Minimum required viscosity (ν1) & kappa calculator
SKF / ISO 281 minimum required viscosity at operating temperature from bearing mean diameter and speed, plus the viscosity the oil must deliver to reach a target κ ratio. Geometry comes from your selected bearing when a calculation string is active.
How this calculator works
The mean diameter is dm = (bore + OD) ÷ 2, in millimetres (inch entries are converted). The rated, or minimum required, viscosity ν₁ at operating temperature uses the ISO 281 expressions, which switch on shaft speed n at 1,000 RPM:
- n below 1,000 RPM:
ν₁ = 45,000 × n^−0.83 × dm^−0.5 - n at 1,000 RPM and above:
ν₁ = 4,500 × n^−0.5 × dm^−0.5
The viscosity ratio is κ = ν ÷ ν₁, so the viscosity the oil must deliver to reach your target κ is ν = κ × ν₁, in cSt. Both values apply at the bearing's operating temperature, not at 40 °C. The results carry into the Lubricant Recommendation calculator.
Inputs explained
- Outer diameter and bore (ID): inches or mm. They are pre-filled from the bearing you selected in the bearing lookup.
- Speed (n): shaft speed in RPM.
- Kappa (κ) target: 1.0 to 4.0 in steps of 0.25. Defaults to 2.5.
Worked example
A 45 mm bore × 100 mm OD bearing at 1,780 RPM with a κ target of 2.0. dm = 72.5 mm, and since n is at least 1,000 RPM, ν₁ = 4,500 × 1,780^−0.5 × 72.5^−0.5.
Calculator output: Min required viscosity ν₁ 12.53 cSt · Viscosity to achieve target κ 25.05 cSt · “dm = 72.5 mm · n·dm = 129,050 mm·RPM · ISO 281 n ≥ 1000 rpm formula.”
Reading the result & common mistakes
- Reading it: ν₁ is the viscosity the oil needs at the bearing’s operating temperature for κ = 1. The second figure is what the oil must deliver to reach your κ target. Then pick an oil grade that gives at least that viscosity at the running temperature.
- κ below 1: the oil film is too thin to fully separate the surfaces. ISO 281 allows credit for proven EP additives in that range; check with your lubricant supplier.
- κ above 4: ISO 281 gives no further life benefit (κ is capped at 4 in the life-modification factor), and a heavier oil adds friction and heat.
- Comparing with the ISO VG: an ISO VG is the viscosity at 40 °C. A VG 68 oil at 70 °C has much less than 68 cSt, so convert to the operating temperature first.
- Wrong speed or diameter: use the speed of the shaft the bearing is on (after any gearbox or belt), and both bore and OD so dm is correct. For grease, compare with the base-oil viscosity.
Next step: find which grade delivers this viscosity at your temperature with the VI Comparator & ASTM D341, then see the effect of κ on bearing life in Component Life & ISO 281 L10.
Frequently asked questions
What is the bearing viscosity ratio κ (kappa)?
κ is the lubricant's actual viscosity at operating temperature divided by the rated viscosity ν₁ that the bearing needs for its size and speed. This calculator returns ν₁ (the κ = 1 reference) and the viscosity the oil must deliver to reach a target κ from 1.0 to 4.0.
How is the minimum required viscosity ν₁ calculated?
It uses the ISO 281 expressions with the mean diameter dm = (bore + OD) ÷ 2 in mm and the shaft speed n in RPM. Below 1,000 RPM, ν₁ = 45,000 × n^−0.83 × dm^−0.5. At 1,000 RPM and above, ν₁ = 4,500 × n^−0.5 × dm^−0.5. For example, a 45 × 100 mm bearing at 1,780 RPM needs 12.53 cSt.
Is ν₁ the oil's viscosity at 40 °C?
No. ν₁ and the target-κ viscosity are needed at the bearing's operating temperature. An ISO VG is the viscosity at 40 °C, so convert using the oil's viscosity–temperature behaviour, for example with the viscosity index calculator, before you choose a grade.