## Background

Accurate conversion calculations are paramount to generating proper data for inventory tracking, invoicing, and other business processes. The most complicated conversions occur between volume and mass units of measure. Understanding the inputs used in these conversions is key to achieving valid data inside your CTRM system and maintaining an error-free process.

Typical volumetric units of measure include barrels, gallons, and cubic meters (m^{3}). Commonly used units of mass are pounds, metric tons, and kilograms. The scenario we will use in this article involves converting a shipment of jet fuel expressed in gallons to the mass quantity in metric tons.

## Product Gravity

The gravity of a product is one of the most important variables used in this equation. Specific gravity (SG) of a liquid is defined as the ratio of the density of a substance to the density of water at the **same** temperature. However, when calculating the specific gravity of gases, air density is considered instead of water density. API (American Petroleum Institute) gravity is widely used in the energy industry to measure the density of crude oil and refined products. Product gravities can be captured in both API and SG in most CTRM systems. However, the gravity of a product is converted behind the scenes from API to SG before the rest of the quantity conversion calculations are performed.

The following equation is used to convert gravities between API and SG:

[latexpage]

\[API\:Gravity = \frac{141.5}{SG\:Gravity^*} – 131.5}\]

**SG Gravity at 60 degrees Fahrenheit*

Most density measurements are taken at 60 degrees Fahrenheit, at which the density of water is 0.99907 gram/cm^{3}. However, many CTRM systems hardcode the density of water as 1 gram/cm^{3} which occurs at 4 degrees Celsius or 39.2 degrees Fahrenheit. This core logic assumption creates a slight discrepancy in the conversion factors which cannot be easily rectified in most cases.

Temperature | Density | Weight |

(°F/°C) | (grams/cm^{3}) | (pounds/ft^{3}) |

32°F/0°C | 0.99987 | 62.416 |

39.2°F/4.0°C | 1 | 62.424 |

40°F/4.4°C | 0.99999 | 62.423 |

50°F/10°C | 0.99975 | 62.408 |

60°F/15.6°C | 0.99907 | 62.366 |

70°F/21°C | 0.99802 | 62.3 |

80°F/26.7°C | 0.99669 | 62.217 |

90°F/32.2°C | 0.9951 | 62.118 |

100°F/37.8°C | 0.99318 | 61.998 |

120°F/48.9°C | 0.9887 | 61.719 |

140°F/60°C | 0.98338 | 61.386 |

## Conversion Example

Depending on which CTRM system is being used, the steps performed behind the scenes to convert volume and mass quantities could slightly differ. Regardless, the following steps can be used to convert quantities on your own to validate results from the software.

For the purposes of this walkthrough, we will convert 10,000 gallons of jet fuel to metric tons. The specific gravity of jet fuel in this example will be 0.82 SG. We can use the equation from earlier to calculate the API gravity in this scenario is 41.06 °API. These inputs will be identified by the yellow fields below.

CTRM systems, like Allegro, that do not allow cross unit-type conversions to be configured require basis units to be defined for each unit type. Most commonly, barrel (bbl) is the basis unit for volume unit types and pound (lb) is the basis unit for mass unit types.

**Step 1: **Convert volume to basis unit

10,000 | GAL |

42 | GAL to BBL Factor |

238.09523810 | BBL |

**Step 2: **Convert basis unit (BBL) to M3

238.09523810 | BBL |

0.15898730 | BBL – M3 Factor |

37.85411905 | M3 |

**Step 3: **Calculate MTV (metric ton in a vacuum) by multiplying the converted M3 quantity times the gravity of the product (in this case jet fuel) in SG

37.85411905 | M3 |

0.82 | Gravity in SG |

31.04037762 | MTV |

**Step 4**: Convert MTV to the basis unit of the mass unit (in this case LB). Since MTV and MT have the same conversion factor to BBL, we could stop at this point in the calculation. However, for conversions to other mass units, steps 4 and 5 are required.

31.04037762 | MTV |

0.00044643 | MTV to LB Factor |

69,530.22336995 | LB |

**Step 5**: Convert the basis unit (LB) to the final mass unit.

69,530.22336995 | LB |

2,239.99283202 | LB to MT Factor |

31.04037762 | MT |

## Conversion Workbook

To convert your firm’s quantities from volume to mass units using the steps above, check out our attached conversion workbook. Simply change the unit conversion factors, quantity and gravity inputs and let the spreadsheet do the rest.

## We Can Help

Small conversion or rounding errors add up exponentially when applied to large shipments and volumes. These issues can be difficult to troubleshoot by the time back office realizes the mistake. Our team has decades of experience working with CTRM systems and complicated product conversions. If you are in need of expertise to properly configure your unit conversions or shrinkage factors, please reach out!