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Easily find percent increase or decrease with this simple equation
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Looking at the change in percent of a number, as opposed to the change in value, can give you a more useful representation of how something has increased or decreased. For example, it can be more helpful to know that a stock went up 5% than to know it went up $10. The equation for percent change is , where V 1 is the original value and V 2 is the new value. We spoke to Grace Imson, a math instructor at the City College of San Francisco to get the best advice on how to calculate percent increase and decrease, plus how to check your work.
Percent Change Formula
To calculate the percent change of two numbers, subtract the old value from the new value, divide the difference by the old value, then multiply your answer by 100. The formula is .
Steps
Sample Percent Change Calculator
Section 1 of 3:
Calculating Percent Increase
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Subtract the original value from the new value. If your original value is smaller than the new value, then you’re calculating percent increase. First, find the difference between the two values.- For example, say you’re trying to figure out how much your income increased from one year to the next. If you made $37,000 last year and $45,000 this year, subtract 37,000 from 45,000, which is 8,000.
- If you got a raise from $20 an hour to $22.50 an hour and want to find the percent change, subtract 20 from 22.50, which is 2.50.
Tip: When dealing with variables with more than one change in value, find the percent change only for the two values you wish to compare.
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Divide your answer by the original value. Imson says that the most common mistake she sees her students make is using the wrong denominator. Because you’re looking at how much the original number increased, the original (smaller) number is your denominator.- So if your difference is 8,000, like the example above, divide 8,000 by 37,000 (which is the original value). The answer is 0.216.
- For the hourly wage example, divide 2.5 by 20, which is .125.
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Multiply your answer by 100 to turn it into a percentage. This is the same as moving the decimal point two places to the right. [1] X Research source- Multiply 0.216 by 100. In this case, the answer is 21.6, so your income increased by 21.6%.
- Move the decimal point two places to turn .125 into 12.5%. So a 12.5% increase from 20 is 22.5.
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Section 2 of 3:
Calculating Percent Decrease
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Subtract the original value from the new value. If you have a decrease (a lower final number) and don’t want to deal with negative numbers, Imson says you can also do the opposite of the standard equation by subtracting the new value from the original value.- You can think of a percent decrease as “percent off,” like when an item is on sale. If a pair of pants was previously sold for $50 and is now on sale for $25, subtract 50 from 25, which is -25.
- To use the reversed equation, if you’re looking at how much a school’s enrollment changed between years, and the enrollment this year is 12,125 and it was 13,500 last year, take 12,125 away from 13,500, which is 1,375.
- By switching the new value and original value in the numerator, all you’re doing is changing the negative sign to a positive. If that’s confusing, just stick to the original formula.
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Divide your answer by the original value. Imson notes that the point of reference is the original number, so divide by the original (larger) value so the answer is in respect to that number.- Divide the difference in price (-$25) by the old value ($50) is -0.5. Another way of thinking of it is that the $25 change is 0.5 of the $50 starting point, and the change of value is in a negative direction.
- For the reverse equation, divide 1,375 (the difference between the numbers) by 13,500 (the original value), which is equal to 0.1019 (when rounded).
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Multiply the decimal by 100 to change the answer to a percentage. You can convert any fraction into a percentage by dividing the numerator by the denominator and multiplying by 100.- To get the final sale percentage, multiply -.05 by 100. -0.5 × 100 = -50%. This means that the new price of the pants is 50% less than the old price. In other words, the pants are 50% off. Another way to think of this is that the $25 difference is 50% of the initial $50.
- Multiply 00.1019 by 100, which is 10.19. So, enrollment decreased by 10.19%.
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Section 3 of 3:
Finding Values From Percentages
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Divide your percentage by 100. If you’re given a value and asked to find, for example, a value 50% higher than it, start by dividing 50 by 100. [2] X Research source You can use this method to check answers from percent change problems. -
Multiply the value by the decimal, then add it to the original value. When you multiply a number by a decimal, you get a value that represents that percentage of the original number. For example, 50 is .5 (half) of 100. By adding that result to the original value, you get a number that is that percentage more than the original number. [3] X Research source- If you’re asked to find a number 87% higher than 8, then multiply 8 by .87, which is 6.96. Then, add 6.96 to 8, which is 14.96.
- If you found a percentage in a percent increase problem and want to check your answer, divide the percentage by 100, multiply it by the original value, and then add the result to the original value. If your percentage was correct, the answer will be the second, increased value.
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Community Q&A
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QuestionWhat is the percent of change from 1/4 to 1/2?Community AnswerSay you were asked to find the change from 0.25 to 0.5, you would say that it got doubled. In percentage form, this equates to 100%.
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QuestionHow do I calculate percent change when the original number is zero?DonaganTop AnswererThat is an "undefined" situation, because any percentage of zero is zero.
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QuestionHow do I calculate percent change when $40 becomes $30?Community AnswerFirst find the difference by subtracting. 40 - 30 = 10. Then divide the result by the original number. 10/40 = 0.25. Then multiply by 100. 0.25 x 100 = 25%.
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Article Summary
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To calculate percent change, start by determining both the old and new values for the amount that has changed. Next, subtract the old value from the new value. Then, divide the answer by the old value. Finally, multiply that number by 100 to get the percent change. For example, if the original value of something was 30 and then went up to 50, you would subtract 30 from 50 to get 20. Then, you would divide 20 by 30 and get 0.033. Finally, multiply that by 100 to get a final answer of 33 percent. For tips on how to find the percent change when there are more than two values, read on.
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Reader Success Stories
- "I like it a lot, unless I am used to work this concept in my mind every time I need to analize any change in my daily life. I think the formmula will be more meaningfull if you call V2 as Vn for new quantity and V1 as Vo for old or original quantity. That is what I am going to try for my students. But thanks for the help." ..." more
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"I like it a lot, unless I am used to work this concept in my mind every time I need to analize any change in my daily life. I think the formmula will be more meaningfull if you call V2 as Vn for new quantity and V1 as Vo for old or original quantity. That is what I am going to try for my students. But thanks for the help."
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"Very helpful and easy to remember. I was struggling before, and now I can even do it in my head."
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