how to find percent decrease

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In mathematics, the concept of percent change is used to describe the relationship between an old value and new value. Specifically, the percent change expresses the difference between the old and new values as a percentage of the old value. Use the equation ((V₂ - V₁ ) / V₁ ) × 100, in which V₁ represents an old or initial value and V₂ represents the new or current value. If the number is positive, it indicates a percent increase and if it's negative, it indicates a percent decrease. You can also use a modified formula to determine percent decrease rather than working with negative numbers.

Sample Percent Change Calculator

1
Subtract the original value from the new value. When calculating percent increase, the smaller number is the original (or old) value and the bigger number is the new (or final) value. The opposite is true when calculating percent decrease. You can use this formula to calculate either percent increase or percent decrease. If your answer is a negative number, rather than a positive one, then you know the percent change is a decrease^[1]
- 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.
- Alternatively, in the world of retail, when a product receives a discount, this is often expressed as the product being "x% off" which is a percent decrease. If a pair of pants was previously sold for $50 and is now sold for $30, $50 is the original value and $30 is the new value. To start, subtract $50 from $30, which is -$20.
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.
2
Divide your answer by the original value. After finding the difference between the numbers, divide that number by the original value, which is the smaller number if the percent increased or the bigger number if the percent decreased.^[2]
- Continuing the example, divide 8,000 (the difference between your incomes) by 37,000 (which is the original value). The answer is 0.216.
- Alternatively, dividing the difference (-$20) by the old value ($50) is -0.40. Another way of thinking of this is that the $20 change in value is 0.40 of the $50 starting point, and that the change of value was in the negative direction.
3
Multiply your answer by 100. To turn your answer into a percentage, all you have to do is multiply it by 100.^[3]
- Take 0.216 and multiply it by 100. In this case, the answer is 21.6, so your income increased by 21.6%.
- Alternatively, to get the final percentage, multiply the decimal answer (-0.40) by 100. -0.40 × 100 = -40%. This means that the new price of $30 for the pants is 40% less than the old price of $50. In other words, the pants are 40% off. Another way to think of this is that the $20 difference in price is 40% of the initial price of $50. Since this price difference results in a lower final price, give it a negative sign.

1
Subtract the new value from the original value. To calculate percent decrease using this formula, subtract the smaller number (the new or final value) from the bigger number (the original or old value). Note that this is the opposite of finding percent change using the standard equation.^[4]
- For instance, say you're trying to figure out how much a school's enrollment changed between years. If the enrollment for this year is 12,125 and it was 13,500 last year, take 12,125 away from 13,500, which is 1,375.
2
Divide your answer by the original value. Remember that when determining percent decrease, the original value is the bigger number.^[5]
- In this case, divide 1,375 (the difference between the numbers) by 13,500 (the original value), which is equal to 0.1019 (when rounded).
3
Multiply your answer by 100. Converting your answer from a decimal to a percentage is easy—just multiply the value by 100.^[6]
- Multiply 0.1019 by 100, which is 10.19. So, enrollment decreased by 10.19%.
Tip: If you use this equation and end up with a negative number, it represents a percent increase.

Add New Question

Question

What is the percent of change from 1/4 to 1/2?

Say 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%.
Question

How do I calculate percent change when the original number is zero?

That is an "undefined" situation, because any percentage of zero is zero.
Question

How do I calculate percent change when $40 becomes $30?

First 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%.
Question

I watched a video that stated the timing of 50ms went down to 20ms. He reported that as 205% improvement. How is that calculated?

It was calculated incorrectly. It's an improvement of 60%.
Question

If the original quantity is 6 and the new quantity is 3, what is the percent decrease?

The percent change is -50%.
Question

Lets say I bought 1360 jeans last year. This number increased by 5% this year. How many jeans did I buy this year?

1,360 + (.05)(1,360) = 1,360 + 68 = 1,428.
Question

How do I find a percent change if the denomenator is not a factor of 100?

The process remains the same: divide denominator into numerator. You'll get a decimal number. Multiply by 100, and add a percent sign.
Question

By what percent will the product of two numbers decrease if one of them is increased by 30% and the other is decreased by 30%?

It will decrease by 0.09%. 30% is the same as 0.3. When 0.3 is multiplied with 0.3, the result is 0.09. Let's say both numbers are 10. If one of them increases to 13 and the other decreases to 7, the product would be 91. Compared to 100, 91 has a 0.09% decrease. Now if the two numbers were 10 and 20, let's say 10 increased to 13 and 20 decreased to 14. The product of 13 and 14 would be 182. When compared to 200, 182 also has a 0.09% decrease.
Question

How can I find out a percent change?

If the number is a decimal, multiply the number by 100. If it is a fraction, divide the numerator by the denominator and then multiply by 100.
Question

I have been asked to provide week-over-week (WoW) numbers at work. Is this calculation what they would be asking for?

Only "they" know for sure what they're asking for, but week-over-week customarily involves real-number changes or percentage changes from week to week. So yes, they may indeed be looking for what this article demonstrates.

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Article SummaryX

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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