Read This and Benefit, in All Areas of Your Life
Knowing how to calculate a percentage is an essential skill that everyone needs to have, for work and outside. Now would you like to feel more comfortable calculating percentages, in your business and beyond? Well, you’ve come to the right place. In this article, we cover everything you need to know. So join our Percentage Calculating Skills Polish-up, and you won’t look back! Now here we go.
First Question – What is a Percentage?
A percentage is an amount out of 100 percent. Furthermore, the word ‘percent’ comes from centum, the Latin for a hundred. Also, instead of writing the word ‘percent’ in full when we write a percentage figure, usually, we use the sign ‘%.’
Let’s Get Started!
To start, you can calculate a percentage in various ways such as using a calculator, a phone or computer app, an Excel spreadsheet, or mentally. Either way, first you need to understand the basic sums.
How do you Calculate the Percentage of a Number?
The ‘percentage of a number’ means what amount out of 100 that number is of another number, known as ‘the whole.’ And to find what percentage a number, X, is of a second number, Y, we divide X by Y. This produces a third figure, the quotient.
Also, you can express the quotient either as a fraction or a number with a decimal point. When expressed as a decimal, it’s called the ‘decimal form’ of the percentage. Now from there, multiply the quotient in either form – fraction or decimal – by 100 percent to give the percentage, which you write with a ‘%’ sign next to it.
What is the Percentage Formula?
So this is another way to think about what you’re doing when you calculate a percentage. Write the expression ‘number divided by total times 100 percent equals percentage’ as an equation, x/y x 100% = z %. This equation is called the percentage formula.
Now leading on from this…
How do You Convert a Decimal to a Percentage?
You multiply the decimal by 100, which is the same as moving the decimal point two places to the right, and add a % sign.
So, 0.691 as a percentage is 0.691 x 100%, which gives 69.1%.
And while we’re here…
How do You Convert a Percentage to a Decimal?
Simply take away the percent sign and divide by 100. This is the same as moving the decimal point two places to the left.
So, 69.1% becomes 0.691.
Now in case it’s getting complicated, let’s look at…
How do you Calculate Percentages Easily, Without Using a Calculator?
To find what percentage a number X is of the total Y without using a calculator, first, we need to express X divided by Y as a fraction.
So, write the two figures as a fraction, X divided by Y, then simplify the fraction to its lowest form.
Simplifying means, say we need to calculate 35 as a percentage of 50. We can see at a glance that both numbers can be divided by 5, so we can write 35 over 50 as 7/10. We multiply this fraction by 100%. 7/10 is 7 times 10%, which is 70%.
For figures that don’t simplify to a round number like this, it’s best to use another method, like a calculator.
How Do You Calculate Percentages With a Calculator?
Let’s try this example. What percentage of 60 is 45? As a sum, this is 45 divided by 60.
- Enter the number 45 on your calculator, or the calculator app on your mobile.
- Press the ‘division’ or ÷ ‘key.’
- Enter the figure 60.
- Press the ‘answer’ or ‘=’ key to give the quotient, or decimal form, as above.
45 divided by 60 gives a quotient of 0.75. Multiply this by 100 (press X then enter 100, to give 75.)
This is the percentage. But you should still use the technique mentioned earlier to find the rough percentage, to check you’ve got it right.
What is The Percentage Difference Between Two Numbers?
This kind of calculation plays a major part in tracking results in business. Note that the difference between two numbers is either an increase or a decrease. Either way, the calculation involves finding the difference between them and expressing this figure as a percentage. Now this brings us to the next question.
How do you Calculate a Percentage Increase?
To find the percentage increase, divide the ‘after’ figure by the ‘before’ figure to give the quotient. Then you multiply the quotient by 100% and then subtract 100% to give the percentage increase.
Say the ‘after’ figure is 126 divided by the ‘before’ figure, 90. This gives a quotient of +1.4. Multiply +1.4 by 100 to give +140%. Take away 100% and we have a percentage increase of +40%.
Now, let’s do it the other way around.
How do you Calculate a Percentage Decrease?
This calculation also involves finding the difference between two numbers and expressing it as a percentage. This time we’re going from a higher number to a lower number.
Say the ‘after’ figure is 63 divided by the ‘before’ figure, 90. What is the percentage decrease?
First, we find the difference between the ‘before’ figure and the ‘after’ figure. This is 63 minus 90, which is -27. Divide -27 by the original number, 90. This gives a quotient of -0.3. Multiply this times 100 percent, and you get -30%. This is the percentage decrease.
Why Is It So Important to Know How to Calculate the Percentage of a Number?
There are three major reasons for knowing about this:
#1. We Use Percentages at Work in Many Different Ways
We use percentages to calculate performance against targets and track trends. Percentages help us find important information like profit margins, returns on investment, agency commissions, and mark-ups. We also use percentages to calculate VAT and duty payable.
#2. People Use Percentages to Grab Our Attention
Retailers use percentages to grab our attention with promotions, in-store and online. Also, percentages worry us in news stories about interest rates and inflation rates. And they depress us when we find out our kids’ school marks and the percentage of ‘baddie’ ingredients in our food.
#3. Percentages Help Us Live a Healthier Life
Doctors like to scare us by telling us our percentage risks chances of health problems if we don’t change our lifestyles. Percentages help us to be sensible about the alcohol in our drinks. So to fully understand percentages, and be healthier, you need to know what they mean.
Where can I find a Percentage Calculator Online?
You will have a calculator app on your smartphone, but there are also various percentage calculators online. Calculatorsoup.com has many different calculators, including one for percentages.
Simply follow the same steps as before. Enter the first figure. Key ‘divided by.’ Enter the second figure. Key “=” to give the quotient, or decimal form, as above. Multiply this figure by 100: press the X key then enter 100, to give 75. This is the percentage.
There are also calculators in computer apps like Excel. This brings us to…
How do you Calculate Percentages in an Excel Spreadsheet?
If you’re working in an Excel spreadsheet, to find what percentage the value in cell C2 is of the value in cell B2, select cell D2 and enter the formula “= C2/B2.” Working in the Home tab on your spreadsheet, go to the Number box and click on Percentage. This will give your answer as a percentage in cell D2.
Now here’s an example. Say we have a table with the customer’s name in the A column, orders in the B column, and deliveries in the C column. Smith’s Stores is in cell A2. They have ordered 30 units. This figure appears as 30 in cell B2. 25 units have been delivered so far, represented as 25 in cell C2.
To find the percentage of orders delivered to Smith’s Stores, we select cell D2 and enter the formula “=C2/B2.” Working in the Home tab on our spreadsheet, we go to the Number box and select Percentage. This gives an answer of 83.33% in cell D2.
Now Let’s Look at Some Different Ways We Use Percentages in Work
So here are some examples of situations involving percentages, for you to think about in our Percentage Calculating Skills Polish Up:
How Do You Calculate Percentages of Money?
To determine the percentage a sum of money is of the total, you use the same method we’ve been talking about. That is, divide the amount by the total amount, then multiply this figure by 100.
How Do You Work Out a Percentage Discount?
Say, I’m giving you £500 off a package that usually sells for £2,000. How much is the percentage discount? £500 divided by £2,000 is 0.25. 0.25 x 100% is 25%. So, I’m giving you a 25% discount.
How Do You Calculate a Percentage Markup?
If you buy something for £300 and sell it to your customer for £360, you are marking it up by £60. Now £60 divided by £300 is 0.2. Multiplied by 100%, this is 20%. So you are making a 20% markup.
How Do You Calculate Average Sales as a Percentage?
Say 5 salespeople sell 25, 30, 35, 40 and 50 units respectively against an individual target of 50 units. Then the total sales figure is 180 units, and the total target is 250.
Now what is the mean, or average, sales versus the target? To calculate the mean percentage, ie the average of the total, first we divide the total of all the units sold, by how many units there were. This gives us a mean value. Multiply this by 100% to give the mean percentage.
So, divide the 180 units sold in total by the number of salespeople, 5, to give the mean sales value, 36. Divide 36 by 50, the individual target, to give the quotient, 0.72. Multiply 0.72 by 100% to give the mean percentage the salespeople achieved of the target, which is 72%.
How Do You Calculate the Percentage for the Gross Profit Margin?
We calculate the gross profit from the sale, first of all, by working out the revenue from the sale minus the cost of the goods sold. So this is the gross profit. Now divide the profit by the costs of the goods to give the quotient. Then multiply the quotient by 100% to give the gross profit margin percentage.
Say we pay £40 for an item and sell it for £60. The gross profit is £20. Now divide the gross profit, £20, by the total revenue, £60, to give the gross profit margin, 0.33. Then multiply this by 100% to get the gross profit margin percentage, which is 33%.
How Do You Use Percentages to Calculate VAT?
To work out a price including the standard rate of VAT, which in the UK is 20%, multiply the price excluding VAT by 120%. Likewise, to work out a price that includes the reduced rate of VAT, which is 5%, multiply the price excluding VAT by 105%.
Note that removing 20% VAT is a very different calculation. To remove the VAT from a sum, you need to divide the figure by 120%, or 1.2. £100 divided by 1.20 is £83.33. Subtracting £83.33 from £100 comes to £16.67. This gives £16.67 as the VAT on an item sold for £100.
How Do You Use Percentages to Calculate APR?
If you want to borrow money from a bank or finance company, before you sign up with one, you need to compare the different lenders. One measure is the Annual Percentage Rate, or APR. This is the interest rate applied to the principal amount borrowed over a year. Yes, the lenders will do the calculations for you when they give you a quote, but it’s good to understand the sums.
So to calculate the APR:
- Calculate the interest rate the lenders are offering you. Multiply this by the principal borrowed to give the interest amount.
- Add the interest to the administrative fees. Divide this combined figure by the loan amount, the principal. Then divide this figure by the number of days in the loan term.
- Multiply the result by 365, for the days in a year. Then multiply the resulting figure by 100 to convert to the percentage APR.
Now let’s put this as an equation:
APR = ((Interest + Fees/Loan amount) / Number of days in loan term)) x 365 x 100%
Percentages are Also Important in Technology and Manufacturing
Here are a few examples:
1. How to Calculate Percentage Error or Uncertainty
The percentage error or uncertainty in a measurement is calculated as the uncertainty or margin for error divided by the measurement, times 100%. So, a 2 mm margin of error on a 100 mm measurement is a percentage error of 2%.
2. What is a Mass Percentage?
Mass percentage is a measurement of the concentration of a component in a mixture. The mass percentage is calculated as the mass of the component divided by the total mass of the mixture, times 100%. This is how you work out, for example, the fat content in milk.
3. How to Calculate a Percentage Yield
Percentage yield is a very important use of percentages in manufacturing. 100g of calcium carbonate produces 56g of calcium oxide, so 1g of carbonate produces 0.56g of oxide. The quotient is 0.56. Multiplied by 100%, this gives a percentage yield of 56%. Now we can use this to work out that 250g of calcium carbonate should produce 140g of calcium oxide.
One Last Tip – How do you Turn Marks into a Percentage Score?
Hopefully, you’ve found our Percentage Calculating Skills Polish-up useful, and you’re feeling much more confident. Before we go, here’s a last tip for those of you who are parents with school-age kids.
Knowing what percentage your kids’ marks are out of the possible total is important for parents. Luckily, the calculation is the same as we’ve been doing to find percentages. Simply divide the mark scored by the total to give the quotient. Then multiply the quotient by 100% to give the final percentage.
FINALLY: How Can I Get Better at Calculating Percentages? Practise, Practise, Practise!
Sorry, there’s no shortcut, practice makes perfect. But work at it and you should reach the point where you can figure out sums in your head, at least roughly, so you can double-check your work as you’re going along.
Updated: November 2023 by Charles Smith
