Content

• To step
• Part 1 of 2: Calculating percentage change in general cases
• Part 2 of 2: Special cases
• Tips
• Tips 2

In mathematics, a percentage change is used to indicate the relationship between an old value / quantity and a new value / quantity. Percent change expresses this difference as a percentage of the old value. In most cases where V.₁ represents the old, initial value and V.₂ the new or current value, the percentage change can be found with the formula ((V.₂-V.₁)/V.₁) × 100. Note that this unit is expressed as one percentage. See Step 1 below for an explanation of this procedure.

To step

Part 1 of 2: Calculating percentage change in general cases

1. Find old and new values ​​for a particular variable. As indicated in the introduction, the purpose of most percent change calculations is to determine the change of a variable versus time. For this you need two different values ​​- an old (or "start") value and a new (or "end") value. The equation for percent change gives the percent change of these two points.
   • You can find an example of this in the world of retail. When a particular product is reduced in price, this is often expressed as "X% discount "- in other words, as the percentage change from the old price. Suppose a particular type of pants used to cost $ 50 and now sell for $ 30. In this example, €50 the "old" value, and €30 is our "new" value. In the next step we will calculate the percentage change between these two prices.
2. Subtract the old value from the new. The first step in determining the percentage change between two values ​​is to find it difference. The difference between two numbers is found by subtracting the two values. The reason we subtract the old value from the new (and not the other way around) is because that very conveniently gives us a negative percentage as the final answer when the value decreases and a positive value when it increases.
   • In the example, we start with $ 30, the new value, and subtract $ 50. 30 - 50 = -€20.
3. Divide your answer by the starting value. Now take the answer you obtained and divide it by the starting value. This gives the proportional relationship of the change in values ​​from the old starting value, expressed as a decimal. In other words, this represents the total change in the value of your variable from its initial value.
   • In our example, dividing the difference (of the start and end values; - $ 20) by the start value ($ 50) will end up -20/50 = -0,40 return. Another way to think about this is that change from $ 20 in value is 0.40 out of $ 50 (the initial value), and that the change in value was in a negative direction.
4. Multiply your answer by 100 for the percentage. The percentage change is (logically) expressed in percentages, and not in decimals. To convert your decimal answer to a percentage, multiply it by 100. After that, all you have to do is add a percent sign. Congratulations! This value indicates the percentage change from the old to the new value.
   • To get the final answer in our example, we multiply the answer (-0.40) by 100. -0.40 × 100 = -40%. This answer means that the new price of € 30 for the pants is a 40% is lower than the old price of € 50. In other words, the pants are 40% cheaper. Another way to think about this is that the $ 20 difference in price is 40% less than the original $ 50 price - because this results in a lower final price, it will be given a negative sign.
   • Note that a positive answer as a final percentage implies an increase in the value of your variable. For example, if the final answer to the sample problem was not -40% but 40%, this would mean that the new price of the pants was $ 70; 40% more than the original price of € 50.

Part 2 of 2: Special cases

1. When dealing with variables where the value changes multiple times, only determine the percentage change for the two values ​​you want to compare. Determining the percentage change for a particular variable that changes in value more than once can seem a bit tricky, but the number of times a value changes doesn't make things more complicated than they are. The equation for a percentage change does not compare more than two values ​​at the same time. This means that if you are asked to calculate the percentage change in a situation where a variable with multiple value changes is involved, then only calculate the percentage change between the 2 indicated values. calculate not the percentage changes between each value in the series, after which you calculate an average or sum. This is not the same as the percentage change between two points and can easily produce nonsensical answers.
   • For example, suppose a pair of pants has a starting price of $ 50. After a discount this will be € 30 and after a price change € 40. Ultimately, after a final discount, the price comes to € 20. The percent change equation can yield the percent change between any two of these values; the other two values ​​are not necessary. For example, to find the percentage change between the starting price and the ending price, take $ 50 and $ 20 as the "old" and "new" values, respectively. Solve this as follows:
     • ((V.₂-V.₁)/V.₁) × 100
     • ((20 - 50)/50) × 100
     • (-30/50) × 100
     • -0,60 × 100 = -60%
2. Divide the new value by the old value and multiply by 100 to find the absolute relationship between both values. A process that is similar (but not identical) to the process used to determine the percentage change is used to determine the absolute percentage relationship between the "old" and "new" values. To do this, simply divide the old value by the new value and multiply it by 100 - this will give you a percentage that directly compares the new value to the old one, rather than expressing the change between the two.
   • Note that by subtracting% 100 from this answer you will get the percentage change again.
   • Let's use this process for along with the discounted pants example. If the pants have a starting price of € 50 and end at € 20, then it follows: 20/50 × 100 = 40%. This tells us that $ 20 equals 40% of $ 50. Note that by subtracting 100% we get the percentage change as calculated above: 40 - 100 = -60%.
   • This process can yield answers above 100%. For example, already € 50 is the old price and €75 the new price, then: 75/50 × 100 = 150%. This means that 75 € is equal to 150% of 50 €.
3. In general, you use absolute change when you are dealing with 2 percentages. The terminology used to calculate percentage change can sometimes be confusing when the two compared values ​​are themselves percentages. In those cases it is important to distinguish between percentage change and absolute change. The latter is the exact number of percentage points that the new value differs from the old value - not the now familiar concept of percentage change as we have dealt with it.
   • For example, suppose a pair of shoes are offered at a discount of 30% (a percentage change of -30% from the old price). If the discount is increased to 40% (a percentage change of -40% from the old price) then it is not incorrect to say that the percentage change of this discount is equal to ((-40 - -30) / -30) × 100 = 33,33%. In other words, the pants have a discount that is 33.33% "higher" than the previous discount.
   • But, this is usually indicated as a "10 percent higher discount". In other words, we usually refer to the absolute change of two percentages than the percent change.

Tips

• If the regular price of an item is $ 50.00 and you bought it on sale for $ 30.00, then the percentage change is equal to:
  • (€50,00 - €30,00)/€50,00 × 100 = 20/50 × 100 = 40%
    
    The price you bought it for was lower than the original price, so this is a 40 percent drop. So you have saved 40% on the starting price.
• Now suppose you want to sell the purchased pants again. For example, if you bought the pants for $ 30 and you later sell them for $ 50, the change would be $ 50 - $ 30 = $ 20. The initial value was $ 30, so the percentage change is:
  • (€50,00 - €30,00)/€30,00 × 100 = 20/30 × 100 = 66,7%
    
    So the value of the pants increased by 66.7% of the original price. A price increase of 66.7%.
• When the value of the pants fell from € 50 to € 30, the depreciation amounted to 40%. When the pants increased in price from € 30 back to € 50, the increase in value was 66.7%. But it's important to note that the win rate at a price of € 50 it was still no more than 40%, because it is based on the increase of € 20. This is in contrast to the valuation value.

Tips 2

• (€50,00 - €30,00)/€50,00 × 100 = 20/50 × 100 = 40%