How To Calculate Percentages Into Grams

You can only calculate a percentage as a figure in grams in some limited situations. If you have a portion of food that is 6 percent fat, and you want to know how much fat you'd be consuming in grams if you ate the food, you can perform the calculation. However, a percentage is a general term for a proportion out of a hundred, so you can only calculate percentages into grams when it's a percentage of a certain mass. To calculate it, you convert the percentage you want into a decimal proportion and then multiply that proportion by the mass of the whole 100 percent.

If the percentage is the proportion of a certain amount of mass, calculate percentages into grams using the formula:

\(\text{mass in grams} = \text{total mass in grams}\times \frac{\text{percentage of mass}}{100}\)

Percent means "per hundred." So, if 10 percent of people are left-handed, and you pick out 100 people, statistically, 10 of them will be left-handed. Work out something as a percentage by taking the number of things you're interested in from a sample and dividing it by the total number of things in the sample. This gives you a proportion out of one. Multiply this by 100 to make it a percentage. For example, if you have a group of 30 people and three are left-handed, you calculate the percentage as follows:

\(\text{percentage of left-handers}=\frac{\text{number of left-handers}}{\text{total number of people}}\times 100 \=\frac{3}{30}\times 100 \=0.1\times 100 = 10\text{ percent}\)

You can only convert percentages into grams when the percentage relates to a mass. For example, imagine you're going on holiday and your case can have a mass of up to 20 kg to be accepted onto the flight. If you're 60 percent of the way to hitting the limit, this percentage tells you the amount of the total allowed mass you've used up. The percentage represents a mass, so you can do the conversion. In a situation like the percentage of left-handed people in the last section, there is no mass involved, and so you can't convert the percentage to a mass.

For percentages of a mass, you can perform the conversion between percentages and grams. For example, if you have a 250 g portion of food that is 8 percent fat, what is the number of grams of fat in the portion?

First, turn the percentage into a decimal number. Divide the percentage by 100, or equivalently, move the decimal place two spots to the left to do this. This means 25 percent is 0.25, 44 percent is 0.44 and 10 percent is 0.1. Using this same method, 8 percent is 0.08.

Multiply the decimal number by the total (100 percent) of the mass that you're interested in. In this example, the total size of the food portion is 250 g, so the mass of fat is:

\(\text{mass of fat in grams} = 250\text{ g}\times 0.08 = 20\text{ g}\)

There are 20 grams of fat in the meal. The general formula for converting a percentage into grams is:

\(\text{massin grams} = \text{ total mass in grams}\times \frac{\text{percentage of mass}}{100}\)

Using the luggage example with a 60 percent full case, 20 kg = 20,000 g, so:

\(\text{mass in grams} = 20,000\text{ g}\times \frac{60\text{ percent}}{100}=20,000\text{ g}\times0.6=12,000\text{ g}\)

This means the case at 60 percent of the maximum allowed mass is 12,000 g or 12 kg.