how to use percent button on calculator

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The Windows calculator

The Windows calculator percent sign works the same way as those cheap pocket calculators (which are often called four-function calculators even though they have around six function nowadays). What you first have to understand is that the percent key on those pocket calculators was not designed for mathematicians and engineers. It was designed for your everyday person doing some simple calculations.

so…

Therefore, the behavior of the key to you, an engineer, seems bizarrely counter-intuitive and even buggy. But to an everyday person, it makes perfect sense. Or at least that’s the theory.

example

Let’s look at it from the point of view of that everyday person. Suppose you want to compute how much a $72 sweater will cost after including 5% tax.¹ Pull out your handy pocket calculator² (or fire up Calc if you don’t have a pocket calculator) and type

72 + 5% =

The result is 75.6, or $75.60, which is the correct answer, because 5% of 72 is 3.6. Add that to 72 and you get 75.6.

Similarly, suppose that sweater was on sale at 20% off. What is the sale price?

72 − 20% =

The result is 57.6 or $57.60. This is the correct answer, because 20% of 72 is 14.4. Subtract that from 72 and you get 57.6.

You can chain these percentage operations, too. For example, how much will you have to pay for that 20%-off sweater after adding 5% tax?

72 − 20% + 5% =

The result is 60.48. A mathematician or engineer would have calculated the same result via the equivalent computation:

72 × 0.80 × 1.05 =

Okay, now that we see how the calculator product designer intended the percent key to be used, let’s look at what the calculator engineer it has to do in order to match the specification. When the user enters A + B % =, the result should be A × (1 + B/100) or A + (A × B/100) after you distribute the multiplication over the addition. Similarly, when the user enters A − B % =, the result should be A × (1 − B/100) or A − (A × B/100).

Aha, the calculator engineer says, we can achieve this result by defining the percent key as follows:

When the user enters a value, an operator, a second value, and then the percent key, the first two values are multiplied and the product divided by 100, and that result replaces the second value in the ongoing computation.

Let’s walk through that algorithm with our first example.

You type	Remarks
72	First value is 72
+	Operation is addition
5	Second value is 5
%	72 × 5 ÷ 100 = 3.6
	3.6 becomes the new second value
=	72 + 3.6 = 75.6, the final result

If you watch the display as you go through this exercise, you will even see the number 3.6 appear in the display once you press the % key. The percentage is calculated and replaces the original value in the ongoing computation.

This algorithm also works for the chained percentages.

You type	Remarks
72	First value is 72
−	Operation is subtraction
20	Second value is 20
%	72 × 20 ÷ 100 = 14.4
	14.4 becomes the new second value
+	72 − 14.4 = 57.6, intermediate result
	57.6 is the new first value
	Operation is addition
5	Second value is 5
%	57.6 × 5 ÷ 100 = 2.88
	2.88 becomes the new second value
=	57.6 + 2.88 = 60.48, the final result

This even works for multiplication and division, but there is much less call for multiplying or dividing a number by a percentage of itself.

500 × 5 % =

The result of this is 12,500 because you are multiplying 500 by 5% of 500 (which is 25). The result of 500 × 25 is 12,500. You aren’t computing five percent of 500. You’re multiplying 500 by 5% of 500. (It appears that the authors of this Knowledge Base article didn’t consult with the calculator engineer before writing up their analysis. The percent key is behaving as designed. The problem is that the percent key is not designed for engineers.)

What if you want to compute 5% of 500? Just pick a dummy operation and view the result when you press the percent key.

500 + 5 %

When you hit the percent key, the answer appears: 25. You could’ve used the minus key, multiplication key, or division key instead of the addition key. It doesn’t matter since all you care about is the percentage, not the combined operation. Once you hit the % key, you get your answer, and then you can hit Clear to start a new calculation.

Footnotes

¹In the United States, quoted prices typically do not include applicable taxes.

²In my limited experiments, it appears that no two manufacturers of pocket calculators handle the percent key in exactly the same way. Casio appears to handle it in a manner closest to the engineering way. TI is closer to the layman algorithm. And when you get into cases like 1 ÷ 2 %, calculators start wandering all over the map. Should the answer be 50, since 1/2 is equal to 50%? Or should it be 0.005 since that is the numeric value of 0.5%? Should that answer appear immediately or should it wait for you to hit the equals sign? I don’t know what the intuitive result should be either.

How to Use a Calculator for Percentages

Learning to use the percent key on your calculator will make your life a lot easier. The percent sign works with multiplication, addition and subtraction. Use multiplication to calculate a percentage of a number, such as when figuring a tip. Use addition and subtraction for calculating percentage increases or decreases, such as when figuring out markups or discounts. By following a few simple tips and examples, you can learn how to use a calculator to quickly figure percentages. Note that not all calculators behave the same way as far as the percent key is concerned. If your calculator does not have the percent key, don’t despair. You can still use it to calculate percentages; you will just have to press a few more buttons.

Step 1

Calculate a tip on your restaurant bill. Suppose your bill happens to be $64.35 and you would like to leave a 15 percent tip. Type the following into your calculator: 64.35 * 15 % Answer: 9.6525 or $9.65 after rounding.

Most simple calculators

Most simple calculators will give an answer right here without having to press the = sign. If yours does not, press = and see if you get the right answer. Alternatively, you can calculate this percentage by typing in 64.35 * 15 / 100 or 64.35 * 0.15 (All that the percent key did here was division by a hundred.)

Step 2

Calculate a sale price. If you bought shoes that originally cost $139, but are now discounted by 35 percent, type the following in your calculator: 139 – 35 % = Answer: 90.35 or $90.35

This calculation is amazingly easy with the percent key. Alternatively, you would first have to calculate what 35 percent of $139 is and then subtract that answer from 139: 139 * 35 / 100 = 48.65 139 – 48.65 = 90.35.

Step 3

Calculate multiple discounts on an item and add the sales tax. Suppose those shoes from the previous step went on clearance for an additional 40 percent off — so 35 percent off, 40 percent off on top of that and then an additional 5 percent sales tax. Again, it’s easy with the percent key: 139 – 35 % – 40 % + 5 % = Answer: 56.9205 or $56.92 after rounding.

So you can add or subtract any increases or decreases in percentages using the percent key. It gets a bit more involved to do this without the percent key, however. You would have to do it the same way as in Step 4 for each subsequent percentage increase or decrease.

How to Calculate Final Price of an Item On Sale.

When you are shopping and find something on sale for 10 percent off of original price, it’s easy to figure out how much the item will be with the discount. But for numbers like 35 percent off, it’s a little harder. With a few simple tips, there are easy ways to do it.

Step 1

If the article you want to buy is 10 percent off of the marked price, it’s easy to figure out. If the scarf originally cost $12 and it’s now 10 percent off that price, simply subtract $1.20 from $12. Once you know that, it’s easy to figure out any of the other discounts that might arise.

Step 2

If the coat you want to buy to match your scarf originally cost $129.99, but is now 35 percent off, first round the price off to $130, in which case 10 percent of $130 is $13. Since you are getting 35 percent off, add $13 three times, which is 30 percent. So, in other words, 30 percent of $130 would be $39. What about the other 5 percent? You know you’re already getting $39 off because 10 percent was $13. Half of $13 is $6.50, so $6.50 is 5 percent off of $130. We already had $39 off the total and now we add the $6.50 for a total of $45.50 off of the original price.

Step 3

To get the total price of the coat after the 35 percent discount, subtract $45.50 from $130. If you are having trouble and can’t calculate it in your head, do it the easy way and subtract $40 from $130. That comes out to $90. Then subtract another $5 to get $85. And let’s not forget the 50 cents. So your total cost of the coat after the discount would be $84.50. Now you have to worry about tax. You can calculate the tax the same way, just adding the numbers to the total.