A percentage increase compares a new number with an old one, as a share of the old one. It’s the way price changes, pay rises, population growth and exam improvements are usually reported.
You can go either way: find the change between two numbers, or push a number up by a percentage.
How to use the Percentage Increase Calculator#
- Choose a mode. Find a percentage between two numbers, or apply a percentage to one.
- Enter your numbers. Type the original value and either the new value or the percentage.
- Read the result. The result also shows the amount of the change.
The formula#
A change from 80 to 100 is 25 percent. Divide the change by the original value and multiply by 100. To apply a percentage, multiply the original by 1 + the percentage as a decimal.
Why the starting value matters#
A percentage always depends on what it’s measured against. A fall of 20 percent followed by a rise of 20 percent doesn’t get you back to where you started: 100 falls to 80, then rises to 96. To undo a 20 percent fall you need a 25 percent rise. This catches out a lot of people when they read headlines about gains and losses.
Related calculators#
For a plain percentage of a number, use the percentage calculator. For the opposite change, try the percentage decrease calculator.
Percent versus percentage points#
If an interest rate goes from 4 percent to 6 percent, it has risen by 2 percentage points, but by 50 percent in relative terms. News reports mix the two, so check which one is meant.
Repeated increases compound. A 10 percent rise each year for three years gives 1.1 × 1.1 × 1.1 = 1.331, so the total increase is 33.1 percent, not 30.
Compound growth#
Percentage increases stack by multiplying, not adding. Three yearly rises of 10 percent give 1.1³ = 1.331, a total increase of 33.1 percent. Salaries, prices, savings and populations all behave this way. The longer the period, the bigger the gap between simple and compound growth.
| Yearly increase | After 5 years | After 10 years | Years to double |
|---|---|---|---|
| 3% | 15.9% | 34.4% | 23.4 |
| 5% | 27.6% | 62.9% | 14.2 |
| 7% | 40.3% | 96.7% | 10.2 |
| 10% | 61.1% | 159.4% | 7.3 |
A quick way to estimate doubling time is the rule of 72: divide 72 by the percentage. At 6 percent growth, money doubles in about 12 years.
Pay rises, prices and inflation#
A rise from ₦150,000 to ₦165,000 a month is 10 percent. If inflation in the same period was 15 percent, the pay rise is smaller than the rise in prices, and your buying power fell. To compare, divide: 1.10 ÷ 1.15 = 0.9565, so real pay is down 4.3 percent. The same method works for rent, school fees or a business’s costs.
When you ask for a raise, state the percentage and the naira amount, since people think about both. For tax on a higher salary, our Nigeria personal income tax calculator shows what you take home.
Working from a percentage to a new value#
The calculator has a second mode that applies a percentage to a starting figure. To raise 40,000 by 12.5 percent, multiply by 1.125, which gives 45,000. Mark-ups work in the same way. If you add 25 percent to a cost of 80, you get 100, but the profit as a share of the selling price is 20 percent, not 25. For that, see the margin calculator.
Frequently asked questions#
Subtract the old value from the new value, divide by the old value and multiply by 100.
Yes, if the value more than doubles.
The percentage change is undefined.
Multiply the original by 1 plus or minus the percentage as a decimal.
Percentage points describe the arithmetic gap between two percentages, and percent describes a relative change. If interest rates go from 4 percent to 6 percent, they rose by 2 percentage points, which is a 50 percent increase. Mixing the two up can make a story sound much bigger or smaller than it is.
Divide the new value by 1 plus the percentage as a decimal. If a price rose 20 percent to 60, the old price was 60 ÷ 1.2 = 50. Do not subtract 20 percent from 60, which gives 48 and is wrong. The percentage was applied to the old value, so you must undo it with division.