Math · Percent
Percent increase and decrease calculator.
Find the percent change between two numbers, apply a percent increase or decrease, or work back to the original value.
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How to calculate percent change
Percent change compares a new value with the old one: subtract the old value from the new value, divide by the old value, then multiply by 100. A positive result is a percent increase and a negative result is a percent decrease.
Worked example. A box held 160 smarties yesterday and now holds 116. The change is 116 − 160 = -44. Divide by the old value: -44 ÷ 160 = -0.275, which is -27.5%, a 27.5% decrease. For socks that went from $5 to $6, 1 ÷ 5 = 0.2, a 20% increase.
Why not reverse it? A 10% increase on 100 gives 110. A 10% decrease on 110 takes off 11 and leaves 99, not 100, because the second percent applies to a different starting value. To undo a percent change, divide by the multiplier: after a 20% decrease the price is 80% of the original, so a final price of 150 means an original of 150 ÷ 0.8 = 187.5.
Frequently asked questions
How do you calculate percent increase or decrease?
Take new minus old, divide by the old value, and multiply by 100. From 160 to 116 that is (116 − 160) ÷ 160 × 100 = -27.5%, a decrease.
Why divide by the old value?
Because the percent says how much a value has changed, and that is measured against where it started.
Does a 10% rise followed by a 10% fall bring me back to the start?
No. 100 up 10% is 110, and 110 down 10% is 99. The second 10% is taken from a larger number.
How do I find the original price before a discount?
Divide the final price by the remaining share. If a price is 150 after a 20% decrease, the original is 150 ÷ 0.8 = 187.5.
What if the old value is zero?
A percent change from 0 is undefined, because you cannot divide by 0. The calculator asks for a non-zero old value.
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For learning
The percent for increase and decrease modes is entered as a positive number. Results are rounded for display. Check with your teacher's required method when you hand in homework.