AtlasCalcsUtility Calculation Suite
August 2026 13 min read

Bearing Selection Calculator

Free bearing selection calculator. Enter radial/axial load, speed and required life to get the minimum dynamic rating C, static rating C₀ and recommended bearing family (deep groove, angular contact or roller).

Bearing Selection Calculator

Bearing Selection Inputs

Unit System
SI — N, rpm Imperial — lbf, rpm
Radial Load F_r (N)
N

Perpendicular-to-shaft force on the bearing

Axial Load F_a (N)
N

Thrust along the shaft axis (0 if none)

Speed n (rpm)
rpm

Shaft rotational speed

Desired Life L_h (hours)
hours

Required service life in hours

Bearing Type Basis

Sets the life exponent p and axial correction

Reliability

a₁ life multiplier

Application Factor f_s

Shock / severity

Static Safety s₀ (—)
—

C₀ / P₀ margin (1 smooth, 2–3 shock)

Auto-calculate instantly

Required Dynamic Rating C

67,148N

Minimum catalogue C for 20,000 h at 1,500 rpm and 90% reliability.

Thrust is high for a deep groove — consider angular contact
Required Static C₀

3,333N

Equivalent Load P

5,520N

Static Equiv. P₀

5,000N

F_a / F_r

0.24

Life Exponent p

3

Reliability a₁

1

L10 (revolutions)

1,800,000,000

Recommended Family

Deep

Required Static C₀

3,333N

For s₀ = 1.5

Equivalent Load P

5,520N

incl. f_s = 1.2

Static Equiv. P₀

5,000N

0.6·F_r + 0.5·F_a

F_a / F_r

0.24

Thrust significant

Life Exponent p

3

Ball

Reliability a₁

1

Life multiplier

L10 (revolutions)

1,800,000,000

1,800 million rev

Recommended Family

Deep

Deep groove ball (heavy series) or angular contact

Result Summary

Bearing TypeDeep Groove Ball (p=3)
Radial Load F_r5,000 N
Axial Load F_a1,200 N
Speed1,500 rpm
Desired Life20,000 h (90% rel.)
Equivalent Load P5,520 N
Required C67,148 N
Required C₀3,333 N
RecommendationDeep groove ball (heavy series) or angular contact
Estimated Result — Uses the ISO 281 rating-life equation rearranged for the required C, with standard p exponents (3 ball, 10/3 roller), reliability factor a₁ and a static safety factor s₀. The axial correction uses representative X/Y values for each family. Lubrication, contamination, temperature and mounting are not included — apply the catalogue life-modification factor a_ISO and verify against the chosen manufacturer's tables.

Interactive Diagram

The decision diagram shows your F_a/F_r ratio and the bearing family that best carries it — switch family if the thrust share is large.

Visualizations

Selection Loads & Required Ratings

5,000NF_r
1,200NF_a
5,520NP (used)
67,148NC required
3,333NC₀ required

Static Safety Achieved

C₀ / P₀67%

Formula

Starting from the ISO rating life L10 = (C/P)^p · 10⁶ revolutions, we solve for the rating C a bearing must have to survive the required life. Reliability is folded in through a₁ (life scales by a₁). The static side ensures the chosen bearing will not brinell under standstill or shock via the safety factor s₀ = C₀/P₀.

C = P · (L10 / 10⁶)^(1/p) | L10 = 60·n·L_h (revolutions)

Alternative Form

C₀ = P₀ / s₀ | P₀ = max(0.6·F_r + 0.5·F_a, F_r) | p = 3 (ball), 10/3 (roller)

Variables

SymbolNameUnitDescription
CRequired dynamic ratingNMinimum catalogue C to meet the life target
PEquivalent dynamic loadNX·F_r + Y·F_a (or F_r)
L10Required liferev60·n·L_h, in millions of revolutions
nSpeedrpmShaft rotational speed
L_hRequired lifehDesired service life in hours
pLife exponent—3 for balls, 10/3 for rollers
a₁Reliability factor—1.0 / 0.62 / 0.21 for 90/95/99%
C₀Required static ratingNP₀ / s₀
s₀Static safety factor—C₀ / P₀ margin against brinelling
f_sApplication factor—Shock / severity multiplier on P

Explanation

Bearing selection is the inverse of the life calculation: instead of asking "how long will this bearing last?", it asks "what rating must a bearing have to last this long?" Because life is a power law of load, the required rating grows gently with life but explosively with load. The reliability factor a₁ lets you trade size for dependability, while the static check guards the many bearings that spend most of their life stationary or crawling under shock.

Derivation

From Lundberg–Palmgren, L10 (revolutions) = (C/P)^p. Setting L10 = 60·n·L_h and solving for C gives C = P·(60·n·L_h / 10⁶)^(1/p). Introducing reliability: L10a = a₁·L10, so the required C scales by a₁^(-1/p). The static requirement C₀ ≥ P₀/s₀ comes directly from the definition s₀ = C₀/P₀ with P₀ the static equivalent load.

Step-by-Step Calculation

Follow each step to understand how the result is calculated from your inputs.

Step 1

Form the equivalent dynamic load from the load direction.

P = X·F_r + Y·F_a
F_r:5,000 N
F_a:1,200 N
Intermediate: F_a/F_r = 0.24 → thrust significant
Result: P = 4,600 N
Step 2

Apply the application (shock) factor.

P_used = f_s · P
f_s:1.2
P:4,600 N
Intermediate: P_used = 1.2 × 4,600
Result: P_used = 5,520 N
Step 3

Convert desired hours of life into revolutions.

L10 = 60 · n · L_h (rev) = 60·n·L_h / 10⁶ (Mrev)
n:1,500 rpm
L_h:20,000 h
Intermediate: L10 = 1,800,000,000 rev = 1,800 Mrev
Result: Life in revolutions established
Step 4

Apply the reliability factor a₁.

a₁ = 1.0 (90%), 0.62 (95%), 0.21 (99%)
Reliability:90%
Intermediate: a₁ = 1
Result: Life derated for reliability
Step 5

Solve the rating-life equation for the required dynamic rating.

C = P_used · (L10 / 10⁶)^(1/p) / a₁^(1/p)
p:3
L10(Mrev):1,800
Intermediate: C = 5,520 × (1,800)^(1/3) / 1^(1/3)
Result: C = 67,148 N
Step 6

Find the required static rating from the static safety factor.

C₀ = P₀ / s₀
P₀:5,000 N
s₀:1.5
Intermediate: P₀ = max(0.6·F_r + 0.5·F_a, F_r) = 5,000 N
Result: C₀ = 3,333 N — choose the larger of C and C₀ in the catalogue
Final Answer
67,148 N

Worked Examples

See how the calculator works with different scenarios.

Scenario

A lightly loaded fan shaft, smooth duty, 90% reliability.

Inputs

F_r:3000 N
F_a:200 N
n:1500 rpm
L_h:20000 h
Type:Deep groove
f_s:1.0

Calculation

F_a/F_r = 0.067 ≤ 0.22 → P = 3000 N; L10 = 60·1500·20000/1e6 = 1800 Mrev; C = 3000·1800^(1/3) = 3000·12.16 = 36,490 N

Result

Required C ≈ 36.5 kN, C₀ ≈ 2000/1.5 = 1333 N; pick a 6208/6308-class bearing

Interpretation

A very standard size meets the need with margin — typical of smooth electric-motor duty.

Understanding Your Result

Your Result: 67,148 N

Typical range: Industrial bearings span C from a few hundred N (instrument sizes) to several MN (massive rollers). Your required C of 67,148 N sits in the medium range — match it to the nearest catalogue size and round up.

What This Means

To meet 20,000 h at 1,500 rpm and 90% reliability, you need a bearing with dynamic rating C ≥ 67,148 N and static rating C₀ ≥ 3,333 N. The equivalent load driving this is 5,520 N.

Why It Matters

Picking the size is the make-or-break step in rotating-machine design. Under-size and you get premature, often catastrophic, failure; over-size and you waste money, space and weight. This calculator gives the quantitative floor — the minimum C and C₀ — so the catalogue choice is defensible rather than guesswork.

Professional Interpretation

Moderate thrust — consider an angular contact for efficiency. Choose the smallest standard bearing whose C and C₀ both exceed the required values, then confirm with a full L10 + a_ISO life check.

Dynamic vs static

Required C = 67,148 N (fatigue over the running life) versus required C₀ = 3,333 N (standstill/shock). Pick a bearing meeting both.

Reliability trade

At 90% reliability a₁ = 1; dropping to 90% would cut the required C by roughly 1.00×.

Family hint

Deep groove ball (heavy series) or angular contact

Recommendations

  • •Always round C up to the next real catalogue size — never down.
  • •Check BOTH C (fatigue) and C₀ (static); the larger requirement governs.
  • •Your thrust share is high for a deep groove ball — switch to angular contact or tapered roller to shrink the required size.
  • •If C comes out impractically large, reduce required life, relax reliability, or cut the shock factor before upsizing indefinitely.
  • •Apply the manufacturer life-modification factor a_ISO for your lubrication and contamination level.

Educational Content

Introduction

Selecting a bearing is where theory meets the shelf. Catalogues list dozens of sizes, each with a dynamic rating C and a static rating C₀. The bearing selection calculator bridges your machine's duty (load, speed, life) and that catalogue, returning the minimum numbers you must match — turning an overwhelming list into a short, rational shortlist.

Concept Explanation

The rating-life equation L10 = (C/P)^p · 10⁶ revolutions links the bearing's capacity C, the equivalent load P and the life exponent p (3 for balls, 10/3 for rollers). Selection inverts it: given the life you need (converted from hours via speed) and the load (collapsed from radial + axial via X/Y factors and a shock factor), solve for C. A parallel static check, C₀ ≥ P₀/s₀, stops the bearing from denting when it is barely turning. Reliability enters through a₁, letting you pay for extra dependability with a larger C.

Applications

▸First-pass sizing of motor, pump and gearbox bearings
▸Choosing between ball and roller families for a given load
▸Trading reliability against size and cost
▸Verifying a static-safety margin for start/stop machinery
▸Teaching the inverse of the L10 life calculation
▸Shortlisting catalogue sizes before a detailed life check

Benefits

  • •Returns the quantitative minimum C and C₀, not a guess
  • •Handles ball vs roller exponents automatically
  • •Folds in reliability and shock in one step
  • •Recommends a bearing family from the load direction
  • •SI / imperial consistent

Limitations

  • •Uses representative X/Y values, not exact catalogue tables
  • •Excludes lubrication, contamination and temperature (a_ISO)
  • •Single bearing only, not paired/duplex arrangements
  • •Does not list actual catalogue part numbers
  • •Assumes steady load and speed

Best Practices

  • •Convert all external forces into F_r and F_a with a free-body diagram first
  • •Pick the reliability (90/95/99%) that matches the consequences of failure
  • •Use the real application factor for shock and start/stop duty
  • •Round the required C up to the next standard size, then re-check life
  • •Confirm both C and C₀ are satisfied by the chosen bearing

Common Misconceptions

Myth: The biggest bearing is always safest.
Truth: Oversizing wastes cost and can hurt if the load is too small to properly distribute — selection is about meeting C and C₀ with margin, not maximising size.
Myth: Speed does not matter if hours are fixed.
Truth: Higher speed packs more revolutions into the same hours, raising the required C as a power of speed.
Myth: C alone is enough.
Truth: A bearing can pass the C check yet brinell under static/shock load if C₀ is too low.
Myth: 90% reliability means a 10% chance of early failure is fine.
Truth: L10 is a mean rating for a population; for a single safety-critical bearing, specify 99% (a₁ = 0.21) and add margin.

Practical Tips

  • •Required C ≈ 67,148 N. Round up to the nearest catalogue size and never down.
  • •If the required C looks enormous, ask whether 99% reliability or a 50,000 h life is really needed — both inflate C sharply.
  • •For combined loads with large thrust, angular contact or tapered roller bearings usually need a smaller C than a deep groove ball.
  • •Keep a static safety factor s₀ ≥ 1.5 for machinery that starts under load or sees shock.
  • •After picking a size, run a bearing life calculation with the actual C to confirm the adjusted life.

Common Mistakes

Mixing unit systems
Entering pounds where newtons are expected scales C and C₀ by 4.45 — set the unit system first.
Forgetting the application factor
f_s = 1.0 for shock-loaded plant under-sizes C; use 1.5–3.0 for gears, crushers and vibrators.
Selecting on C and ignoring C₀
A stationary or shock-loaded bearing can brinell even when C is ample; always check C₀ = P₀/s₀.
Rounding C down
Always round up to the next real size; running above rating accelerates fatigue dramatically.
Wrong reliability assumption
Assuming 90% for a safety-critical part under-sizes C by ~2× versus 99%; choose reliability to match consequences.

Assumptions

This calculator makes the following assumptions to provide estimates:

ISO 281 rating life: Basic L10 life with p = 3 (ball) or 10/3 (roller) is assumed.
Representative X/Y: Approximate axial-correction factors are used for each family rather than exact catalogue tables.
Steady duty: Constant load and speed; variable duty needs equivalent-load / duty-cycle methods.
a_ISO = 1: Lubrication, contamination and temperature life modification is not applied.

Limitations

Be aware of these limitations when using this calculator:

No catalogue numbers: Outputs the required ratings; the actual part number comes from the manufacturer catalogue.
Single row: Paired/duplex/back-to-back arrangements are not modelled.
Static only via s₀: Edge loading, misalignment and moment loads are outside this check.
No a_ISO: Real life may differ with lubrication cleanliness and contamination.

Frequently Asked Questions

Answers to common questions about this calculator.

What does a bearing selection calculator do?
It works backwards from your duty: the radial and axial loads, shaft speed and required service life. It returns the minimum dynamic load rating C and static rating C₀ a catalogue bearing must have, and suggests a bearing family that suits the load direction.
What is the dynamic load rating C?
C is the constant load a bearing can carry for a rated life of one million revolutions (L10, 90% reliability). It is the single number you match against in a manufacturer catalogue to pick a size.
What is the static load rating C₀?
C₀ is the load that produces a total permanent deformation of about 0.0001 of the rolling-element diameter at the contact. It bounds the load a stationary or very slowly rotating bearing can take without brinelling.
How is required C calculated?
From the ISO life equation rearranged: C = P · (L10 / 10⁶)^(1/p), where L10 is the required life in revolutions, P the equivalent dynamic load and p = 3 for ball bearings or 10/3 for roller bearings. Speed and life in hours feed L10 = 60·n·L_h.
What is equivalent dynamic load P?
P collapses the real combined radial and axial loads into one constant radial load giving the same fatigue life: P = X·F_r + Y·F_a when F_a/F_r exceeds the limit e, otherwise P = F_r.
Why does ball life use p = 3 but roller p = 10/3?
The exponent comes from the contact stress-life relationship. Ball bearings have point contact (stress ∝ load^(1/3)), rollers line contact (stress ∝ load^(1/10/3)), so roller life is less sensitive to overload — a 25% overload halves a ball bearing's life but only shortens a roller by ~45%.
What reliability factor a₁ should I use?
a₁ scales life for reliability other than 90%: about 1.0 at 90%, 0.62 at 95% and 0.21 at 99% (ISO 281). Higher reliability requires a larger C, since C ∝ (1/a₁)^(1/p).
How does speed affect the required bearing?
For a fixed number of operating hours, higher speed means more revolutions, so the required C grows as the cube (ball) or 3/10 root (roller) of speed. A bearing fine at 500 rpm may be far too small at 5000 rpm for the same hours.
What is a static safety factor s₀?
s₀ = C₀ / P₀ is the margin against permanent indentation when the bearing is stationary or shock-loaded. Smooth duty needs s₀ ≈ 1, vibrating or shock duty needs 1.5–3 or more.
How do I pick the bearing family from loads?
Pure radial → deep groove ball or cylindrical roller. Pure axial → thrust bearing. Combined with small F_a/F_r → deep groove ball. Combined with large F_a/F_r → angular contact ball or tapered roller, which are built for thrust.
What is the L10 life in hours?
L10 hours = (10⁶ / 60·n) · (C/P)^p. It is the life that 90% of identical bearings exceed under identical load and speed — the industry rating life, not a guaranteed minimum.
Do I need to include a shock factor?
Yes for real machinery. Multiply P by an application factor (1.0–1.2 smooth, 1.5 moderate, 2–3 heavy shock) so start/stop and impact duty do not quietly halve the life.
What if my required C is between two catalogue sizes?
Always round up to the next available size and re-check life. Running a bearing above its rating sharply accelerates fatigue — never round down for cost.
Should I select on C or on C₀?
Selecting on C alone can fail a stationary or low-speed check. Verify both: C for fatigue life and C₀ for static/start-up safety, then choose a bearing that meets the larger of the two.
How accurate is this selection estimate?
It reproduces the ISO 281 rating-life algebra to within a few percent. Real life also depends on lubrication, contamination, temperature and mounting, which ISO's life modification factor a_ISO would further adjust.
What is the load-life relationship in plain words?
Doubling the load cuts ball-bearing life by 8× (2³) and roller life by about 6.3× (2^(10/3)). Load dominates bearing life far more than speed or size changes of the same percentage.
Can I select a bearing from load alone without speed?
No — speed converts the desired hours into revolutions, which is what the life equation actually consumes. Without speed you can only size for the static rating C₀.
What is the difference between required C and required C₀?
Required C protects against fatigue over the running life; required C₀ protects against permanent denting during standstill, slow creep or shock. A bearing can pass one and fail the other.
How does temperature change the selection?
Above ~150°C the steel softens and the catalogue ratings must be derated (≈0.95 at 150°C, 0.75 at 250°C). Use high-temperature steels or derate C and C₀ accordingly.
Are angular contact bearings better for combined loads?
Yes. Their built-in contact angle carries thrust efficiently, so the equivalent load stays close to F_r. A deep groove ball under the same thrust needs a large Y correction and a bigger size.
What is a matched pair / duplex arrangement?
Two angular contact bearings mounted back-to-back or face-to-face share thrust in both directions and resist moment loads. The selection must then account for the pair, not a single row.
How do I handle an overhung load?
Resolve the overhung force into bearing reactions with statics first (reaction grows as the overhang grows), then enter those reactions as F_r in the selection.
What does the L10rev result mean?
L10rev is the required life expressed in millions of revolutions: 60·n·L_h / 10⁶. It is the quantity inside the (L10/10⁶) term of the rating equation.
Should I design for 90% or 99% reliability?
Critical, hard-to-replace or safety-related bearings justify 99% (a₁ = 0.21, much larger C). Non-critical, easily serviced ones are fine at 90%.
What is a_ISO life modification?
a_ISO multiplies the basic rating life for lubrication cleanliness, fatigue limit and other conditions (often 0.1–10). This tool gives the basic L10; apply a_ISO from the catalogue for a adjusted life.
How do preloaded bearings affect selection?
Preload adds a constant internal load, so the effective P is higher and the required C grows. Account for it in the application factor or add the preload to P.
Can this replace a catalogue search?
It tells you the minimum C and C₀ to look for and the family to choose. The final pick still comes from the manufacturer catalogue, which lists the exact size that meets those numbers.
What if I only have an axial load?
Use a thrust bearing (ball or roller). This tool still works if you enter F_r = 0, but a dedicated thrust bearing will be far more efficient than a radial bearing pressed into thrust service.
How often should I re-verify the selection?
Whenever the load, speed, duty cycle or environment changes. A bearing correctly sized for continuous running may fail under frequent start/stop because of the shock factor.
Is the result a guaranteed life?
No. L10 is a statistical rating: 10% of bearings may fail before it. It is a design target, not a warranty — always include a margin for unknown dynamic effects.
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Glossary

Technical terms used in mortgage calculations explained in plain language.

Dynamic Load Rating (C)
Catalogue load giving a rated life of 1 million revolutions at 90% reliability.
Static Load Rating (C₀)
Load producing ~0.0001 rolling-element-diameter permanent deformation at the contact.
Equivalent Dynamic Load (P)
Constant radial load equal in fatigue effect to the real combined load: P = X·F_r + Y·F_a (or F_r).
L10 Life
Rated fatigue life; the life exceeded by 90% of identical bearings under identical conditions.
Reliability Factor (a₁)
Life multiplier for reliability other than 90%: 1.0 at 90%, 0.62 at 95%, 0.21 at 99%.
Life Exponent (p)
3 for ball bearings, 10/3 for roller bearings in the rating-life equation.
Static Safety Factor (s₀)
s₀ = C₀ / P₀; margin against brinelling for stationary or shock-loaded bearings.
Application Factor (f_s)
Multiplier on P for shock, vibration and duty severity (1.0 smooth to 3.0 severe).
Bearing Family
The structural type — deep groove ball, angular contact, tapered/cylindrical roller, thrust — chosen by load direction.
F_a / F_r
Axial-to-radial load ratio; decides whether thrust must enter the equivalent load.
L10rev
Required life in millions of revolutions: 60·n·L_h / 10⁶.

Authoritative References

Trusted sources and standards referenced by this calculator.

Applicable Standards

ISO 281ISO 76 (static)ABMA / ANSISKF General CatalogueSchaeffler Calculation

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Page Information

Last Updated:

August 2026

Version:

2.1.0

License:

Free to use for educational and professional purposes.