Hydraulic oil Density is the ratio of its mass to the volume of space it occupies:
## \rho=\frac{m}{V} ##
The accepted units of measurement for density according to ASTM are kilograms per cubic meter (kg/m3, SI unit) or grams per milliliter (g/mL).
Hydraulic oil Specific Gravity (or “Relative Density”) is the ratio of Hydraulic oil density to water density at the specific temperature:
## SG_{oil}=\frac{\rho_{oil}}{\rho_{water}} ##
Substance with SG <1 will float on water (like hydraulic oil); substance with SG >1 will sink in water (like honey).
Next, both hydraulic oil density and Specific Gravity vary with temperature and pressure.
Reference: [https://www.internetchemistry.com/chemical-data/water-density-table.php]
Reference: [https://webbook.nist.gov/chemistry/fluid/]
This is why the ASTM D1298-12b “Standard Test Method for Density, Relative Density, or API Gravity of Crude Petroleum and Liquid Petroleum Products by Hydrometer Method” states that accurate determination of the API gravity, density or relative density (specific gravity) uses a standard temperature of 60 degrees F (15 degrees C).
Reference: [https://www.astm.org/d1298-12b.html]
You can find in the oil specification table of every hydraulic oil manufacture either Oil Specific Gravity or Oil Density at the specific temperature of 60°F or 15°C.
As a result, to calculate Specific Gravity or Hydraulic oil density at 15°C and, respectively, Hydraulic oil density or Specific Gravity at 15°C. By ASTM D1298-12b water density at 15°C is 0.999103 g/ml, therefore:
## SG_{oil}=\frac{\rho_{oil}}{0.999103} ##
## \rho_{oil}=\frac{SG_{oil}}{0.999103} ##