Determine the equivalent static load P₀ of a rolling bearing from radial and axial force to DIN ISO 76:2019 and check the static load safety S₀ = C₀/P₀ against the guideline values of the standard.
The rating life to ISO 281 answers how long a bearing survives under a rotating load. This check answers the other question: whether a single high load – shock, standstill, an overload case – already presses a permanent flat into the raceway. Calculate rating life to ISO 281.
Enter bearing data and determine the static load safety.
Determine the equivalent static load P₀ from radial and axial force and check S₀ = C₀/P₀ against the guideline values of DIN ISO 76.
Bearing type, number of rows and – where the standard requires it – the nominal contact angle set the factors X₀ and Y₀. Add the catalogue static load rating C₀, the largest radial and axial force of the load case to be verified, and the operating mode that sets the guideline for S₀.
Bearing type and contact angle give X₀ and Y₀. For radial bearings the equivalent static load is the larger of X₀·F_r + Y₀·F_a and F_r; for thrust bearings P₀a = 2.3·F_r·tan α + F_a. The safety is S₀ = C₀/P₀, compared with the guideline of the operating mode.
A deep groove ball bearing with C₀ = 19.6 kN under F_r = 4 kN and F_a = 2.5 kN: X₀·F_r + Y₀·F_a gives 3.65 kN, below F_r, so P₀ = 4 kN and S₀ = 4.9. Normal running requires at least 1.0 – the check passes.
Sources and limits: DIN ISO 76:2019-04 defines static load ratings, the equivalent static load and the load safety. According to the standard the guideline values for S₀ rest on experience with rotating bearings. Deriving C₀ from the internal geometry and the fatigue rating life to ISO 281 are not part of this calculation.
Determine the equivalent static load P₀ from radial and axial force and check S₀ = C₀/P₀ against the guideline values of DIN ISO 76.
When a rolling bearing stands still or turns very slowly under a high load, the most heavily loaded rolling element presses a permanent flat into the raceway. That is exactly what the static load rating C₀ bounds: it is the load at which the permanent deformation at the most heavily loaded contact reaches about 0.0001 times the rolling element diameter. This damage differs from the fatigue that the ISO 281 rating life describes – it does not build up over millions of revolutions but happens in a single load case. That is why the static check is needed even when the rating life is ample: under shock loads, under assembly and transport loads, and for stationary or oscillating bearings.
The two standards address different damage mechanisms. ISO 281 describes material fatigue under a rotating load and returns a life in revolutions or hours. DIN ISO 76 describes permanent deformation at the contact and returns a safety against a single load case.
In practice both are needed: the rating life governs bearing size in continuous operation, the static load safety governs behaviour under shock, at standstill and under assembly or transport loads. A bearing with ample rating life can still fail the static check – and the other way round.
The fatigue rating life of the same bearing is covered by the ISO 281 rolling bearing life calculator.
The factors capture how strongly an axial force reaches the rolling elements in each bearing type. For deep groove ball bearings they are fixed: X₀ = 0.6 and Y₀ = 0.5, for single and double row alike. For angular contact ball bearings DIN ISO 76 tabulates Y₀ over the nominal contact angle from 5° to 45°; for intermediate values the standard explicitly prescribes linear interpolation, and that is what this calculator does.
For self-aligning ball bearings and radial roller bearings with α ≠ 0°, Y₀ follows the cotangent of the contact angle instead – 0.22·cot α single row, 0.44·cot α double row. The shallower the angle, the larger Y₀ becomes: an axial force loads a shallow-angle bearing disproportionately.
The tabulated factors apply to raceway groove radii within the limits named by the standard. For different internal geometries DIN ISO 76 refers to ISO/TR 10657; this calculator does not cover that special case.
S₀ = C₀ / P₀
P₀r = max(X₀ · F_r + Y₀ · F_a ; F_r)P₀a = 2.3 · F_r · tan α + F_aDeep groove ball bearings: X₀ = 0.6 · Y₀ = 0.5Self-aligning ball and angled roller bearings: Y₀ = 0.22 · cot α (single row) · 0.44 · cot α (double row)C₀ required = S₀ min · P₀| Symbol / input | Meaning |
|---|---|
| C₀ | Static load rating from the bearing catalogue, radial or axial depending on the type. |
| F_r, F_a | Largest radial and axial force of the load case to be verified. |
| X₀, Y₀ | Static radial and axial load factor by bearing type and contact angle. |
| α | Nominal contact angle of the bearing according to the catalogue. |
| P₀ | Equivalent static load – the notional pure radial or axial force of equal effect. |
| S₀ | Static load safety, compared with the guideline of the operating mode. |
Bearing type, number of rows and – where the standard requires it – the nominal contact angle set the factors X₀ and Y₀. Add the catalogue static load rating C₀, the largest radial and axial force of the load case to be verified, and the operating mode that sets the guideline for S₀.
Select the bearing type and the number of rows; for angular contact, self-aligning and thrust bearings also enter the nominal contact angle from the catalogue. Add the static load rating C₀ from the same catalogue entry and the largest radial and axial force of the load case to be verified, then choose the operating mode. The calculator returns X₀ and Y₀, the equivalent load, the load safety and the minimum load rating required for it.
A deep groove ball bearing with C₀ = 19.6 kN under F_r = 4 kN and F_a = 2.5 kN: X₀·F_r + Y₀·F_a gives 3.65 kN, below F_r, so P₀ = 4 kN and S₀ = 4.9. Normal running requires at least 1.0 – the check passes.
The equivalent static load P₀ is the notional pure radial or axial force that would cause the same permanent deformation as the actual combined load. It is the real calculation step – the division S₀ = C₀/P₀ afterwards is trivial. An S₀ below the guideline does not mean immediate failure but that the flat spot exceeds what is usually accepted for the selected running smoothness; the consequences are noise, rough running and a shorter service life. The reported required load rating is the figure to select against in the catalogue. Not covered by this check are the fatigue rating life, the capacity of cage and seals, the strength of the surrounding structure, and deflection of shaft and housing.
Forces and load ratings in kilonewtons (pounds-force in the US unit system), contact angle in degrees. Load safety and load factors are dimensionless.
DIN ISO 76 gives guideline values rather than fixed limits, and they differ markedly between ball and roller bearings. Ball bearings need at least 2 for quiet running with high rotational accuracy, 1 for normal running and 1.5 under pronounced shock loads. For roller bearings the same steps are 3, 1.5 and 3.
There is a physical reason for the difference: roller bearings carry load over a line rather than a point, so a flat spot affects running accuracy more strongly. For thrust spherical roller bearings the standard recommends at least 4 throughout, and at least 3 for case-hardened drawn-cup needle roller bearings.
These are explicitly experience-based values for rotating bearings, not a mandatory requirement. Where the magnitude of a shock load is accurately known the standard permits lower values; where it is unknown, at least 1.5 (ball) or 3 (roller) should be applied. For other operating conditions it refers to the manufacturer.
Verifying bearings under shock load, checking stationary or slowly oscillating bearings, reviewing assembly and transport load cases, and selecting bearing size where a single peak load rather than the rating life governs.
DIN ISO 76:2019-04 defines static load ratings, the equivalent static load and the load safety. According to the standard the guideline values for S₀ rest on experience with rotating bearings. Deriving C₀ from the internal geometry and the fatigue rating life to ISO 281 are not part of this calculation.
Common mistake: Don't enter the operating average of the load – what governs is the largest force of the load case, even if it acts only briefly or at standstill. Nor should C₀ be confused with the dynamic load rating C: both sit side by side in the catalogue but describe different damage mechanisms. And for radial roller bearings with α = 0° no axial force may be applied – the standard deliberately gives no equation for it.
The ratio of static load rating C₀ to equivalent static load P₀. It describes the margin to the load at which the permanent deformation at the most heavily loaded contact reaches about 0.0001 times the rolling element diameter.
C is the dynamic load rating and feeds the fatigue rating life to ISO 281. C₀ is the static load rating and bounds permanent deformation. Both appear side by side in the catalogue and are not interchangeable.
Whenever a high load occurs at standstill, at very low speed or as a shock – and for assembly and transport load cases. Even for bearings sized dynamically, the standard advises additionally checking that the static load rating is sufficient.
For radial bearings as the larger of X₀·F_r + Y₀·F_a and F_r alone. For thrust bearings with α ≠ 90° the equation is P₀a = 2.3·F_r·tan α + F_a; at α = 90° it is simply P₀a = F_a.
Because the standard requires the larger of the two values. If the axial share is small, X₀·F_r + Y₀·F_a falls below F_r – the first equation would then be unsafe, so P₀ = F_r applies.
X₀ = 0.6 and Y₀ = 0.5, for single and double row alike. The permissible maximum of F_a/C₀r however depends on internal clearance and raceway groove depth and has to come from the manufacturer.
The shallower the angle, the more heavily an axial force loads the bearing, and the larger Y₀ becomes. For angular contact ball bearings Y₀ falls from 0.52 at 5° to 0.22 at 45°; for self-aligning and angled roller bearings it follows the cotangent.
DIN ISO 76 prescribes linear interpolation of Y₀ between the tabulated angles. This calculator implements that and reports the value it used.
Roller bearings carry load over line contact rather than point contact. A permanent flat spot affects running accuracy and noise more strongly there, which is why the standard gives consistently higher guideline values for roller bearings.
Not with this standard. DIN ISO 76 gives only P₀r = F_r for α = 0° and explicitly notes that the axial capacity of such bearings varies considerably by design; it refers to the bearing manufacturer for that case.
Not immediate failure, but permanent deformation above what is usual for the selected running smoothness. In practice that shows up as noise, rough running and a shorter service life.
No, the two answer different questions. The static check looks at a single load case, the ISO 281 rating life at fatigue over the operating period. A bearing should satisfy both.
No. C₀ follows from the number and diameter of the rolling elements, the pitch diameter and the raceway geometry, and it is given in the bearing catalogue. You enter that value; the calculator derives P₀ and S₀ from it.