# Percentage Decrease Formula

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## Percent Decrease Formula

Percent decrease refers to the percentage change in the value when it is decreased over a period of time. For example, a decrease in the level of rainfall, a decrease in the number of Covid patients, etc. Percent decrease can be calculated by using the percent decrease formula. In this section, we will be discussing the percent decrease formula. Let us learn the percent decrease formula with a few solved examples.

## What is Percent Decrease Formula?

The percent decrease formula gives the decrease in quantity with respect to its initial value. To calculate the decrease in percentage, we first need to find the difference in the values. Then, divide the difference by the initial value and multiply it by 100. The percent decrease formula is given as:

## Percent Decrease Formula

There are two simple steps to calculate the percent decrease using the percent decrease formula, they are:

• Step 1: Find out the difference between the numbers, i.e., Decrease = Old value – New value
• Step 2: Divide the decrease by the old value and multiply it by 100. This makes the percent decrease formula, Percent Decrease = [(Old Value – New Value) / Old Value] × 100]

## Percentage Increase and Decrease

Percentage increase and decrease is the percentage change in the value. Percentage change is the difference between the new value and the old value that is given. In order to find the percentage change, this difference is divided by the old value and multiplied by 100 to get the percentage increase or decrease.

Now, it should be noted that when the new value is more than the old value, then it is a percentage increase. For example, if the price of a book changes from $5 to$8, there is an increase in the price. Whereas, when the old value is greater than the new value, in that case, it is a percentage decrease. For example, if the price of a table changes from $10 to$8, there is a decrease in the price.

## Examples Using Percent Decrease Formula

Example 1: The number 53 is misread as 35. Find the percent decrease using the percent decrease formula.

Solution:

Here, new value = $35 and old value =$53

Using the Percent decrease formula, we get

Percent Decrease = [(Old Value – New Value) / Old Value] × 100

= [(53 – 35)/53] × 100

= 18/53 × 100

= 33.9%

Therefore, the percent decrease of the number is approximately 34%

Example 2: An article whose CP is $250 was sold for$230. Use the percent decrease formula to find the percent decrease in the price of the article.

Solution:

Here, new value = $230 and old value =$250

Using the Percent decrease formula, we get

Percent Decrease = [(Old Value – New Value) / Old Value] × 100

= [(250 – 230)/250] × 100

= 20/250 × 100

= 8%

Therefore, the percentage decrease in the price of the article is 8%.

Example 3: A fruit seller used to sell strawberries for $80 per dozen. Now, he reduced the cost of a dozen strawberries by 5%. What is the price of a dozen strawberries now? Calculate by using the percent decrease formula. Solution: Let the new value for a dozen strawberries be x. According to the percent decrease formula, Percent Decrease = [(Old Value – New Value) / Old Value] × 100 It is given that percent decrease = 5%; New value = x, old value = 80 So, putting these values in the equation, 5 = [(80 – x)/80] × 100 x = 76 So, the new price of a dozen of strawberries is$76.

## FAQs on Percent Decrease Formula

### What is meant by Percent Decrease?

Percent decrease refers to the percent change in the value when it is decreased over a period of time. Percentage decrease expresses the decrease in the given value with respect to its initial value in the form of a percentage.

### What is the Formula for Percent Decrease?

The percent decrease formula is formed when we find the difference between the old value and the new value, divide it by the old value and multiply it by 100. The percent decrease formula is expressed as:

Percent Decrease = [(Old Value – New Value) / Old Value] × 100]

### What are the Steps to Calculate the Percent Decrease using the Percent Decrease Formula?

There are three simple steps to calculate the percent decrease using the percent decrease formula, they are:

• Step 1: Find out the difference between the numbers, i.e., Decrease = Old value – New value
• Step 2: Divide this ‘decrease’ by the old value and multiply it by 100. This makes the percent decrease formula, Percent Decrease = [(Old Value – New Value) / Old Value] × 100]
• Step 3: The given values are substituted in the formula to find the percentage decrease.

### Using the Percent Decrease Formula, Calculate the Percent Decrease in the price of Pencils from $12 to$9.

We will use the percent decrease formula to calculate the percentage decrease in the price of pencils. In the given example, new value = $9 and old value =$12. Percent Decrease = [(Old Value – New Value) / Old Value] × 100. Substituting the values in the formula, Percent Decrease = [(12 – 9)/12] × 100 = 25%. Therefore, the percent decrease in the price of pencils is 25%.

### What is the Percent Decrease from 20 to 16?

The percentage decrease from 20 to 16 can be calculated using the formula, Percent Decrease = [(Old Value – New Value) / Old Value] × 100. In this case, old value = 20, new value = 16. So, after substituting the values in the formula, Percent Decrease = [(20 – 16) / 20] × 100 = 20%

### What is an Example of Percent Decrease?

Examples of percentage decrease can be seen in our day-to-day lives. Suppose the price of fuel decreases from $7 to$4. The percentage decrease of the fuel price can be calculated by using the formula, Percent Decrease = [(Old Value – New Value) / Old Value] × 100. Here, old value = 7, new value = 4. So, after substituting the values in the formula, Percent Decrease = [(7 – 4) / 7] × 100 = 42.8%

### What is the Percentage Decrease from 12500 to 11625?

The percentage decrease from 12500 to 11625 can be calculated using the formula, Percent Decrease = [(Old Value – New Value) / Old Value] × 100. In this case, old value = 12500, new value = 11625. So, after substituting the values in the formula, Percent Decrease = [(12500 – 11625) / 12500] × 100 = 7 %

## Example Problem: Percentage Decrease

You have a lamp with a 60-watt traditional light bulb. Your lamp uses 60 watts of electricity per hour. You’re considering replacing the bulb with an LED light bulb that uses 8 watts of electricity per hour. What is the percentage decrease in the lamp’s hourly energy use if you switch to an LED light bulb?

Percentage Decrease = [ (Starting Value – Final Value) / |Starting Value| ] × 100

60 – 8 = 52
52 / 60 = 0.8667
0.8667 × 100 = 86.67%

## What is percentage decrease?

Percentage decrease is the difference between starting and ending values. It shows a loss of value from the original expressed as a percentage regardless of units. The amount of decrease is the original amount minus the final amount.

For instance, if you spent $200 to heat your home last month, but only$140 this month, the cost has decreased by $60. Expressed as a percentage decrease, you can conclude the cost of heating your home has decreased by 30%. ## How to calculate percentage decrease Use these steps and formula to calculate percentage decrease: Percentage decrease = (starting value – ending value)/starting value x 100 1. Determine the starting value and ending value. For example, Joe is considering changing jobs. He works for a company making$22.75 per hour. He has been offered a position closer to home that pays $20.50 per hour. To find the percentage decrease in pay: 2. Subtract the ending value from the starting value. *Using the example above, subtract the new rate of pay from the original rate of pay.$22.50 – $20.20 =$2.25*
3. Divide this number by the starting value.
*Divide this number, the difference between rates of pay, by the original rate of pay. $2.25 /$22.50 = .1*
4. Multiply by 100 to find the percentage change (Note: if the percentage is a negative, this means the percentage change is positive.)
*Multiply this number by 100 to determine the percentage decrease. .1 x 100 = 10% decrease*

If Jose takes the new job, his pay would decrease by 10%.

## Examples of how to calculate percentage decrease

The following examples show how to solve for percentage decrease when given a starting and ending value:

Example 1

Brenda scored an 87 on her first biology test and an 82 on her second biology test. To find the percentage decrease between test scores:

1. *Subtract the new test score from the old test score. 87 – 82 = 5*
2. *Divide the difference of the two scores by the original test score. 5 / 87 = .057 (rounded)*
3. *Multiply this number by 100 to determine the percentage decrease. .057 x 100 = 5.7%*

The rate of percentage decrease between Brenda’s test scores was 5.7%.

Example 2

Dianne averaged 70 mph driving to St. Petersburg. On the return trip during rush hour, she averaged 54 mph. To find the percentage decrease in her rate of travel:

1. *Subtract the new rate of travel from the original rate of travel. 70 mph – 54 mph = 16 mph*
2. *Divide this difference by the original rate of travel. 16mph / 70mph = .229 (rounded)*
3. *Multiply this quotient by 100 to determine the decrease as a percentage. .229 x 100 = 22.9%*

The decrease in the rate of travel between trips was 22.9%. Dianne traveled 22.9% more slowly on her second trip.

Example 3

If the results indicate a negative percentage decrease, this means the rate of change is positive. This is most likely to occur as a result of misunderstanding the problem. When calculating for a rate of decrease between an original cost of $75 and a new cost of$80:

1. *Subtract the second cost from the original cost. $75 –$80 = -$5* 2. *Divide the difference by the original cost. -5 / 75 = -.067* 3. *Multiply by 100 to express the number as a percent. -.067 x 100 = -6.7%* 4. Recognize the negative means that the answer is the opposite of a rate of decrease. Instead, it expresses a rate of increase. In this case, the rate of cost increase is 6.7%. ## How to calculate value based on percentage decrease Use the following steps and formula to calculate value based on percentage decrease: New value = original value – (percentage decrease/100 x original value) You may know the percentage decrease and the starting value but want to find the ending value. For example, you might consider paying a service fee of$9.75 per month for a streaming service running a promotion of a 20% discount for one month. The discounted rate would be $7.80 for the first month. Here’s how to calculate this: 1. Convert the percentage decrease into a decimal by dividing by 100. 2. Multiply the resulting decimal by the starting value. 3. Subtract this value from the starting value. 4. This is the new value based on the given percentage decrease. Much like in the previous examples, the most common errors involve arithmetic. In the case of calculating value based on percentage decrease, the most common is forgetting to subtract the change in value from the original. ## Examples of how to calculate value based on percentage decrease The following examples include the steps to finding a new value when given a starting value and the percentage decrease: Example 1 Crystal uses a home cleaning service that charges$125 per visit. She receives a coupon for 30% off her next home cleaning. To find the cost of her next home cleaning:

1. *Convert the percentage decrease into a decimal by dividing by 100. 30% / 100 = .30*
2. *Multiply the original cost by the decrease to find the value of the discount. .30 x $125 =$37.50*
3. *Subtract the value of the discount from the original cost. $125.00 –$37.50 = $87.50* By using the percentage decrease, the cost of Crystal’s next home cleaning is$87.50 and, further, her savings is $37.50. Example 2 Deondre pays$114 per month for his cell phone. He sees an advertisement that a cellular provider will beat his existing monthly rate by 25%. To find the new provider’s rate:

1. *Convert the percentage decrease into decimal form by dividing by 100. 25% / 100 = .25*
2. *Multiply this decimal by the original cost to determine the discounted rate. $114 x .25 =$28.50*
3. *Subtract the discount from the original cost to determine the new rate. $114.00 –$28.50 = $85.50* Deondre’s new rate will be$85.50 per month. His savings is $28.50 per month. Example 3 One year ago, Andrea bought a new car for$21,350. Her accountant tells her it has lost 17% of its value since then. To find the value of Andrea’s car now:

1. *Convert the percentage decrease into decimal form by dividing by 100. 17% / 100 = .17*
2. *To determine the loss of value multiply this decimal by the original cost. $21,350 x .17 =$3,629.50*
3. *Subtract the loss of value from the original value. $21,350 –$3,629.50 = $17,720.50* Andrea’s car is now worth$17,720.50. Her car lost $3,629.50 in value, or depreciated, over the first year. ## Formula for Percent Decrease Percentage decrease formula can be obtained by simply dividing the decreased value by the original value and multiplying that with 100. Here, • Decreased Value = Original Value – New Value This formula for percentage decrease will help to solve several questions. Some important questions involving this formula are given below. ### Example Questions Using Percent Decrease Formula Example 1: A shopkeeper used to sell a pair of pens for Rs. 25. He then reduced the price of the same pair of pens to Rs. 21. Calculate the percentage decrease in cost. Solution: In this question, the decrease amount is = Rs. (25 – 21) = Rs. 4 Now, the decrease in percentage = (4/ 25) × 100 = 16% Example 2: A fruit seller used to sell bananas for Rs. 40 per dozen. Now he reduced the cost of a dozen bananas by 10%. What is the price of a dozen bananas now? Solution: Let the new value for a dozen bananas be Rs. x. Now, decrease value = Rs. (40 – x) According to the percent decrease formula, % D = (Decrease/ Old value) × 100 It is given that %D = 10. So, putting these values in the equation, 10/100 = (40 – x)/40 => 40 – x = 4 => x = 36 So, the new price of a dozen of bananas is Rs. 36. Example 3: The cost of a membership card of a club was reduced by 20% and costs Rs. 550 now. What was the original price of the membership card before its cost reduced? Solution: Let the original cost be Rs. x As the new cost is Rs. 550, decrease = Rs. (x – 550) %D = decrease/original × 100 ∴ (x – 550)/x = 20/100 So, 5x – 2750 = x => x = 687.5 Hence, the original price was Rs. 687.5. ### Examples of Percentage Decrease Formula (With Excel Template) Example #1 Let us take the example of John, who invested$500 to purchase 10 equity shares of company XYZ Ltd last year. In the current year, he again purchased 15 more equity shares of the company for $600. Check whether the price has declined in the current year and if yes, then calculate the percentage decrease in the equity share price. Solution: Therefore, it can be seen that the equity share price has declined from$50 last year to $40 in the current year. Percentage Decrease is calculated using the formula given below Percentage Decrease = (Equity Share Price Last Year – Equity Share Price Current Year) / Equity Share Price Last Year * 100 • Percentage Decrease= ($50 – $40) /$50 * 100
• Percentage Decrease= 20%

Therefore, the equity share of XYZ Ltd decreased by 20% during the last year.

Example #2

Let us take the example of crude oil price that has witnessed significant volatility with a downward trend during the last year. The crude price was $68.58 per barrel as of June 22, 2018, while the crude price has gone down to stand at$57.43 per barrel today, i.e. June 21, 2019. Calculate the percentage decrease in the crude oil price.

Solution:

Percentage Decrease is calculated using the formula given below

Percentage Decrease = (Crude Price One Year Back – Crude Price Today) / Crude Price One Year Back * 100

• Percentage Decrease = ($68.58 –$57.43) / $68.58 * 100 • Percentage Decrease = 16.26% Therefore, the crude price had decreased by 16.26% during the last year. Example #3 Let us take the example of Apple Inc.’s total asset size. As per the annual report for the year ending on September 29, 2018, the total asset size had decreased from$375,219 million in 2017 to $365,725 million in 2018. Calculate the percentage decrease in Apple Inc.’s asset size during the last one year. Solution: Percentage Decrease is calculated using the formula given below Percentage Decrease = (Total Assets in 2017 – Total Assets in 2018) / Total Assets in 2017 * 100 • Percentage Decrease = ($375,219 – $365,725) /$375,219 * 100
• Percentage Decrease = 2.53%

Therefore, the total asset size of Apple Inc. had decreased by 2.53% during the financial year 2018.

Explanation

The formula for percentage decrease can be derived by using the following steps:

Step 1: Firstly, note the original value of the variable at the beginning of the period.

Step 2: Next, determine the new value of the variable at the end of the period, which is lower than its original value.

Step 3: Next, determine the change or decrease in the value of the variable over the period of time by deducting the new value of the variable from its original value, as shown below.

Decrease in Value = Original Value – New Value

Step 4: Finally, the formula for percentage decrease can be derived by dividing the change in value by the original value of the subject variable and then multiplying the result by 100% to express the result in terms of percentage, as shown below.

Percentage Decrease = Decrease in Value / Original Value * 100%

Percentage Decrease = (Original Value – New Value) / Original Value * 100%

## Percentage decrease examples

Example 1: non-calculator

Decrease £80 by 30%

1. Calculate 30% of £80

To do this without a calculator, the easiest way is to calculate 10% (by dividing by 10) and then multiply by 3 to get 30%.

10% of £80 = £8

30% of £80 = £24

2 Subtract it from the initial value

£80 – £24 = £56

Example 2: non-calculator

Decrease 250km by 45%

Calculate 45% of 250km

10% of 250km = 25km

40% of 250km = 100km

5% of 250km = 12.5km

45% of 250km = 112.5km

Subtract it from the original value

250–112.5=137.5km

Example 3: calculator

Decrease 760 by 39%

Calculate 39% of 760

This time we are going to use a calculator. When using a calculator we divide the value by 100 to find 1% and then multiply by the percentage that we want.

760÷100=7.67.6×39=296.4

Subtract it from the original value

760–296.4=463.6

Example 4: calculator

A jumper costing £13.20 is reduced by 15% in a sale. Calculate the new price of the jumper.

Calculate 15% of £13.20

Subtract it from the original price

£13.20 – £1.98 = £11.22

## How to decrease a value by a percentage using a percentage multiplier

We can decrease a value by a percentage using a percentage multiplier. A percentage multiplier is a decimal that is related to the percentage you are trying to find.

1. Subtract the percentage we are decreasing by from 100%

We subtract it from 100% because we are decreasing the value and 100% represents the original value.

2. Convert to a decimal

3. Multiply the original amount by the decimal

Example 5: using a multiplier

Decrease 84m by 46%

Here we are calculating a 46 percent decrease so subtract 46% from 100%

Convert to a decimal. To do this we divide the percentage by 100.

Multiply the starting value by the decimal

Example 6: using a multiplier

Daniel has £3600. He spends 27.5% of his money. How much does he have left?

This is a 27.5 percent decrease so subtract 27.5% from 100%

Convert to a decimal.

Multiply the value by the decimal

## Calculating percentage decrease

Given two values, we can calculate the percentage difference. This can also be called percentage decrease or percentage loss.

We can calculate percentage change using the percentage change formula:

The same formula can be used to calculate percentage increase.

1. Work out how much the value has changed by subtracting the final value from the original value
2. Apply the percentage change formula

Example 7: calculating percentage change

Ricky weighed 70kg in March. By June his weight had decreased to 64.4kg. Calculate the percentage decrease in his weight.

His weight has changed from 70kg to 64.4kg. Work out the change:

Apply the percentage change formula. The change is 5.6kg and the original amount is 70kg.

Percentage decrease = 8%

Example 8: calculating percentage loss

Louise buys a car for £7500 and sells it for £6150. Calculate Louise’s percentage loss.

The value has changed from £7500 to £6150. Work out the change:

£7500 – £6150 = £1350

Apply the percentage change formula. The change is £1350 and the original amount is £7500.

### Common misconceptions

• Converting between percentages and decimals

Incorrectly converting percentages to decimals. The most common mistakes are with single digit percentages (e.g. 5%), multiples of 10 (e.g. 40%) and decimal percentage (e.g. 3.2%)

Remember to divide the percentage by 100 to find the decimal.

E.g.

• Using an incorrect value for the denominator in the percentage decrease formula

Using the new value instead of the original value for the denominator when calculating percentage change

### Examples – Percentage Increase and Decrease

In January Dylan worked a total of 35 hours, in February he worked 45.5 hours – by what percentage did Dylan’s working hours increase in February?

To tackle this problem first we calculate the difference in hours between the new and old numbers.  45.5 – 35 hours = 10.5 hours.  We can see that Dylan worked 10.5 hours more in February than he did in January – this is his increase.  To work out the increase as a percentage it is now necessary to divide the increase by the original (January) number:

10.5 ÷ 35 = 0.3  (See our division page for instruction and examples of division.)

Finally, to get the percentage we multiply the answer by 100.  This simply means moving the decimal place two columns to the right.

0.3 × 100 = 30

Dylan therefore worked 30% more hours in February than he did in January.

In March Dylan worked 35 hours again – the same as he did in January (or 100% of his January hours).  What is the percentage difference between Dylan’s February hours (45.5) and his March hours (35)?

First calculate the decrease in hours, that is: 45.5 – 35 = 10.5

Then divide the decrease by the original number (February hours) so:

10.5 ÷ 45.5 = 0.23 (to two decimal places).

Finally multiply 0.23 by 100 to give 23%. Dylan’s hours were 23% lower in March than in February.

You may have thought that because there was a 30% increase between Dylan’s January hours (35) and February (45.5) hours, that there would also be a 30% decrease between his February and March hours. As you can see, this assumption is incorrect.

The reason is because our original number is different in each case (35 in the first example and 45.5 in the second). This highlights how important it is to make sure you are calculating the percentage from the correct starting point.

Sometimes it is easier to show percentage decrease as a negative number – to do this follow the formula above to calculate percentage increase – your answer will be a negative number if there was a decrease.  In Dylan’s case the increase in hours between February and March is -10.5 (negative because it is a decrease). Therefore   -10.5 ÷ 45.5 = -0.23.  -0.23 × 100 = -23%.

Dylan’s hours could be displayed in a data table as:

## Calculating Values Based on Percentage Change

Sometimes it is useful to be able to calculate actual values based on the percentage increase or decrease.  It is common to see examples of when this could be useful in the media.

UK rainfall was 23% above average this summer.
Unemployment figures show a 2% decline.
Bankers’ bonuses slashed by 45%.

These headlines give an idea of a trend – where something is increasing or decreasing, but often no actual data.

Without data, percentage change figures can be misleading.

Ceredigion, a county in West Wales, has a very low violent crime rate.

Police reports for Ceredigion in 2011 showed a 100% increase in violent crime. This is a startling number, especially for those living in or thinking about moving to Ceredigion.

However, when the underlying data is examined it shows that in 2010 one violent crime was reported in Ceredigion. So an increase of 100% in 2011 meant that two violent crimes were reported.

When faced with the actual figures, perception of the amount of violent crime in Ceredigion changes significantly.

In order to work out how much something has increased or decreased in real terms we need some actual data.

Take the example of “UK rainfall this summer was 23% above average” – we can tell immediately that the UK experienced almost a quarter (25%) more rainfall than average over the summer. However, without knowing either what the average rainfall is or how much rain fell over the period in question we cannot work out how much rain actually fell.

Calculating the actual rainfall for the period if the average rainfall is known.

If we know the average rainfall is 250mm, we can work out the rainfall for the period by calculating 250 + 23%.

First work out 1% of 250, 250 ÷ 100 = 2.5. Then multiply the answer by 23, because there was a 23% increase in rainfall.

2.5 × 23 = 57.5.

Total rainfall for the period in question was therefore 250 + 57.5 = 307.5mm.

Calculating the average rainfall if the actual amount is known.

If the news report states the new measurement and a percentage increase, “UK rainfall was 23% above average… 320mm of rain fell…”.

In this example we know the total rainfall was 320mm. We also know that this is 23% above the average.  In other words, 320mm equates to 123% (or 1.23 times) of the average rainfall. To calculate the average we divide the total (320) by 1.23.

320 ÷ 1.23 = 260.1626.  Rounded to one decimal place, the average rainfall is 260.2mm.

The difference between the average and the actual rainfall can now be calculated:
320 – 260.2 = 59.8mm.

We can conclude that 59.8mm is 23% of the average rainfall amount (260.2mm), and that in real terms, 59.8mm more rain fell than average.

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