Bearing Life Calculator (L10).
Calculate basic rating life L10 in millions of revolutions and L10h in operating hours per ISO 281. Handles combined radial and axial load, ball and roller exponents, and reliability adjustment above 90%.
Bearing
Duty
L₁₀ = (C / P)p million revolutions
L₁₀ₕ = L₁₀ × 10⁶ / (60 · n) hours
p = 3 (ball) p = 10/3 (roller)
What L10 Bearing Life Actually Means
L10 is the life that 90% of a large group of identical bearings will reach or exceed under a given load before the first sign of rolling-contact fatigue. It is a statistical figure, not a guarantee. One bearing in ten is expected to fail before L10 — that is the definition, not a caveat.
Two consequences follow, and both matter on the shop floor. First, an individual bearing failing early is not necessarily a defect claim. Second, the average life is roughly five times L10, which is why bearings routinely outlast their calculated life by a wide margin and engineers stop trusting the number. Both behaviours are what the statistics predict.
The Life Equation
L₁₀ = (C / P)p million revolutions
L₁₀ₕ = L₁₀ × 10⁶ / (60 × n) hours
C is the basic dynamic load rating from the catalogue — the load that gives exactly one million revolutions of L10 life. P is the equivalent dynamic load your application actually applies. The exponent p is 3 for ball bearings and 10/3 for roller bearings.
That exponent is the most important number on this page. Life varies with the cube of the load ratio, so:
- Cut the load by 20% → life rises 95% (1/0.8³).
- A load 25% above design → life falls to 51%.
- Double the load → life falls to one eighth.
This is why belt over-tensioning destroys bearings so reliably. A 30% excess in belt tension does not cost 30% of bearing life — it costs more than half of it.
Equivalent Dynamic Load P
When a bearing carries both radial and axial load, the two are combined into a single equivalent radial load:
If Fa/Fr ≤ e: P = Fr
If Fa/Fr > e: P = X·Fr + Y·Fa
Below the limiting ratio e the axial load is carried within the existing contact geometry and adds nothing. Above it, the contact angle shifts and the axial component starts to dominate. Typical values:
| Bearing type | p | e | X | Y |
|---|---|---|---|---|
| Deep groove ball | 3 | ≈0.30 | 0.56 | ≈1.5 |
| Angular contact ball 40° | 3 | 1.14 | 0.35 | 0.57 |
| Self-aligning ball | 3 | ≈0.35 | 0.65 | ≈3.5 |
| Cylindrical roller | 10/3 | — | 1.0 | 0 (no axial) |
| Tapered roller | 10/3 | ≈0.35 | 0.40 | ≈1.6 |
| Spherical roller | 10/3 | ≈0.30 | 0.67 | ≈3.5 |
For deep groove bearings e and Y vary with the ratio Fa/C₀ — the values above are representative mid-range figures. For a final design always take X, Y and e from the specific bearing's catalogue page.
Reliability Above 90%
If one failure in ten is unacceptable — a gearbox in a continuous plant, a machine tool spindle — multiply L10 by the reliability factor a₁:
| Reliability | Designation | Factor a₁ |
|---|---|---|
| 90% | L10 | 1.00 |
| 95% | L5 | 0.64 |
| 96% | L4 | 0.55 |
| 97% | L3 | 0.47 |
| 98% | L2 | 0.37 |
| 99% | L1 | 0.25 |
Going from 90% to 99% reliability costs three quarters of the calculated life. In practice you buy that back with a larger bearing, not by accepting the shorter figure.
Typical Design Life Targets
| Application | L10h target (hours) |
|---|---|
| Household appliances, hand tools | 1,500 – 4,000 |
| Intermittent industrial machinery | 4,000 – 8,000 |
| Machines for 8-hour single-shift duty | 12,000 – 20,000 |
| Continuous 24-hour plant machinery | 40,000 – 60,000 |
| Water works, large fans, paper mills | 60,000 – 100,000 |
Static Safety Factor
Rating life covers fatigue under rotation. A bearing that is stationary, oscillating, or shock-loaded is limited instead by permanent indentation of the raceway, controlled by the static rating C₀:
s₀ = C₀ / P₀
Target s₀ ≥ 1.0 for smooth-running applications, ≥ 1.5 for normal duty, and ≥ 2.0 to 4.0 where shock loads or high running accuracy are involved. A bearing can pass the L10 check comfortably and still brinell on the first shock load if s₀ was never checked.
Why Real Bearings Miss Their Calculated Life
The equation assumes clean lubrication, correct fits, correct alignment and pure fatigue as the failure mode. In practice most failures are none of those:
- Contamination — the largest single cause. Dirt indents raceways and starts fatigue at those points.
- Inadequate lubrication — too little, wrong viscosity for the speed, or degraded by heat.
- Misalignment — concentrates load on part of the raceway; a fraction of a degree matters.
- Wrong shaft and housing fits — a loose inner ring creeps and fretting-corrodes the shaft. Use an ISO 286 fit, typically k5/m5 for the rotating ring.
- Mounting damage — pressing through the balls rather than on the ring being fitted brinells the raceway before the machine ever runs.
ISO 281 addresses these through the aISO modified life factor, which accounts for lubrication film ratio and contamination level and can swing the answer by an order of magnitude in either direction. Treat the L10 figure here as the clean baseline and derate it for real conditions.
Worked Example
A 6208 deep groove ball bearing (C = 32.5 kN, C₀ = 19.0 kN) carries 4.5 kN radial and 1.2 kN axial at 1450 rpm.
- Fa/Fr = 1.2/4.5 = 0.267, below e ≈ 0.30 → P = Fr = 4.5 kN
- C/P = 32.5/4.5 = 7.22
- L10 = 7.22³ = 377 million revolutions
- L10h = 377 × 10⁶ / (60 × 1450) = ≈ 4,330 hours
- Static safety s₀ = 19.0/4.5 = 4.2 (ample)
4,330 hours suits intermittent duty but falls well short of a 20,000 hour single-shift target — this application needs the next size up, or the load reduced.
Related Tools
For the shaft and housing fits that keep the bearing seated, use the ISO 286 Fits Calculator. For belt tension driving the radial load, see V-Belt Drive. For gear separating forces see Gear Calculator, and for mounting interference see Press Fit.