What the Viscosity Index Calculator Does
The Viscosity Index (VI) is a dimensionless number that describes how much a lubricant's viscosity changes with temperature. A high VI means the oil stays relatively stable as temperature rises and falls, while a low VI means it thins dramatically when heated. This calculator works out the VI from just two laboratory measurements: the kinematic viscosity of your oil at 40°C and at 100°C. It is widely used in engineering, automotive maintenance, and lubricant manufacturing to compare oils and confirm they meet specification.
The Two Inputs You Need
- Kinematic Viscosity at 40°C (cSt) — the oil's flow resistance at the lower reference temperature, in centistokes.
- Kinematic Viscosity at 100°C (cSt) — the same measurement at the higher reference temperature.
Both values are normally obtained from a standard test (such as ASTM D445) and are printed on most oil data sheets.
The Formula Explained
The calculator follows the established ASTM D2270 method for oils with a VI under 100. Using your 40°C value (v40) and 100°C value (v100):
- L = 0.8353 × v_{40}^{2} - 14.67 × v_{40} - 216 (viscosity at 40°C of a reference oil with VI = 0)
- H = 0.1684 × v_{40}^{2} - 11.85 × v_{40} - 97 (viscosity at 40°C of a reference oil with VI = 100)
- U = 10^{≤ft(((v_{100} - 0.7) ÷ (0.2))\right)} - 1
- VI = (\log H - \log U) ÷ (\log H - \log L) × 100
In plain terms, the formula compares your oil against two reference oils that bracket its behaviour, then expresses where it falls between them.
Worked Example
Suppose an oil measures v40 = 73 cSt and v100 = 8.6 cSt. Then L = 0.8353 × 5329 - 14.67 × 73 - 216 ≈ 3163, H = 0.1684 × 5329 - 11.85 × 73 - 97 ≈ 36.3, and U = 10^{≤ft(((8.6 - 0.7) ÷ (0.2))\right)} - 1, which is a very large number. Plugging into the VI equation gives an index in the low-to-mid range, telling you the oil's viscosity is fairly sensitive to temperature.
Typical Viscosity Index Values for Common Oils
The table below gives orientation values only. Base-oil groups follow the API 1509 (American Petroleum Institute) base-stock definitions, and every VI figure is computed by ASTM D2270 from kinematic viscosities measured per ASTM D445. Real products vary between suppliers, blends and additive treat rates — always take \nu_{40} and \nu_{100} from the actual product data sheet or laboratory report rather than from a table like this one.
| Oil / base stock | Typical \nu_{40} (cSt) | Typical \nu_{100} (cSt) | Typical VI range |
|---|---|---|---|
| Naphthenic base oil (light) | ≈ 25 – 100 | ≈ 4 – 8 | 0 – 60 |
| Group I solvent-refined mineral (e.g. SN 150) | ≈ 30 | ≈ 5.2 | 90 – 105 |
| Bright stock (Group I residual) | ≈ 450 – 500 | ≈ 30 – 32 | 90 – 100 |
| Group II hydroprocessed mineral | ≈ 20 – 45 | ≈ 4 – 7 | 95 – 120 |
| Group III / VHVI (severely hydrocracked) | ≈ 19 – 22 | ≈ 4.1 – 4.3 | 120 – 140 |
| Group IV PAO synthetic (PAO 4 / PAO 6) | ≈ 17 – 31 | ≈ 4 – 6 | 130 – 150 |
| Group V esters (diester / polyol ester) | ≈ 20 – 30 | ≈ 4 – 6 | 140 – 180 |
| Engine oil, SAE 15W-40 (mineral, multigrade) | ≈ 100 – 120 | ≈ 13.5 – 15 | 130 – 140 |
| Hydraulic oil, ISO VG 46 (mineral, HM type) | ≈ 46 | ≈ 6.7 – 7.0 | 95 – 105 |
| Hydraulic oil, ISO VG 46 (high-VI, HV type) | ≈ 46 | ≈ 8 – 9 | 140 – 180 |
| Automatic transmission fluid (modern ATF) | ≈ 29 – 35 | ≈ 6.5 – 7.5 | 160 – 190 |
| Gear oil, SAE 80W-90 (mineral, API GL-5) | ≈ 140 – 160 | ≈ 14.5 – 15.5 | 95 – 105 |
How the API groups relate to VI
API 1509 classifies base stocks by saturates content, sulphur content and viscosity index: Group I has less than 90 % saturates and/or more than 0.03 % sulphur with VI from 80 to 120; Group II has at least 90 % saturates and no more than 0.03 % sulphur, also with VI 80–120; Group III meets the same purity limits but with VI of 120 or higher; Group IV is polyalphaolefin (PAO); Group V covers everything else, including esters, PAG and naphthenics. The narrower ranges in the table are typical commercial values, not the wider regulatory bands — a Group II stock can legitimately sit anywhere from VI 80 to 120.
Note also that finished-oil VI is not simply the base-oil VI: polymeric viscosity-index improvers raise the measured VI of multigrade engine, gear and hydraulic oils well above that of the base stock they are blended from, which is why a mineral SAE 15W-40 can show VI 135 while its Group I base oil shows VI 95.
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