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Percentage Increase Calculator
To find the percentage increase from 80 to 100, subtract to get the increase, 20, divide by the original 80 to get 0.25, and multiply by 100: a 25% increase. To undo an increase, divide instead: 120 after a 20% rise was 120 ÷ 1.2 = 100, not 96.
Increase, apply, or undo.
- The change: new minus original = 100 − 80 = 20.
- Divide by the original: 20 ÷ 80 = 0.25.
- Multiply by 100: 25%.
| Result | Value |
|---|---|
| Percentage increase | 25% |
| Amount of change | +20 |
| New value as a percent of the original | 125% |
| Multiplier | 1.25 |
| From 100 back to 80 | a decrease of 20% |
The figures above are an example: put in your own. A new value lower than the original gives a decrease, named as one. For a change between two percentages, use the percentage change calculator, which counts percentage points too. Worked out exactly in this browser and kept there; nothing is sent anywhere.
Find the increase between two numbers, add a percentage to a number, or work back to the original before an increase. Each answer comes with its working, the multiplier and the percentage that reverses it.
A percentage increase is the rise from an original value to a new one, written as a percentage of the original: (new − original) ÷ original × 100. A rise from 80 to 100 is 20 on 80, which is 25%.
- No sign-up
- Nothing uploaded
- Shows every step
- Works offline
- Exact, no rounding errors
Key facts
| Detail | Answer |
|---|---|
| Questions | Increase from A to B; A increased by P%; original before a P% increase |
| Example | 80 to 100 is a 25% increase; 100 back to 80 is a 20% decrease |
| Formula | (new − original) ÷ original × 100 |
| Undo an increase | Divide by 1 + P/100: 120 ÷ 1.2 = 100 |
| Refuses | An increase from 0, which has no percentage |
| Where your numbers are kept | This browser only |
How to calculate a percentage increase
Subtract, divide by the original, multiply by 100. The calculator writes each step out.
Enter the original value
The figure before the change: last year’s price, the old salary.
Enter the new value
The figure after the change.
Subtract
New minus original gives the increase itself.
Divide by the original
Always the original, never the new value.
Multiply by 100
The result is the percentage increase; a negative one is a decrease.
Check the way back
The table gives the percentage that returns the new value to the original.
Who uses a percentage increase calculator
Anyone comparing a before and an after, or adding a rate to a figure.
Employees
A pay rise as a percentage of the old salary.
Shop owners
A selling price from a cost and a markup, and the margin it leaves.
Shoppers
The price before tax, from a receipt that includes it.
Landlords and tenants
A rent increase checked against the percentage allowed.
Students
Percent increase problems, worked step by step.
Trainers and coaches
A rise in weekly reps or distance, as a percentage, from session totals out of the training volume calculator.
Reverse percentages: undoing an increase, and why 120 less 20% is not 100
The commonest percentage mistake with money is taking an increase back off. A price of 120 that includes 20% tax was 100 before tax, and the tax was 20. Taking 20% off 120 gives 96, which is wrong by 4, because 20% of 120 is bigger than 20% of 100. The increase was a percentage of the original, so it has to be removed by dividing by 1 plus the rate.
| After the increase | Divide by | Original | Taking the % off (wrong) | Error |
|---|---|---|---|---|
| 120 including 20% tax | 120 ÷ 1.2 | 100 | 96 | 4 |
| 57.50 including a 15% tip | 57.50 ÷ 1.15 | 50 | 48.875 | 1.125 |
| 1,080 after an 8% rise | 1,080 ÷ 1.08 | 1,000 | 993.6 | 6.4 |
| 260 after a 30% markup | 260 ÷ 1.3 | 200 | 182 | 18 |
| 150 after a 50% increase | 150 ÷ 1.5 | 100 | 75 | 25 |
Choose “Original before a P% increase” in the calculator and it does the division, shows the wrong answer beside the right one, and says what share of the final figure the increase is: a 20% increase is 16.67% of the new total. This is the Grade 6 standard of finding the whole, given a part and the percent (6.RP.A.3c): after a 20% increase the new value is 120% of the whole, so the whole is the new value divided by 1.2.
UK schools call this a reverse percentage, and it works after a decrease too, dividing by 1 minus the rate: a sale price of 80 after 20% off was 80 ÷ 0.8 = 100, not 96. The percentage calculator does that one as “80 is 80% of what?”.
Markup and margin: 25% up is 20% of the price
A markup is a percentage increase on cost; a margin is the same profit as a percentage of the selling price. They describe one sale with two different wholes, so a 25% markup is only a 20% margin. Shops, quotes and price lists mix them up all the time, and the gap grows with the size of the figure.
| Markup on a cost of 100 | Selling price | Margin on the price |
|---|---|---|
| 10% | 110 | 9.09% |
| 20% | 120 | 16.67% |
| 25% | 125 | 20% |
| 33.(3)% | 133.33 | 25% |
| 50% | 150 | 33.33% |
| 100% | 200 | 50% |
| 200% | 300 | 66.67% |
The conversion is margin = markup ÷ (1 + markup), and markup = margin ÷ (1 − margin). A 50% margin needs a 100% markup: double the cost. In the calculator, “Increase a number by P%” gives the selling price from a cost and a markup, and the table row “to get back” is the margin: the percentage of the price that has to come off to return to cost. The Common Core lists markups and markdowns, percent increase and decrease among the Grade 7 percent problems (7.RP.A.3) for exactly this reason.
Two 10% rises make 21%
Percentage increases do not add. Two 10% rises are a 21% rise, because the second 10% is taken on the already raised figure: 100 becomes 110, then 121. The same is true of a rise followed by a fall, which is why a 50% rise and a 50% fall leave you 25% down, and a 20% fall needs a 25% rise to recover.
| Changes | Multiply the multipliers | Overall |
|---|---|---|
| +10%, then +10% | 1.1 × 1.1 = 1.21 | +21% |
| +10% a year for 5 years | 1.15 = 1.61051 | +61.051% |
| +50%, then −50% | 1.5 × 0.5 = 0.75 | −25% |
| −20%, then +25% | 0.8 × 1.25 = 1 | 0% |
| −50%, then +100% | 0.5 × 2 = 1 | 0% |
| +3% a year for 10 years | 1.0310 = 1.3439… | +34.39% |
To combine changes, turn each into a multiplier (a 10% rise is 1.1, a 50% fall is 0.5), multiply them, and read the overall change from the product. To find the overall increase from a start and an end value directly, use the first question in the calculator: from 100 to 161.051 is a 61.051% increase.
What this calculator does not do
The calculator works one increase at a time on two numbers. It does not compound over periods, model interest, work out tax rules or annualise growth. Percentage increase from 0 is refused, because any rise from nothing is infinitely many percent; give the change itself instead. When the original is negative (a loss of 10 becoming a profit of 5), the calculator divides by the size of the original and says so, but a percentage of a negative base is easy to misread: quote the plain change alongside it.
| Question | Formula | Example |
|---|---|---|
| Percentage increase from A to B | (B − A) ÷ |A| × 100 | 80 to 100: 25% |
| Increase A by P% | A × (1 + P ÷ 100) | 80 + 25%: 100 |
| Original before a P% increase | B ÷ (1 + P ÷ 100) | 120 after 20%: 100 |
| Back from B to A | (A − B) ÷ |B| × 100 | 100 to 80: −20% |
For a percentage of a number with nothing added, use the percentage calculator; for changes between rates such as 2.1% and 1.8%, the percentage change calculator separates percent from percentage points.
This calculator or an answer-only one
What this page does that a typical answer-only widget does not.
| This page | A typical calculator | |
|---|---|---|
| Undo an increase | Yes, with the wrong answer shown | Rarely offered |
| Way back | Up 25% needs down 20%, stated | Not shown |
| Decreases | Named as a decrease | A negative increase |
| Shows the working | Every step | Answer only |
| Exact arithmetic | No floating-point drift | Floating point |
| Your numbers leave the browser | Never | Varies |
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Frequently asked questions
How do you calculate percentage increase?
Subtract the original value from the new value, divide by the original, and multiply by 100. From 80 to 100 the increase is 20, and 20 ÷ 80 = 0.25, so the increase is 25%. Always divide by the original value: dividing by the new one gives 20%, which answers a different question.
How do I increase a number by a percentage?
Multiply it by 1 plus the percentage as a decimal. To add 25% to 80, multiply by 1.25 to get 100. Or work out 25% of 80, which is 20, and add it on. The calculator shows both ways and the multiplier, and the percentage that takes the new value back down.
How do I find the original price before a percentage increase?
Divide the new price by 1 plus the rate. A price of 120 that includes a 20% increase was 120 ÷ 1.2 = 100. Taking 20% off 120 gives 96, which is wrong, because 20% of 120 is more than 20% of 100. Choose the third question in the calculator to do this.
Why is a 50% increase followed by a 50% decrease not back to the start?
The decrease is taken from the larger, raised value. 100 up 50% is 150, and 50% of 150 is 75, so you end at 75: 25% down. Successive percentage changes multiply: 1.5 × 0.5 = 0.75. To get back from 150 to 100 you need a 33.33% decrease.
What is the difference between markup and margin?
Markup is profit as a percentage of cost; margin is the same profit as a percentage of the selling price. An item costing 100 and selling for 125 has a 25% markup and a 20% margin. Margin = markup ÷ (1 + markup), so a 100% markup is a 50% margin.
Can a percentage increase be more than 100%?
Yes. Doubling is a 100% increase and tripling is 200%: from 50 to 150 is a rise of 100 on 50, which is 200%. A decrease, on the other hand, cannot go beyond 100% for a positive value, since a 100% decrease takes it to zero.
What is the percentage increase from 0?
It is not defined. Any rise from 0 means dividing by 0, which has no value, so the calculator refuses it with a message. Report the increase itself (from 0 to 5 is a rise of 5) or measure from a different starting point.
Is two 10% increases the same as a 20% increase?
No, it is 21%. The second 10% is taken on the already increased value: 100 becomes 110, then 121. Multiply the multipliers, 1.1 × 1.1 = 1.21, to combine any run of increases and decreases into one overall change. Over five years, 10% a year is 61.05%, not 50%.
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