To calculate a percentage increase, subtract the original number from the new number, divide by the original and multiply by 100: from 50 to 75 is (75 − 50) ÷ 50 × 100 = 50%. This percentage increase calculator also works the other way round. It increases or decreases a number by a percent, finds the original value before a change, and separates percentage points from percent change. Every mode shows the steps.
Use it for price rises, rent and salary changes, sales growth, test-score improvements, population figures, or any "by what percent did this go up?" question. If you just need a part of a number, such as 20% of 60, the percentage calculator is quicker.
How to use the calculator
- Choose what you know. Two numbers gives the percent change. A number and a percent gives the new value. A new value and a percent gives the original.
- Enter the values. The percent fields accept decimals such as 2.5 and, in the reverse mode, negative percents for decreases.
- Read the headline result, then the before and after values, the amount of change, the multiplier and the change needed to get back to the start.
- Follow the numbered steps to see the formula worked through with your numbers, then copy the link to share it.
Percentage increase formula
percent change = (new − original) ÷ original × 100
OpenStax Prealgebra describes it in two steps: first find the amount of increase (new amount − original amount), then find that increase as a percent of the original amount. A percent decrease is the same, with the decrease equal to original − new. The U.S. Bureau of Labor Statistics computes price-index changes the same way: in its CPI questions and answers, an index that moves from 112.5 to 121.5 has changed 9.0 points, and 9.0 ÷ 112.5 × 100 = 8%.
The original value always goes on the bottom. That is the single rule that decides whether an answer is right, and it is why an increase from 80 to 100 (+25%) is not the same size as a decrease from 100 to 80 (−20%).
Worked examples: percentage increase from two numbers
- College fees, $26 to $36 (OpenStax Example 6.23): increase 10; 10 ÷ 26 = 0.3846; that is a 38.5% increase.
- Rent, $1,450 to $1,525: increase 75; 75 ÷ 1,450 × 100 = 5.17%.
- Price index, 110 to 128 (BLS example): 18 ÷ 110 × 100 = 16.4%. A second index from 225 to 243 also rose 18 points, but that is only 8%, because it started higher.
- Weight, 180 lb to 171 lb: (171 − 180) ÷ 180 × 100 = -5%, a 5% decrease.
Which number is the original?
The original is the value you are comparing from: usually the earlier one in time (last year's price, the old rent, the score before practice). When two things are compared side by side rather than over time, say what the base is. "Store B is 25% more expensive than store A" uses A's $40 as the base; "store A is 20% cheaper than store B" uses B's $50. Both are correct descriptions of the same $10 gap, which is why a headline percent means little until you know what it is a percent of. If neither value is a natural base, some fields use the percent difference, which divides by the average of the two; this calculator always uses the first number you enter as the base.
How to increase a number by a percentage
Multiply by the growth factor 1 + P ÷ 100. A 10% increase multiplies by 1.10, a 3.5% increase by 1.035 and a 150% increase by 2.5. Doing it in one multiplication avoids the slip of adding the percent itself (200 + 10 = 210) instead of the percent of the number (200 + 20 = 220). To decrease, multiply by 1 − P ÷ 100: 200 decreased by 15% is 200 × 0.85 = 170.
10% increase calculator: quick values
A 10% increase is the most common case: move the decimal one place to get 10%, then add it. 10% more than 50 is 55, than 85 is 93.5, than 250 is 275, and than 1,200 is 1,320. To reverse it, divide by 1.1: a number that is 10% higher at 132 started at 120.
Common percentage increases table
Each cell is the starting value (top) increased by the percent (left), rounded to at most two decimals. For a decrease, use the percent off calculator or the decrease mode above.
| Increase | 10 | 20 | 25 | 50 | 75 | 100 | 150 | 200 | 250 | 500 | 1,000 |
|---|---|---|---|---|---|---|---|---|---|---|---|
| +1% | 10.1 | 20.2 | 25.25 | 50.5 | 75.75 | 101 | 151.5 | 202 | 252.5 | 505 | 1,010 |
| +2% | 10.2 | 20.4 | 25.5 | 51 | 76.5 | 102 | 153 | 204 | 255 | 510 | 1,020 |
| +3% | 10.3 | 20.6 | 25.75 | 51.5 | 77.25 | 103 | 154.5 | 206 | 257.5 | 515 | 1,030 |
| +4% | 10.4 | 20.8 | 26 | 52 | 78 | 104 | 156 | 208 | 260 | 520 | 1,040 |
| +5% | 10.5 | 21 | 26.25 | 52.5 | 78.75 | 105 | 157.5 | 210 | 262.5 | 525 | 1,050 |
| +7% | 10.7 | 21.4 | 26.75 | 53.5 | 80.25 | 107 | 160.5 | 214 | 267.5 | 535 | 1,070 |
| +8% | 10.8 | 21.6 | 27 | 54 | 81 | 108 | 162 | 216 | 270 | 540 | 1,080 |
| +10% | 11 | 22 | 27.5 | 55 | 82.5 | 110 | 165 | 220 | 275 | 550 | 1,100 |
| +12% | 11.2 | 22.4 | 28 | 56 | 84 | 112 | 168 | 224 | 280 | 560 | 1,120 |
| +15% | 11.5 | 23 | 28.75 | 57.5 | 86.25 | 115 | 172.5 | 230 | 287.5 | 575 | 1,150 |
| +20% | 12 | 24 | 30 | 60 | 90 | 120 | 180 | 240 | 300 | 600 | 1,200 |
| +25% | 12.5 | 25 | 31.25 | 62.5 | 93.75 | 125 | 187.5 | 250 | 312.5 | 625 | 1,250 |
| +30% | 13 | 26 | 32.5 | 65 | 97.5 | 130 | 195 | 260 | 325 | 650 | 1,300 |
| +40% | 14 | 28 | 35 | 70 | 105 | 140 | 210 | 280 | 350 | 700 | 1,400 |
| +50% | 15 | 30 | 37.5 | 75 | 112.5 | 150 | 225 | 300 | 375 | 750 | 1,500 |
| +75% | 17.5 | 35 | 43.75 | 87.5 | 131.25 | 175 | 262.5 | 350 | 437.5 | 875 | 1,750 |
| +100% | 20 | 40 | 50 | 100 | 150 | 200 | 300 | 400 | 500 | 1,000 | 2,000 |
Reverse percentage: the original before an increase
When you know the value after a change and the percent, divide by the multiplier: original = new ÷ (1 + P ÷ 100). A $54 meal that already includes an 8% tax had a pre-tax price of 54 ÷ 1.08 = $50. Subtracting 8% from $54 gives $49.68, which is too low, because the 8% was calculated on the smaller original.
| First change | Change to undo it |
|---|---|
| −50% | +100% |
| −40% | +66.67% |
| −25% | +33.33% |
| −20% | +25% |
| −10% | +11.11% |
| +10% | −9.09% |
| +20% | −16.67% |
| +25% | −20% |
| +50% | −33.33% |
| +100% | −50% |
Percentage points vs percent
When the two numbers are themselves percentages, such as interest rates, tax rates or unemployment rates, there are two different "changes". The percentage-point change is the plain difference: 4% to 6% is up 2 points. The percent change is relative: the rate is 50% higher than before. A mortgage rate going from 6.5% to 7% is a 0.5-point rise and a 7.69% increase in the rate. Choose "Percentage points vs percent change" in the calculator to see both. The BLS reasoning for reporting index changes as percents rather than points applies here too: a point change says nothing about size until you know where it started.
Repeated increases compound
Two 10% increases are not 20%. The second one is applied to the larger number, so the total is 1.1 × 1.1 = 1.21, a 21% increase. Five years of 3% raises add up to 15.93%, not 15%. To find the percent per period from a total change, take the root: a 21% rise over two years is √1.21 − 1 = 10% a year. The pay raise calculator applies this to salaries, including the new hourly and monthly amounts.
Common mistakes
- Dividing by the new value. From 80 to 100 is 20 ÷ 80 = 25%, not 20 ÷ 100 = 20%.
- Assuming equal ups and downs cancel. −50% then +50% leaves you at 75% of the start.
- Reversing by subtracting the percent. Divide by the multiplier instead.
- Mixing points and percents. "Up 2%" for a rate moving from 4% to 6% is wrong; it is up 2 points, or 50%.
- Starting from zero. A change from 0 has no percent value, because you cannot divide by zero. Report the amount instead.
- Negative starting values. Going from −50 to −25 is an improvement; the calculator divides by the size of the original (50) so the result reads as +50%.
See also the percentage calculator for parts of a number, the discount calculator for sale prices, and the pay raise calculator for salary increases.
Frequently asked questions
How do you calculate a percentage increase?
Subtract the original value from the new value, divide by the original value and multiply by 100. From 50 to 75: (75 − 50) ÷ 50 × 100 = 50%.
How do you calculate a percentage decrease?
Use the same formula; the result comes out negative. From 80 to 60: (60 − 80) ÷ 80 × 100 = -25%, a 25% decrease.
How do I increase a number by a percentage?
Multiply it by 1 + percent ÷ 100. To increase 200 by 10%, multiply by 1.10: 200 × 1.10 = 220.
What is a 10% increase on 50?
55. 10% of 50 is 5, and 50 + 5 = 55. A 10% increase on 1,500 is 1,650.
How do I find the original number before a percentage increase?
Divide the new number by 1 + percent ÷ 100. If a price is $220 after a 10% rise, the original was 220 ÷ 1.10 = 200. Taking 10% off $220 gives 198, which is wrong.
What is the percentage increase from 26 to 36?
38.5%. The increase is 10, and 10 ÷ 26 = 0.3846. OpenStax Prealgebra uses this example for college fees that rose from $26 to $36 per unit.
Is a 20% decrease followed by a 20% increase back to the start?
No. 100 × 0.8 × 1.2 = 96. After a 20% drop you need a 25% rise to recover, because the rise is measured on the smaller number.
What is the difference between percent and percentage points?
Percentage points are the plain difference between two percentages; percent change is relative. A rate moving from 4% to 6% is up 2 percentage points, which is a 50% increase in the rate.
Can a percentage increase be more than 100%?
Yes. Doubling is a 100% increase and tripling is 200%. From 40 to 130 is a 225% increase. A decrease, though, can never be more than 100% unless the value goes below zero.
What is two 10% increases in a row?
21%, not 20%, because the second increase applies to the already-increased value: 1.1 × 1.1 = 1.21. Three 10% increases compound to 33.1%.
Sources & method
- OpenStax Prealgebra 2e, §6.2 Solve General Applications of Percent — percent increase and percent decrease
- U.S. Bureau of Labor Statistics — CPI questions and answers: calculating percent change from index points
- OpenStax Prealgebra 2e, §6.1 Understand Percent — converting percents to decimals
Results are estimates for general information. Found an error? It helps everyone — see our methodology.