A percentage increase calculator tells you how far a value has grown compared with where it began, using (new - old) / old x 100. If your marks climb from 56 to 70, the rise is 14, and 14 / 56 x 100 = 25 percent.
Students use it to compare a mock test with the last one, to see how much a cut off moved, or to track growth in a project report. Below you will find the formula, a multiplier table for adding a percent, examples checked by hand and the traps that catch people when increases stack up.
At a glance
Formula
(new - old) / old x 100Base
Always the old or starting valueAdd X% to a number
number x (1 + X / 100)Example
56 to 70 is a 25% increaseTwo rises of 10%
Total rise is 21%, not 20%
Percentage increase = (New value - Old value) / Old value x 100
The old value is the starting figure. The new value is the later, larger figure. If the new value is smaller, the answer comes out negative and is really a decrease.
Using the calculator above
Type the starting figure in the old value box and the later figure in the new value box. The tool subtracts, divides by the old value and shows the rise as a percent to two decimals, along with the raw rise so you can see both.
Whether you need a daily percentage increase calculator for a habit tracker or want to know how much percentage increase a new cut off shows, the steps are the same. If you type a new value that is lower than the old one, the result shows a fall, so the box doubles as a percentage calculator for increase or decrease. For that case the percentage decrease calculator explains the wording you should use. If you want the signed answer for any move, up or down, use the percentage change calculator.
- Note the starting value and the later value.
- Subtract the starting value from the later value to get the rise.
- Divide the rise by the starting value.
- Multiply by 100 to get the percent increase.
Percentage increase calculator formula, step by step
Rise = new value - old value
Percentage increase = rise / old value x 100
The division by the old value is the heart of it. A rise of 10 marks means a lot when you started at 40 (25 percent) and much less when you started at 80 (12.5 percent). The percent tells you how big the jump was relative to where you stood.
The reverse job, which a percentage addition calculator does, takes a number and grows it by a set rate: multiply by the factor (1 + rate / 100). To raise 450 by 12 percent, 450 x 1.12 = 504.
Worked examples with marks and counts
Mock test growth. First mock 118, second mock 147. Rise 29. 29 / 118 x 100 = 24.58 percent.
Canteen sales. A college canteen sold 1,250 plates in the first week of term and 1,500 in the second. Rise 250. 250 / 1,250 x 100 = 20 percent growth.
Overall percentage. Your semester percentage went from 68 to 76. That is 8 percentage points, but the increase in percentage terms is 8 / 68 x 100 = 11.76 percent.
The last example is the one that causes most arguments in a hostel room. Both numbers are correct. Points describe the plain gap; the percent increase describes the gap relative to 68.
Multiplier table for adding a percent
To increase any number by a given percent, multiply it by the factor in the second column. The last two columns show the result for 80 and 250.
| Increase | Multiply by | 80 becomes | 250 becomes |
|---|---|---|---|
| 5% | 1.05 | 84 | 262.5 |
| 10% | 1.10 | 88 | 275 |
| 12% | 1.12 | 89.6 | 280 |
| 15% | 1.15 | 92 | 287.5 |
| 18% | 1.18 | 94.4 | 295 |
| 20% | 1.20 | 96 | 300 |
| 25% | 1.25 | 100 | 312.5 |
| 40% | 1.40 | 112 | 350 |
| 50% | 1.50 | 120 | 375 |
| 100% | 2.00 | 160 | 500 |
| 150% | 2.50 | 200 | 625 |
A 100 percent increase doubles a number. A 150 percent increase leaves you with two and a half times the start, not one and a half times.
Growth over several steps: daily, monthly or yearly
Rises stack by multiplying, not by adding. Two increases of 10 percent take 100 to 110 and then to 121, a total rise of 21 percent. Three rises of 10 percent take 100 to 133.1.
To find the steady rate behind a total, divide the end by the start and take the root for the number of steps. A count that grew from 200 to 288 over two terms: 288 / 200 = 1.44, and the square root of 1.44 is 1.2, so the growth was 20 percent per term. The same method gives a daily, monthly or yearly percentage increase when you know how many steps passed.
Common mistakes with increases
| What people do | The problem | Do this instead |
|---|---|---|
| Divide the rise by the new value | Gives 20% for 56 to 70 instead of 25% | Divide by the starting value |
| Add up step rises | 10% and 10% is not 20% | Multiply the factors: 1.1 x 1.1 = 1.21 |
| Mix points and percent | 68% to 76% is 8 points, 11.76% growth | Name which one you mean |
| Undo a rise with the same percent | 80 up 25% is 100, but 100 down 25% is 75 | Undo a 25% rise with a 20% cut |
Increase, decrease, change or difference
Use this page when a value went up from a known starting point. If it went down, the decrease page uses the same base and reports a fall. The change page gives one signed figure for either direction, which suits tables where some rows rise and some fall. When neither value came first, such as two branches or two shifts, use the percentage difference calculator, which divides by the average of the pair. All six modes sit together on the main percentage calculator.
Questions students ask
What is the percentage increase formula?
Subtract the old value from the new value, divide by the old value and multiply by 100. From 56 to 70 that is 14 / 56 x 100 = 25 percent.
How much percentage increase is 40 to 50?
The rise is 10 on a base of 40, so 10 / 40 x 100 = 25 percent. Going back from 50 to 40 is only a 20 percent fall.
How do I add 18 percent to a number?
Multiply by 1.18. For 250, that gives 295. The percentage addition is 45, which is 18 percent of 250.
Can one tool work as a percentage increase and decrease calculator?
Yes. Type the old and new values in the tool above; a negative answer means the value fell. For signed results in a table, the percentage change page is the better fit.
Is a growth percentage calculator the same thing?
Yes. Growth percentage, percentage of increase and increase in percentage all use the same formula with the starting value as the base.
How do I use this as a price increase percentage calculator?
Put the old price in the old value box and the new price in the new value box. The tool divides the rise by the old price and multiplies by 100.