Bearing Life (L10)

Calculate rolling bearing rated service life using speed factor, life factor, and basic dynamic load rating. Supports ISO 281 modified life calculation.

Inputs

C

Dynamic Load Rating

W

Applied Load

n

Rotational Speed

r/min

Correction Factors (optional, default 1.0)

a_1

Reliability Factor

90%→1.0 95%→0.62 99%→0.21

a_{ISO}

Combined Factor

Clean/good lube >1, contaminated <0.1

Formula Interpretation

① Speed Factor

f_n = \left(\dfrac{33.3}{n}\right)^{\!\!1/3}

Reference speed 33.3 r/min corresponds to the rated life baseline (1 million revolutions at 500 h). $n$ is the actual rotational speed (r/min).

② Life Factor

f_h = f_n \cdot \dfrac{C}{W}

$C$ is the basic dynamic load rating (N); $W$ is the applied load on the bearing (N). A higher ratio C/W extends bearing life significantly.

③ Rated Service Life

L_h = 500\,{f_h}^3 \quad \text{(h)}

The cubic exponent applies to ball bearings (for roller bearings the exponent is 10/3). Life scales as the cube of the life factor.

④ Modified Life (ISO 281)

L_{nm} = a_1 \cdot a_{ISO} \cdot L_{10}

$a_1$ is the reliability factor (1.0 for 90%, 0.62 for 95%, 0.21 for 99%); $a_{ISO}$ jointly accounts for lubrication viscosity ratio κ and contamination factor e_C. Well-lubricated, clean conditions push it above 1; contaminated or starved conditions can reduce it below 0.1.

Knowledge: Bearing Life

The rated life (L10) is the service life that 90% of an identical batch of bearings will reach or exceed before fatigue spalling. The ISO 281 modified formula extends this with two correction factors: $a_1$ adjusts for reliability level (higher reliability = lower $a_1$ ), and $a_{ISO}$ captures the combined effect of lubrication quality and contamination. Under clean, well-lubricated conditions $a_{ISO}$ can exceed 1 and extend calculated life; in contaminated or poorly-lubricated applications it can drop to 0.1, leaving the bearing with just 10% of the basic calculated life.

$a_1$ — Reliability Factor

可靠度	$a_1$
90 %	1.00
95 %	0.62
96 %	0.53
97 %	0.44
98 %	0.33
99 %	0.21

$a_{ISO}$ — Combined Factor

工况	$a_{ISO}$ 参考范围
清洁 + 良好润滑	> 1
一般工业润滑	0.5 – 1
中等污染	0.1 – 0.5
严重污染/润滑不足	< 0.1

Worked Example

A single-row deep-groove ball bearing (6206) carries a radial load of $2\,000\,\text{N}$ and rotates at $800\,\text{r/min}$ . The basic dynamic load rating is $19\,500\,\text{N}$ . Find the rated service life.

Step 1 — Compute speed factor $f_n$ (Formula ①)

f_n = \left(\dfrac{33.3}{800}\right)^{1/3} = 0.347

Step 2 — Compute life factor $f_h$ (Formula ②)

f_h = f_n \cdot \dfrac{C}{W} = 0.347 \times \dfrac{19\,500}{2\,000} = 3.38

Step 3 — Compute rated life $L_h$ (Formula ③)

L_h = 500 \times {f_h}^3 = 500 \times 3.38^3 \approx 19\,300 \text{ h}

Therefore, the rated service life is approximately $19\,300\,\text{h}$ .

Extended Knowledge

•The static load rating C₀ is the load at which the sum of plastic deformations at the most heavily loaded rolling element–raceway contact equals one ten-thousandth of the rolling element diameter.
•Bearing life is expressed as the total number of revolutions (or operating hours at a given speed) before the onset of fatigue spalling.
•For smooth operation without impact, a load factor of 1 to 1.5 is typically applied to the calculated load before entering the formula.
•The reliability factor $a_1$ maps the required failure probability to a multiplier: standard L10 uses 10% failure probability ( $a_1$ = 1.0); 5% failure (95% reliability) gives $a_1$ = 0.62; 1% failure (99% reliability) gives $a_1$ = 0.21. High-reliability applications such as aerospace, medical devices, and wind turbines typically require 99% or better.
•The combined factor $a_{ISO}$ is obtained from charts using the viscosity ratio κ = ν/ν₁ (actual kinematic viscosity to reference viscosity) and contamination factor $e_C$ . Skipping this factor and applying the old basic formula can overestimate bearing life by a factor of 5–10 in moderately contaminated environments.

Related Standards & Articles

Authoritative references for the formulas used in this calculator

Article

Bearing Life Beyond L10: A Practical Engineering Guide

A grounded guide to rolling bearing service life — what L10 actually means statistically, why rated life diverges from real-world performance, how to apply ISO 281 modified life factors, and the three calculation mistakes that silently wreck bearing selections.

可靠度

a_1

90 %

1.00

95 %

0.62

96 %

0.53

97 %

0.44

98 %

0.33

99 %

0.21

工况

a_{ISO}

参考范围

清洁 + 良好润滑

> 1

一般工业润滑

0.5 – 1

中等污染

0.1 – 0.5

严重污染/润滑不足

< 0.1