Cargo Calculations on Tankers with
ASTM Tables: Here is all you need to
know
Written by Capt Rajeev Jassal on September 23, 2018
Basics about Volume and weight
Before we proceed to the complex things, it is better to start with the
basics.
Volumes and weights!!!
Volume changes with temperature but the weight remains the same.
Even when we hear some weight of cargo, let us say 30000 Tons of
cargo, there are two things that we need to be aware of.
1. Unit of weight
What is the unit of this weight? Is it

Metric Ton

Long Ton

Short Ton
2. In air or in Vacuum
Apart from the units, weight is measured in air or in Vacuum.
Even though on ships it is more common to measure the cargo weights
in the air, sometimes you may find that the charterers would give the
requirements for measuring weight in Vacuum.
Remember, for stability and draft calculation we still would need to use
the weight in air.
Coming back to the topic, can you guess for the same amount of cargo
which weight would be more? Weight in air or weight in Vacuum?
No problems, make a wild guess even if you don’t know.
Well, the weight is Vacuum is always more than the weight in Air.
This is because, like with water, air (and any other medium in which the
weight is present) would offer some kind of buoyancy which reduces the
weight.
In the vacuum, there is no buoyancy and hence the weight is more than
the same weight when measured in air.
Converting weight in Vacuum to Weight in Air and vice-versa
Ok, so now here is the first thing that we can learn. How to convert
weight in Vacuum to weight in Air?
The first page of the ASTM table 56 provides the factor for converting
weight in vacuum to weight in air and vice versa.
Basics of cargo calculations
Ok, now let us get back to basics of cargo calculations on tankers. And it
is not that complicated.
We first measure ullage (or Sounding) of the tanks by UTI tape (or radar
gauge in CCR).
We also measure the temperature of the cargo preferably at three levels
and take the mean of these three temperatures to get the temperature
of the cargo.
So here is what we have.
Now we get the volumes for each of these tanks for the corrected ullage
that we have got.
This will be the volume at the observed temperature. Remember volume
changes with temperature.
This will be the volume at the observed temperature. Remember volume
changes with temperature.
Let us say we got the volumes from the ullage tables and the volumes for
each tank are as per below.
As the volume changes with the temperature, this cannot be the
measure of how much cargo we have loaded or discharged.
We need to convert the volumes to the weight of the cargo in each tank.
We need the density of the cargo to convert the volume of cargo to the
weight.
And as the density also changes with the temperature, we would need
the density of the cargo at the cargo temperature to convert the
observed volume to weight.
If that was not enough, humans on this planet earth have managed to
confuse it further.

Volumes are measured in cubic meters at some places and barrels (like
in the US) in other

Weight is measured in Metric tons at some places and in long tons at
other places and barrels at 60 deg F at other places.

Densities are measured as Density in t/m3 at some places and API or
specific gravity at other places
But don’t let all these confuse you. I won’t let you confuse yourself. Take
a deep breath and read on.
First, check what cargo surveyor has provided you.
The cargo surveyor will provide

Density at a particular temperature and correction factor

A Table of densities at different temperatures

Density at 15 Deg C and ASTM table to use

API Gravity at 60 Deg F and ASTM Table to use
Let us calculate the weight of cargo in each of these situations.
1. Density at a particular temperature and correction
factor
So let us say that cargo surveyor has provided us with the density at a
particular temperature and correction factor.
Let us say the provided values are

Density at 25 Deg C: 0.9155

Density correction factor: 0.0006 per Deg C
This means that at every degree rise in temperature, the density would
decrease by 0.0006.
This means that

Density at 31 Deg C would be: 0.9119

Density at 32 Deg C would be: 0.9113

Density at 34 Deg C would be: 0.9101

Density at 35 Deg C would be: 0.9095
So, in this case, we just apply these densities to get the weight of cargo
in each tank and thus the total weight of the cargo.
Here is how the ullage report will look like.
2. A Table of densities at different temperatures
The cargo surveyor may provide a table of densities at different
temperatures. This is even easier than the previous section that we
discussed.
The density table could look something like this.
The cargo calculations, in this case, are also easy. We just take the
density of the cargo to the corresponding cargo temperature that we
measured.
Rest of the calculations is the same as what we discussed in the previous
section.
If the cargo temperature is between two values in the density table, we
just interpolate to the get the density at the desired temperature.
3. Density at 15 Deg C and ASTM table to use
The previous two methods are useful and applicable for cargoes the
density for which changes proportionally with temperature.
These methods are mostly used for calculation of chemical cargoes.
But for petroleum products and crude oils, ASTM tables are used for
calculating cargo weights.
ASTM tables give the Volume correction factors (VCF) to find the volumes
at temperature for which the density is given.
Let us say cargo surveyor provided the density at 15 deg C as 0.816 and
ASTM table 54B to be used.
Let us use the same volumes and temperatures that we have used in our
initial example.
So first we need to find the VCF from ASTM table 54 for temperature 34
Deg C.
Go to ASTM table 54 and look under density@15 C of 816.0 and
temperature 34.0 Deg C.
So as we can see for temperature 34 Deg C, the volume correction factor
is 0.9830.
Similarly, we need to find the VCF for cargo temperatures of other tanks.
And when the VCF is applied to the volumes at observed temperature,
we get the volumes at 15 Deg C which is also called “Standard Volume”.
Here is how the ullage report would look like so far.
Now at many places may be using the standard volume instead of
weight. The standard volume of the cargo would also remain same as
this is the volume at the fixed temperature (15 Deg C).
But in any case, we still need the weight of the cargo as the stability
calculations need the weight of the cargo in each tank and not the
standard volume.
Getting the weight from standard volume is simple. We have the volume
at 15 Deg C and we have the density at 15 Deg C.
If we multiply these two, we get the weight by a simple formula.
But wait.
The density at 15 Deg C is always the density in Vacuum. So if simply
multiply this density with standard volume, we get the weight in
Vacuum.
So we then need to either convert the weight in vacuum to weight in the
air as we discussed earlier or we can simply convert the density in
Vacuum to density in Air.
There is a simple co-relation between density in vacuum and density in
the air.
And we call this as weight correction factor (WCF).
So in our case, the WCF would be: 0.8149.
When we apply this WCF to the standard volume, we get the weight of
cargo in Air.
In above ullage report, I have applied the WCF to the Gross standard
volume but we can easily make one additional column and apply the WCF
to the standard volume of each tank to get the weight in the air for each
tank.
4. API Gravity at 60 Deg F and ASTM Table to use
Ports like those in the US do not use the metric system and hence do not
use density.
Instead these port use API gravity at 60 Deg F.
And as you might have guessed correctly, these ports also do not
measure the temperature in Deg C but in Deg F.
Also, the volume is measured in Barrels and not in cubic meters.
So when in these ports, we need to have the volumes in Barrels and
temperature in Deg F.
This is not so difficult a task. There is a simple formula to convert these.
So for these ports here is what the volumes and temperatures in ullage
report would look like.
Following the same principle as earlier, we need to bring this volume to
volume at 60 Deg F.
And to do that we need to apply the volume correction factor.
We need to use a table that we can enter with provided API gravity at 60
Deg F and observed temperature in the tank to get the VCF (Volume
correction factor).
This the ASTM Table 6B.
Let us say the cargo surveyor has provided the API gravity at 60 F to be
66.0
Let us find the VCF for temperature 95 Deg F.
As we can see from table 6B, the volume correction factor for API at 60
Deg F of 66.0 and temperature 95 Deg F is 0.9748.
Of course, if the temperature or API is between the two values listed in
ASTM Table 6B, we need to interpolate to get the correct VCF.
Ok. So, in the same manner, we get the VCF (Volume correction factor)
for other required temperatures that we have measured in each tank.
And when we multiply the volume at observed temperature with VCF, we
get the standard volume, this time the volume at 60 Deg F.
We need to apply Weight correction factor (WCF) to the standard volume
to get the weight of the cargo.
There are different ASTM tables to get the WCF for the known API at 60
Deg F.

ASTM Tabel 9: To get the WCF to convert Barrels at 60 Deg F to Short
Ton in the air.

ASTM Table 11: To get the WCF to convert Barrels at 60 Deg F to Long
Ton in the air.

ASTM Table 13: To get the WCF to convert Barrels at 60 Deg F to Metric
Ton in the air.
Let us say we are interested in calculating the weight in Metric Tons in
the air.
In this case, we will use ASTM Table 13 to get the weight correction
factor (WCF).
So in the ASTM table, look for the API gravity 66 and find out the WCF
(which is given as Tonnes per Barrels).
So as we found out the weight conversion factor for API 66 is 0.11362.
We can apply this WCF to the standard volume to get the weight of cargo
in the air.
Now the final ullage report will look like this.
Other ASTM Tables
So far we know that we need to use ASTM table 54 (54A for crude oils
and 54B for products) for VCF and table 56 for WCF when we have been
provided with density at 15 C.
And In Port like US where API gravity at 60 F is provided, we need to use
ASTM Table 6 (6A for crude oils and 6B for products) for VCF.
And ASTM tables 9, 11 or 13 for WCG.
But there are other ASTM tables that supplement these tables that we
discussed so far.
For example, to calculate the weight of the cargo with ASTM table 6 (6A
or 6B), we need to have API gravity at 60F provided to us.
But what if we are provided with API gravity at some other temperature,
say at 80 deg F?
Then there is ASTM table 5 (5A for crude oils and 5B for products) that
can be used to convert API at any temperature to API at 60 Deg F.
Similarly, ASTM table 53 (53A for crude oils and 53B for products) can be
used to convert density at some temperature to the density at 15 Deg C.
Ohh!!! And what if you load a cargo from US where API Gravity at 60
Deg F is used and to discharge this cargo at a port where they want to
use Density at 15 Deg C.
Well, there is ASTM table 3 for converting API at 60 Deg F to Density at
15 Deg C.
While the ASTM tables that we discussed in previous sections are the one
that is used mostly, there are other ASTM tables that supplement these
main tables.
And even for the main ASTM tables, the information about which table
need to be used for cargo calculation is provided by cargo surveyor.
We need to follow the information provided by the cargo surveyor
because that would be the table that is used for shore calculations and
we need to use the same to avoid ship shore quantity difference.
Conclusion
Cargo calculations are sometimes tricky.
Not because these are difficult but because there are so many variations
to it.
But we need to understand that at the very basic level, we calculate the
volume from ullage tables and we need to be provided with density at
the same temperature as the cargo.
We multiply both and we get the weight of the cargo.
But for oil cargoes, we are either provided with density at 15 C or API at
60 F.
In this case, we need to get the volume correction factor (VCF) to
convert the volume at the observed temperature to the standard volume
which is volume at 15 Deg C or Volume at 60 F respectively.
We then need to apply the weight correction factor (WCF) to convert the
standard volume to weight.
Different ASTM tables provide the value for VCF and for WCF.
There are different ASTM tables for crude oil and for product oils.
The one with letter A is for crude oils and the one with letter B is for
product oil. ASTM tables without any letter are common for both crude
oils and product oils.
Get your hands on ASTM tables and you will find that cargo calculations
are not as difficult as it seems.