Bearing Load Calculator estimates equivalent dynamic load and bearing life from radial load, axial load, dynamic load rating, RPM, and bearing type. Formula: P = XFr + YFa; L10 = (C/P)^p.
The Number on the Bearing Box Is Not the Number You Need
Every bearing catalog lists a Dynamic Load Rating (C). What it does not list is how long that bearing will survive at your specific combination of radial and axial load, at your shaft speed. Choosing a bearing on C alone — without calculating the equivalent dynamic load P and running the ISO 281 life equation — is why machines go down between scheduled service intervals.
The full chain runs from raw Fr and Fa inputs, through a weighted P calculation that accounts for bearing geometry, to L10 life expressed in millions of revolutions and then translated into operating hours and 24/7 days. Six bearing profiles are modelled here, each with distinct load weighting factors and a life exponent that reflects whether contact is along a point or a line.
Calculator Used Formulas
Step 1 — Bearing Type Constants (X, Y, p)
Each bearing type carries a unique radial factor X, axial factor Y, and life exponent p. The calculator assigns these automatically based on your Bearing Type selection:
| Bearing Type | Radial Factor (X) | Axial Factor (Y) | Life Exponent (p) |
|---|---|---|---|
| Standard Ball — Combined | 0.56 | 1.5 | 3 |
| Standard Roller — Combined | 0.40 | 1.5 | 10/3 ≈ 3.333 |
| Pure Radial Ball | 1 | 0 | 3 |
| Pure Radial Roller | 1 | 0 | 10/3 ≈ 3.333 |
| Pure Thrust Ball | 0 | 1 | 3 |
| Pure Thrust Roller | 0 | 1 | 10/3 ≈ 3.333 |
Step 2 — Equivalent Dynamic Load (P)
P = (X × Fr) + (Y × Fa)
Where Fr is the radial load and Fa is the axial (thrust) load, both in the same unit (N or lbf).
Step 3 — Minimum Load Floor (Combined and Radial modes only)
For Standard Ball, Standard Roller, Pure Radial Ball, and Pure Radial Roller types, P cannot fall below the raw radial load:
P = max[ (X × Fr) + (Y × Fa), Fr ]
This floor does not apply to Pure Thrust Ball or Pure Thrust Roller.
Step 4 — Load Rating Ratio
C/P = C ÷ P
Where C is the Dynamic Load Rating from the bearing’s data sheet.
Step 5 — Basic Rating Life (L10)
L10 (millions of revolutions) = (C ÷ P) ^ p
Ball bearings use p = 3. Roller bearings use p = 10/3.
Step 6 — Operational Life (L10h)
L10h (hours) = (L10 × 1,000,000) ÷ (60 × RPM)
Step 7 — Operating Days (continuous 24/7)
Operating Days = L10h ÷ 24
Step 8 — Life per 1,000 RPM
Life per 1,000 RPM (hours) = (L10 × 1,000,000) ÷ (60 × 1,000)
This speed-normalised figure allows direct bearing comparison regardless of the shaft speed entered.
Alternate Unit Conversions (Card 4)
Metric mode → P in lbf P (lbf) = P (N) × 0.224809 Metric mode → C in lbf C (lbf) = C (N) × 0.224809 Metric mode → P in tonne-force P (tf) = P (N) ÷ 9,806.65 Imperial mode → P in N P (N) = P (lbf) ÷ 0.224809 Imperial mode → C in N C (N) = C (lbf) ÷ 0.224809 Imperial mode → P in tonne-force P (tf) = [P (lbf) ÷ 0.224809] ÷ 9,806.65
How It Works
The calculation starts with your bearing type selection, which sets three constants internally: X (how much the radial load contributes), Y (how much the axial load contributes), and p (the life exponent). Combined-load ball bearings split the load between both directions using X = 0.56 and Y = 1.5. Pure radial types set Y = 0, so the axial input has zero effect on P. Pure thrust types set X = 0, meaning the radial load contributes nothing — only Fa drives the result.
With X, Y, and both load inputs known, the calculator multiplies each component and sums them: P = (X × Fr) + (Y × Fa). For any mode that is not purely thrust-loaded, the result is then checked against the raw radial load Fr. If the formula produces a P that is numerically less than Fr, the calculator sets P = Fr. This is the minimum load floor described in ISO 281 — a bearing carrying a radial load cannot have an effective dynamic load lower than that radial force alone.
From P, the C/P ratio is computed directly. This ratio is the central argument of the Lundberg–Palmgren life equation: L10 = (C/P)^p. The result is in millions of revolutions. The calculator then converts to hours using your RPM entry — dividing total revolutions by the revolutions per minute gives minutes, and dividing again by 60 gives hours. A further division by 24 converts to continuous 24/7 operating days.
The “Life per 1,000 RPM” sub-figure on the Operational Life card is computed at a fixed normalised speed of 1,000 RPM, independent of your actual RPM, so you can compare bearings across different operating conditions.
The Alternate Units card performs straight mathematical conversions on the already-computed P and C values. In metric mode, Newtons convert to lbf via the factor 0.224809 and to tonne-force by dividing by 9,806.65 N/tf. In imperial mode, lbf are first converted to N (dividing by 0.224809) before the tonne-force conversion is applied. These are displayed as parallel values — they do not affect the life calculation, which always runs in the unit system you selected.
Why the Equivalent Load Can’t Drop Below Fr — Even When the Formula Says It Should
Here is a scenario that catches engineers out: you enter a large radial load (say, Fr = 10,000 N) and a very small axial load (Fa = 50 N) with Standard Ball selected (X = 0.56, Y = 1.5). The formula gives P = (0.56 × 10,000) + (1.5 × 50) = 5,600 + 75 = 5,675 N. But the calculator outputs P = 10,000 N — the raw radial load — because 5,675 is less than Fr.
This is not a bug. The ISO 281 equivalent dynamic load equation with X and Y factors is derived for bearings operating with a meaningful axial-to-radial load ratio. When the axial component is small relative to the radial load, applying the combined formula produces a P lower than the pure-radial case, which would overstate the predicted life. The standard therefore mandates a floor: for combined and radial bearing modes, P is always at least Fr. The calculator enforces this with a direct comparison after computing the formula result.
The practical consequence is straightforward: if your axial load is low compared to your radial load on a combined-type bearing, the axial input makes no difference to the life estimate. The bearing is effectively in a radial-dominant regime, and the life is governed by Fr and C alone. Only when the weighted axial term (Y × Fa) is large enough to push P above Fr does the axial load begin to extend or shorten the predicted life.
Pure Thrust Ball and Pure Thrust Roller modes are exempt from this floor. In those modes, X = 0, so Fr is already contributing nothing, and the only physically meaningful input is Fa. Entering Fr = 0 with Fa > 0 in a pure thrust mode is the correct setup and computes normally.
Worked Example: Induction Motor Drive-End Bearing
A 4-pole induction motor runs at 1,500 RPM. The drive-end bearing is a standard deep-groove ball bearing with a Dynamic Load Rating C = 30,000 N from the manufacturer’s datasheet. The shaft produces a radial load Fr = 5,000 N from belt tension and a axial load Fa = 2,000 N from a slight helical gear thrust. You need to know whether this bearing will survive a 3-year continuous maintenance cycle.
Inputs entered:
- Measurement System: Metric (Newtons)
- Bearing Type: Standard Ball (Combined)
- Radial Load (Fr): 5,000 N
- Axial/Thrust Load (Fa): 2,000 N
- Dynamic Load Rating (C): 30,000 N
- Operating Speed: 1,500 RPM
Step-by-step calculation:
- X = 0.56, Y = 1.5, p = 3 (Standard Ball constants)
- X × Fr = 0.56 × 5,000 = 2,800 N — shown in Load Rating Ratio card as “X × Fr Component”
- Y × Fa = 1.5 × 2,000 = 3,000 N — shown as “Y × Fa Component”
- P = 2,800 + 3,000 = 5,800 N
- Floor check: 5,800 > 5,000, so no clamp applies
- C/P = 30,000 ÷ 5,800 = 5.17 — shown in Load Rating Ratio card
- L10 = 5.17³ = 138.38 million revolutions — shown in Basic Rating Life card
- L10h = (138.38 × 1,000,000) ÷ (60 × 1,500) = 138,380,000 ÷ 90,000 = 1,537.58 hours — shown in Operational Life card
- Operating Days = 1,537.58 ÷ 24 = 64.07 days — shown as sub-value in Operational Life card
Verdict: At 64 continuous 24/7 days, this bearing is nowhere near a 3-year maintenance interval. A bearing with a higher C rating is needed, or the radial load must be reduced (longer belt centre distance, change of pulley ratio), or the maintenance cycle must be shortened. The Life per 1,000 RPM figure of 2,306.37 hours lets you quickly re-evaluate the same bearing at a different shaft speed without re-entering everything.
Frequently Asked Questions
Why does the Equivalent Dynamic Load (P) equal Fr even though I entered an axial load?
This is the minimum load floor. For Standard Ball, Standard Roller, Pure Radial Ball, and Pure Radial Roller types, the calculator always sets P = max[(X × Fr) + (Y × Fa), Fr]. When the axial load is small relative to the radial load, the formula result falls below Fr and the floor takes over. Your axial entry is not being ignored — it was computed and found to be insufficient to raise P above the radial baseline. See the dedicated section above for a full explanation.
What happens if I enter Fr = 0 and Fa = 0 with a Pure Thrust Bearing selected?
The calculator blocks this and shows a “Load Required” warning. In Pure Thrust mode, X = 0, so the formula produces P = (0 × 0) + (1 × 0) = 0. The code explicitly checks P > 0 before proceeding and will not run the life equation on a zero load. You must enter a non-zero axial load (Fa) for Pure Thrust modes to produce results.
Why do roller bearings use p = 10/3 instead of 3?
The life exponent p = 3 applies to ball bearings, where contact stress is distributed across a theoretical point. Line contact in roller bearings produces a different stress distribution and a shallower fatigue slope, which ISO 281 represents with the exponent 10/3 ≈ 3.333. The practical effect is that roller bearings gain life slightly faster than ball bearings as the C/P ratio increases. At C/P = 5 for example, a ball bearing gives (5³) = 125 M revs while a roller bearing gives (5^3.333) ≈ 184 M revs — a 47% difference from the exponent alone.
Why do my inputs reset when I switch between Metric and Imperial?
This is intentional. The calculator detects a unit system change and replaces your entered values with sensible defaults for the new unit: Metric defaults to Fr = 5,000 N, Fa = 2,000 N, C = 30,000 N; Imperial defaults to Fr = 1,120 lbf, Fa = 450 lbf, C = 6,740 lbf. These pairs are approximately equivalent, so the default output stays consistent across systems. If you switch units mid-entry, re-enter your actual values after the switch.
The Alternate Units card shows “P in tf” — what is tonne-force and when does it matter?
Tonne-force (tf) is a metric unit equal to the force exerted by one metric tonne under standard gravity: 1 tf = 9,806.65 N. It appears in older European and Asian industrial bearing catalogues — particularly those predating widespread SI adoption — and is still used by some press and forging equipment manufacturers. The calculator converts P to tf so you can cross-reference directly with these catalogues without a separate conversion step. In Metric mode, P (tf) = P (N) ÷ 9,806.65. In Imperial mode, the lbf value is first converted to N (÷ 0.224809) and then divided by 9,806.65.
Does entering zero for the Dynamic Load Rating (C) produce a result?
No. The code requires C to be strictly greater than zero (cVal > 0). A zero or negative C value fails the input validation check and triggers a “Data Required” warning, clearing all output fields. This is correct behaviour — C = 0 is physically meaningless and would cause a division-by-zero when computing the C/P ratio.