Your $80 jacket is 15 percent off. What do you actually pay? You do not need to guess or add up small steps. Multiply the price by 0.85 and you get $68, all in one move. That single trick, multiplying by one number, is the fastest way to raise or lower any value by a percent. This guide shows the method for both directions and how to reverse it.
To increase a number by p percent, multiply it by (1 + p/100). To decrease it, multiply by (1 – p/100).
So 80 up 15% is 80 x 1.15 = 92, and 80 down 15% is 80 x 0.85 = 68.
To find the original before an increase, divide: old = new / (1 + p/100).
Increase a Number by a Percent
To raise a value by a percent, you do not add a separate piece. You multiply the whole number by one factor. That factor is (1 + p/100), where p is the percent.
The idea is simple. You keep 100% of the original, then add the extra percent on top. For a 15% rise, you keep 100% and add 15%, giving 115%, or 1.15 as a decimal.
Say a $80 item goes up 15%. Turn the percent into a factor, then multiply:
- Factor: 1 + 15/100 = 1 + 0.15 = 1.15
- New value: 80 x 1.15 = 92
So the new price is $92. You can check the logic: 15% of 80 is 12, and 80 + 12 = 92. Both paths agree, but the multiply method is quicker. This is different from measuring the change between two numbers you already have. For that, see our percentage change formula guide.
Decrease a Number by a Percent
Lowering a value works the same way, but you subtract the percent from 100% first. The factor becomes (1 – p/100).
Here you keep less than the whole. For a 15% drop, you keep 100% minus 15%, which is 85%, or 0.85 as a decimal. You are keeping most of the value and taking a slice away.
Back to the $80 jacket that is 15% off. Build the factor, then multiply:
- Factor: 1 – 15/100 = 1 – 0.15 = 0.85
- New value: 80 x 0.85 = 68
You pay $68. As a check, 15% of 80 is 12, and 80 – 12 = 68, which matches. Sale prices are the most common decrease people meet. If you want the discount-specific angle, our guide on how to calculate a discount covers it in full. For the plain “what is 15% of 80” question on its own, see how to calculate a percentage.
Work Backward to the Original
Sometimes you see the final number and want the starting one. A price tag reads $92 after a 15% markup, and you want the original. You reverse the multiply by dividing.
The rule for an increase is old = new / (1 + p/100). You divide the new value by the same factor you would have multiplied by.
- Factor: 1 + 15/100 = 1.15
- Original: 92 / 1.15 = 80
So the price before the markup was $80. The same logic reverses a decrease: divide the new value by (1 – p/100). If a discounted price is $68 after 15% off, then 68 / 0.85 = 80, the original tag. The key mistake to avoid is adding the percent back on. You must divide, not multiply, to undo the change.
Why an Increase Then a Decrease Does Not Cancel
Here is a trap that fools a lot of people. If a number goes up 20% and then down 20%, you do not land back where you started. You end up lower.
The reason is that the second percent works on a bigger number than the first one did. The 20% drop is taken from the raised value, not the original. Watch it step by step:
- Start: 100
- Up 20%: 100 x 1.20 = 120
- Down 20%: 120 x 0.80 = 96
You finish at 96, not 100. The 20% rise added 20, but the 20% fall removed 24, because it came off 120. The gap is real money in the real world. This is why a price that jumps and then gets an equal percent cut is still cheaper than before, and why equal percent swings never fully undo each other.
Quick Steps to Remember
When you need to apply a percent fast, follow this short routine. It works for both increases and decreases.
- Write down the percent, p, and the starting value.
- For an increase, build the factor 1 + p/100. For a decrease, build 1 – p/100.
- Multiply the starting value by that factor to get the new value.
- To go backward and find the original, divide the new value by the same factor.
- Sanity-check: an increase should give a bigger number, a decrease a smaller one.
Keep the two factors in mind and the rest follows. A 10% rise means multiply by 1.10, and a 10% cut means multiply by 0.90. Once the factor is set, it is one multiplication either way.
Do not want to build factors by hand? Enter your number and percent into our free Percentage Calculator. It handles increases, decreases, and reverse lookups in seconds, so you can check your work or skip the arithmetic entirely.
Frequently Asked Questions About Percentage Increase and Decrease
How Do I Increase a Number by a Percent?
Multiply the number by (1 + p/100), where p is the percent. You keep 100% of the value and add the extra percent on top. For a 15% rise, the factor is 1.15, so 80 x 1.15 = 92. That single multiplication gives the new, higher value in one step.
How Do I Decrease a Number by a Percent?
Multiply the number by (1 – p/100). You subtract the percent from 100% first, then multiply. For a 15% drop, the factor is 0.85, so 80 x 0.85 = 68. This keeps most of the value and takes the percent slice away in one clean move.
How Do I Find the Original Value Before a Percentage Increase?
Divide the new value by the same factor, using old = new / (1 + p/100). If a price is 92 after a 15% increase, then 92 / 1.15 = 80, the original. Do not simply take 15% off the new number, because that would remove the wrong amount and give the wrong answer.
Why Is 20% Off After 20% On Not Back to the Start?
Because the second percent is taken from a different, larger number. A 20% rise on 100 gives 120, and a 20% drop then comes off 120, not 100. That removes 24 while the rise only added 20. You end at 96, below the starting 100. Equal percent swings never fully cancel.
What Is the Fastest Way to Add 15% to a Price?
Multiply the price by 1.15 in one step. There is no need to find 15% separately and then add it. The factor 1.15 already includes the full price plus the extra 15%. For a $80 item, 80 x 1.15 = 92, so the total is $92 right away.
How Do I Turn a Percent Into a Multiplier?
Divide the percent by 100 to get a decimal, then add it to 1 for an increase or subtract it from 1 for a decrease. So 15% becomes 0.15, giving 1.15 for an increase or 0.85 for a decrease. The multiplier is the number you multiply your value by.
Can I Apply Two Percentage Changes in a Row?
Yes. Multiply by each factor in turn, one after the other. For a 20% rise then a 20% drop on 100, do 100 x 1.20 = 120, then 120 x 0.80 = 96. Always apply each factor to the value at that moment, not to the original starting number.
Sources
Authoritative Sources Used in This Article
This article is for general education only, not professional or financial advice. Always double-check the math for your own numbers before you rely on it. Reviewed for accuracy by Prof. Dr. Khalil Mudassar, PhD. Last updated September 11, 2026.
Author
Shakeel Muzaffar is the Founder and Editor-in-Chief of MultiCalculators.com, bringing over 15 years of experience in digital publishing, product strategy, and online tool development. He leads the platform's editorial vision, ensuring every calculator meets strict standards for accuracy, usability, and real-world value. Shakeel personally oversees content quality, formula verification workflows, and the platform's commitment to publishing tools that are genuinely useful for students, professionals, and everyday users worldwide.
