Bearing Life (L10)
Compute rated bearing life L10 (10⁶ rev) and L10h (hours). Optional reliability a₁ and ISO 281 combined factor a_iso give modified life Lnm.
Inputs
Formula
L10 = (C/P)^p; L10h = 10⁶/(60n)·L10; Lnm = a1·aiso·L10h (p=3 ball / 10/3 roller)
Use p=3 for ball bearings, p=10/3 for roller bearings.
Fundamentals
Bearing life is the total revolutions (or hours) a group of identical bearings runs before 90% show fatigue spalling.
Rated life $L_{10}=(C/P)^p$ (ball $p=3$, roller $p=10/3$), $C$ basic dynamic load rating, $P$ equivalent dynamic load. At speed $n$, $L_h=10^6 L_{10}/(60n)$ hours.
History
The fatigue-statistical bearing-life theory was built by Lundberg and Palmgren (1947-1950), giving the Weibull-based L10 rating life.
Engineering applications
Used to select motor, fan, machine-tool spindle and wheel-hub bearings and to plan reliability-based maintenance.
Glossary
| Dynamic rating $C$ | Load giving a basic rating life of $10^6$ revolutions. |
| Equivalent load $P$ | Radial + axial loads reduced to an equivalent radial load. |
| $L_{10}$ life | Basic rating life at 90% reliability (million revolutions). |
How to use
- Fill in Basic dynamic load C, Equivalent load P, Speed n, Life exponent p, Reliability a₁, ISO factor a_iso in the Inputs section (watch the unit on each field).
- Click Calculate; the tool evaluates the formula shown above.
- Read Basic life L10, Life L10h, Modified life Lnm in the results area.
Formula notesRated life L10 = (C/P)^p · 10⁶ rev; ball p=3, roller p=10/3. C = dynamic load rating, P = equivalent load.
Formula · Worked Example · Knowledge
Formula
Rated life $L_{10}$ is the total revolutions (or hours at a given speed) before 90% of a batch of identical bearings suffer fatigue spalling:
$$L_{10}=\left(\frac{C}{P}\right)^{p}\cdot 10^{6}\ \text{rev}$$
$C$ = dynamic load rating (N), $P$ = equivalent dynamic load (N); ball bearing $p=3$, roller bearing $p=10/3$. In hours:
$$L_{10h}=\frac{10^{6}}{60\,n}\left(\frac{C}{P}\right)^{p}\ (\text{h})$$
ISO 281 adds reliability factor $a_1$ and condition factor $a_{ISO}$ for lubrication/contamination.
$$L_{10}=\left(\frac{C}{P}\right)^{p}\cdot 10^{6}\ \text{rev}$$
$C$ = dynamic load rating (N), $P$ = equivalent dynamic load (N); ball bearing $p=3$, roller bearing $p=10/3$. In hours:
$$L_{10h}=\frac{10^{6}}{60\,n}\left(\frac{C}{P}\right)^{p}\ (\text{h})$$
ISO 281 adds reliability factor $a_1$ and condition factor $a_{ISO}$ for lubrication/contamination.
Worked Example
Deep-groove ball bearing 6206, radial load $P=2000\ \text{N}$, speed $n=800\ \text{r/min}$, dynamic rating $C=19500\ \text{N}$ ($p=3$). Find rated life in hours.
Step 1 — life in revolutions:
$$L_{10}=\left(\frac{19500}{2000}\right)^{3}\cdot10^{6}\approx 9.27\times10^{8}$$
Step 2 — life in hours:
$$L_{10h}=\frac{9.27\times10^{8}}{60\times800}\approx 19270\ \text{h}$$
Step 1 — life in revolutions:
$$L_{10}=\left(\frac{19500}{2000}\right)^{3}\cdot10^{6}\approx 9.27\times10^{8}$$
Step 2 — life in hours:
$$L_{10h}=\frac{9.27\times10^{8}}{60\times800}\approx 19270\ \text{h}$$
Key Points
- $L_{10}$ is the 90%-reliability rated life; multiply by $a_1$ for higher reliability (e.g. 0.62 at 95%).
- Equivalent load $P$ lumps axial and radial loads into an effective radial load per the duty.
- Good lubrication / clean conditions give $a_{ISO}>1$; severe contamination can drop it to 0.1.
Parameters
Inputs
| Parameter | Symbol | Unit | Default |
|---|---|---|---|
| Basic dynamic load C (kN) | C | kN | 50 |
| Equivalent load P (kN) | W | kN | 10 |
| Speed n (rpm) | n | rpm | 1500 |
| Life exponent p | p | 3 | |
| Reliability a₁ | a1 | 1 | |
| ISO factor a_iso | aiso | 1 |
Outputs
| Result | Symbol | Unit |
|---|---|---|
| Basic life L10 | L10 | ×10⁶ r |
| Life L10h | L10h | h |
| Modified life Lnm | Lnm | h |
Applications
- Common engineering use cases
FAQ
What formula does this tool use?
This tool computes per ISO / AGMA / ASME standard formulas: L10 = (C/P)^p; L10h = 10⁶/(60n)·L10; Lnm = a1·aiso·L10h (p=3 ball / 10/3 roller)
How accurate are the results?
Results match input precision, based on SI units and common engineering approximations; for critical duty re-check with a safety factor.
Where is it used?
Common engineering use cases