Percentage Increase Calculator
How to use this percentage increase calculator
Using this free percentage increase calculator is simple, and it takes less than a minute. First, type the starting number, called the original value, into the first box. Next, type the later number, called the new value, into the second box. The result updates live on every keystroke, so you do not need to press a button or wait for a page reload. You can change either number at any time, and the answer, the difference, and the worked formula all update straight away.
This percentage increase calculator is useful in everyday life. People use it to check a pay rise, a price rise, a savings balance, a test score, or the growth of a small business. Because the formula is shown with your own numbers filled in, you can see exactly how the answer was worked out, rather than having to trust a mystery number. That transparency matters when you are checking homework, a bill, or a quote from a shop or supplier.
Worked example: 50 to 75
Suppose a price rises from 50 to 75. First, find the difference: 75 minus 50 equals 25. Next, divide that difference by the original value: 25 divided by 50 equals 0.5. Finally, multiply by 100 to turn it into a percentage: 0.5 times 100 equals 50. The answer is therefore a 50% increase, with a difference of 25. Try it in the calculator above: type 50 as the original value and 75 as the new value, and you will see the same 50% increase and the same formula, step by step.
How the percentage increase formula works
The percentage change formula is: (new value minus original value) divided by the absolute value of the original value, multiplied by 100. In symbols, that is (new – original) / |original| x 100. The difference tells you how much the number moved in plain units, while the percentage tells you how large that move is compared with where you started. That comparison is the whole point of a percentage: a rise of 25 means something very different when you started at 50 than when you started at 5,000.
We divide by the absolute value of the original number so that the sign of the answer is decided by the direction of the change, not by whether the starting number was negative. A positive answer means an increase, and a negative answer means a decrease. If the two numbers are the same, the difference is zero and the percentage change is 0%, which the calculator labels honestly as no change.
The calculator also shows decreases, labelled honestly
Although this page is called a percentage increase calculator, the same tool also handles falls, and it labels them honestly as decreases. For example, if a value falls from 200 to 150, the difference is minus 50, and the percentage change is a 25% decrease. If a value rises from 80 to 100, the difference is 20, and the result is a 25% increase. Showing the direction in plain words avoids a common confusion: a bare number such as -25% can be misread, but 25% decrease is clear at a glance.
It is also worth knowing the difference between a percentage change and a change in percentage points. If an interest rate moves from 4% to 6%, that is a rise of 2 percentage points, but a 50% increase in the rate itself. The calculator on this page reports the percentage change, which is the figure most people mean when they ask how much something went up or down in percentage terms.
Frequently asked questions
What is percentage increase?
Percentage increase is a way of expressing how much a number has grown, compared with its starting value. A 50% increase means the new number is half as large again as the original number, so a value of 50 growing by 50% becomes 75.
How do you calculate percentage increase?
Subtract the original value from the new value, divide the result by the original value, and multiply by 100. For 50 to 75, that is (75 – 50) / 50 x 100, which equals 50%.
What is the difference between percentage increase and percentage change?
Percentage change is the general term for a rise or a fall expressed as a percentage. Percentage increase is the special case where the new value is larger than the original value. This calculator reports percentage change, and labels it as an increase, a decrease, or no change.
What if the new value is smaller than the original?
Then the result is a decrease. For example, 200 falling to 150 is a 25% decrease, with a difference of -50. The calculator shows the negative difference and labels the result as a decrease, so the direction is never ambiguous.
What if the original value is zero?
Percentage change can’t be worked out from zero, because dividing by zero has no answer. The calculator says so in plain words instead of showing a meaningless number, and it simply waits until you enter a non-zero original value.