How to Calculate Percentage Increase and Decrease

Percentage increase and decrease show how much a number has changed compared to where it started. Whether you are checking a price rise, a pay raise, or a store discount, the same simple formula works every time. In this guide you will learn the formula, walk through real examples, and see how a few common situations play out in everyday life.

The Percentage Increase Formula

To find a percentage increase, compare the new value to the old value using this formula:

(new value − old value) ÷ old value × 100

The steps are always the same:

Subtract the old value from the new value to find the amount of change.
Divide that difference by the old value.
Multiply by 100 to turn the result into a percentage.

Dividing by the old value matters. The starting number is your reference point, so it always goes on the bottom.

Worked Example: A Price Rise

Suppose a monthly subscription goes from 40 dollars to 50 dollars. Start with the difference: 50 − 40 = 10. Divide by the old value: 10 ÷ 40 = 0.25. Multiply by 100 and you get a 25 percent increase.

Here is a second one. A house was valued at 300,000 dollars last year and 330,000 dollars this year. The change is 30,000, and 30,000 ÷ 300,000 = 0.10, which is a 10 percent increase.

Calculating a Percentage Decrease

A decrease uses the exact same formula. When the new value is smaller than the old value, the difference is negative, so the answer comes out negative too, which simply means the number went down.

Imagine a jacket marked down from 80 dollars to 60 dollars. The change is 60 − 80 = −20. Divide by the old value: −20 ÷ 80 = −0.25. That is a 25 percent decrease, otherwise known as a 25 percent discount.

A quick way to think about discounts: if an item is 25 percent off, you pay 75 percent of the original price. So 80 dollars × 0.75 = 60 dollars, which matches.

Percentage Increase vs. Percentage Points

These two ideas are easy to mix up, but they mean different things. A percentage point is the plain difference between two percentages, while a percentage increase is that difference relative to the starting value.

Say an interest rate moves from 4 percent to 6 percent. That is a rise of 2 percentage points. But as a percentage increase, it is 2 ÷ 4 × 100 = a 50 percent increase. Both statements are correct; they just answer different questions. When you read news about rates, taxes, or poll results, notice which one is being used.

Common Real-Life Uses

The same math shows up constantly once you start looking:

Tips: A 20 percent tip on a 45 dollar meal is 45 × 0.20 = 9 dollars, for a total of 54 dollars.
Raises: If your salary rises from 52,000 dollars to 54,600 dollars, that is 2,600 ÷ 52,000 × 100 = a 5 percent raise.
Sales tax: An 8 percent tax on a 25 dollar purchase adds 25 × 0.08 = 2 dollars, bringing the total to 27 dollars.
Sales and discounts: Use the decrease formula to confirm an advertised percentage off is really what it claims.

Let a Calculator Do the Work

Once you understand the formula, you rarely need to do the arithmetic by hand. A tool removes the guesswork, especially with awkward numbers or when you are comparing several options quickly. Try our free percentage calculator to work out increases, decreases, tips, and discounts in seconds.

The key takeaway is simple: find the difference, divide by the starting value, and multiply by 100. Master that one formula and you can handle price changes, raises, tips, taxes, and sales without a second thought.