catalog and you will find, next to each part, a number called the dynamic load rating, C. It is tempting to read it as "the load this bearing can carry." It is not. C is a reference figure tied to a specific, statistical definition of life — and once you understand that definition, the catalog stops being a mystery and becomes a design tool. Bearing life is fundamentally a fatigue and probability calculation, not a static strength check.
This article explains what L10 life means, works the calculation from load rating to service hours, and connects it to the contact stress that ultimately sets the limit.
Why this calculation matters
A bearing rarely fails because it is overloaded in one moment. It fails because rolling contact, repeated millions of times, drives subsurface fatigue cracks until a piece of the raceway spalls. Because fatigue is inherently scattered, two identical bearings under identical loads will not fail at the same time. There is no single "the bearing lasts X hours."
So bearing life is quoted as a statistic. L10 life is the life that 90 % of a population of bearings will reach or exceed before the first sign of fatigue — equivalently, the life at which 10 % are expected to have failed. Designing to L10 is designing with a defined, 90 % reliability. Treat C as a maximum allowable load and you have no idea what reliability you are buying.
The core formula
The basic rating life, in millions of revolutions, comes from the load rating and the actual load:
L10 = (C / P) ^ p
- C is the dynamic load rating from the catalog — by definition, the load that gives an L10 of one million revolutions.
- P is the equivalent dynamic load actually seen by the bearing.
- p is the life exponent: 3 for ball bearings, 10/3 for roller bearings.
Two consequences are worth absorbing. First, the exponent makes life ferociously sensitive to load. For a ball bearing, cutting the load in half multiplies life by 2^3 = eight. Doubling the load divides life by eight. Load is by far the strongest lever you have.
Second, P is rarely just the radial force. A bearing carrying both radial load Fr and axial load Fa uses an equivalent dynamic load:
P = X * Fr + Y * Fa
where the factors X and Y come from the bearing type and the load ratio. Skipping this and using the raw radial force underestimates P and overestimates life.
To convert revolutions into something a customer understands — hours of service at a rotational speed n in rpm:
L10h = L10 * 1e6 / (60 * n)
A worked example
A deep-groove ball bearing has a catalog dynamic load rating C = 30 kN. In service the equivalent dynamic load works out to P = 3.0 kN, and the shaft turns at n = 1500 rpm.
Step 1 — basic rating life in revolutions. Ball bearing, so p = 3:
L10 = (C / P)^3 = (30 / 3.0)^3 = 10^3 = 1000 million revolutions
Step 2 — convert to hours.
L10h = 1000e6 / (60 x 1500) = 1000e6 / 90000 = 11,100 hours
So 90 % of these bearings should run past about 11,100 hours before fatigue spalling — roughly 16 months of continuous duty. If that is not enough, the formula tells you exactly what to do: a 26 % increase in C, or a 21 % reduction in P, doubles the life. Because of the cube, small load reductions buy disproportionate life.
The basic L10 is the starting point. A modified rating life multiplies it by factors for reliability other than 90 %, and for lubrication and contamination — the ISO 281 modified life. Clean lubrication and a thick oil film can extend life severalfold; contamination can slash it. The catalog number assumes good conditions.
Common mistakes
Reading C as a load limit. C is a statistical reference, not a capacity. Running a bearing near C gives an L10 of only one million revolutions — minutes of life at speed. Real designs operate well below C.
Using radial load when there is an axial component. Most bearings see combined loading. The equivalent dynamic load P, with its X and Y factors, is the value the life formula needs.
Ignoring lubrication and contamination. The basic L10 assumes adequate lubrication and clean operation. A starved or dirty bearing can fall far short. Use the modified life when conditions are not ideal.
Forgetting the speed. L10 in revolutions says nothing about calendar time until you divide by speed. The same bearing and load give very different service hours at 300 rpm versus 3000 rpm.
Try the interactive NovaSolver calculator
The cube-law sensitivity is something you really feel by moving the inputs. The bearing life calculator on NovaSolver takes the load rating, equivalent load, bearing type, and speed, and returns L10 in revolutions and hours — so you can watch a small load change swing the life dramatically.
Related calculators
- Rolling bearing analysis — for equivalent load, speed limits, and bearing selection.
- Rolling contact fatigue — the fatigue mechanism that L10 statistics actually describe.
- Ball-bearing Hertz stress — the contact pressure on the raceway that drives the whole process.
The full set is in the mechanical engineering tools hub.
Closing note
The L10 number is more honest than it first looks. It admits openly that fatigue is statistical and tells you the life at a stated 90 % reliability rather than pretending failure is a single fixed event. Underneath it sits Hertzian contact stress and subsurface fatigue — the same physics that governs gears and cams. Respect the cube-law sensitivity to load, compute the equivalent load properly, account for lubrication and speed, and the catalog's C value turns into a service life you can actually design around.
