## Calculations

The tables below provide a convenient means of making common calculations in lubricant formulations.

If your browser does not support calculations of this type, please refer to the formulas.

Weight and Volume

Additives are sold by volume or mass; blends can be manufactured either way. Product data sheets provide densities for additive packages that enable conversions to be made:

```                    Additive Density x Additive (%vol)

Density of Finished Oil

```

(% vol)
(% mass)
=

Sulfated Ash

Oil specifications frequently limit the sulfated ash content of the blend. This limits the amount of metallic elements in the additive package or the maximum treatment level. The contribution of some common additive metals to sulfated ash is:

Element Factor Element Factor
Barium 1.70 Magnesium 4.95
Boron 3.22 Manganese 1.291
Calcium 3.40 Molybdenum 1.50
Copper 1.252 Potassium 2.33
Lithium 7.92 Zinc 1.50

Example: An additive package is recommended for use at 8.5% by mass. The product data sheet gives the following information:

 Density at 15°C 0.97 kg/L Calcium 0.47% by mass Magnesium 1.15% by mass Zinc 1.66% by mass

What will be the sulfated ash content of the finished blend?

Calcium: 0.47(3.40)(8.5)/100 = 0.136
Magnesium: 1.15(4.95)(8.5)/100 = 0.484
Zinc: 1.66(1.5)(8.5)/100 = 0.21
Total Sulfated Ash = 0.136 + 0.484 + 0.21 = 0.83% by mass.

Gross Additive Treating Cost (GATC) is the cost of additive in one volume unit of finished product not including base fluid credit or shipping costs:

```                  Add. (\$/U.S. gal) x % vol

GATC \$/U.S. gal = -------------------------

100

Add. Cost (\$/kg) x % mass

GATC \$/liter = -------------------------  x Density

100

```
=

(% mass)
Density   GATC (\$/liter)
=

Net Additive Treating Cost (NATC) is the cost of additive in one unit of finished product including base oil credit (BOC), but not shipping costs. (Base oil credit is the cost of oil displaced.)

```                  (Add. Cost - BOC) x % vol

NATC \$/U.S. gal = -------------------------

100

(Add. Cost - BOC) x % mass

NATC \$/liter = --------------------------  x Density

100

```
(% vol)
NATC
(\$/US gal)
=

(% mass)
Density   NATC
(\$/liter)
=

Fuel Consumption

In calculating Corporate Average Fuel Economy (CAFE), the automobile industry uses actual consumption figures (expressed as liters/100 km), and may then convert them to the more familiar fuel economy values (miles/U.S. gallon or miles/Imperial gallon) for advertising purposes. The conversions are:

```  1 liter     235.2 miles      282.5 miles

--------- = ------------- = --------------

100 km        U.S. gal      Imperial gal

```