How to Calculate Percentage Increase and Decrease

By HSP · Published October 5, 2026 · 5 min read · Math & Dates

Percentage change is one of the most useful bits of everyday maths. It tells you how big a pay rise really is, whether a “sale” is a good deal, how fast prices are rising or how much your test score improved. The formula has only three steps, and once you remember to divide by the starting value, you will get it right every time.

The formula in three steps

1. Find the difference: new value − old value.
2. Divide by the old value.
3. Multiply by 100 to turn the decimal into a percentage.

percentage change = (new − old) ÷ old × 100

A positive result is an increase; a negative result is a decrease. The “old value” is always the number you are comparing against: last year’s price, your previous salary or the score on your first test.

Example 1: a price increase

Your monthly phone bill goes from 80 to 100.

1. Difference: 100 − 80 = 20.
2. Divide by the old value: 20 ÷ 80 = 0.25.
3. Multiply by 100: 25% increase.

Example 2: a decrease

A jacket drops from 100 to 80.

1. Difference: 80 − 100 = −20.
2. Divide by the old value: −20 ÷ 100 = −0.20.
3. Multiply by 100: 20% decrease.

Notice that going from 80 to 100 is a 25% increase, but going back from 100 to 80 is only a 20% decrease. The difference is the same 20, but the starting value is different. This is the most important idea in percentage change.

Example 3: a pay rise

Your hourly pay rises from 18.50 to 19.80. The difference is 1.30, and 1.30 ÷ 18.50 ≈ 0.0703, so the rise is about 7.0%. If prices rose 3% over the same period, your pay grew faster than prices.

Checking your answer quickly

Estimate before you calculate. In example 1, 20 is a quarter of 80, and a quarter is 25%. If your calculator had shown 20%, you would know you divided by the new value by mistake. Our percentage calculator has a “percentage change” mode: enter the old and new values and it shows the change with the working.

Increasing or decreasing a number by a percentage

Sometimes you know the percentage and want the new value. Convert the percentage to a decimal and multiply:

• Increase by p%: new = old × (1 + p ÷ 100). 250 increased by 12% = 250 × 1.12 = 280.
• Decrease by p%: new = old × (1 − p ÷ 100). 250 decreased by 12% = 250 × 0.88 = 220.

Shops use the second formula for discounts; see the discount calculator for sale prices.

Reverse percentages: finding the original value

If a price is 84 after a 20% increase, what was it before? Do not take 20% off 84 (that gives 67.20, which is wrong). Divide by the multiplier instead: 84 ÷ 1.20 = 70. Check: 70 × 1.20 = 84. The same idea is used to remove sales tax from a receipt total, explained in how to calculate sales tax.

Why +50% then −50% does not bring you back

Start with 100. A 50% increase gives 150. A 50% decrease from 150 gives 75, not 100. Each change is applied to a different base. This matters for investments: a stock that falls 50% needs to rise 100% to get back to where it started. When you combine percentage changes, multiply the factors: 1.50 × 0.50 = 0.75, a 25% overall fall.

Percent versus percentage points

If an interest rate rises from 4% to 5%, it has gone up by one percentage point, but by 25 percent (because 1 ÷ 4 = 0.25). News reports and loan offers mix these up. Percentage points describe the simple difference between two percentages; percent describes the relative change. Both are correct, they just answer different questions.

Percentage change for more than two values

If you track something over several years, you might want the average yearly change. Adding the yearly percentages and dividing gives only a rough answer, because each year starts from a different base. For growth, the compound annual growth rate is more accurate: (final ÷ start)1/years − 1. For example, growth from 100 to 150 over 5 years is (1.5)^0.2 − 1 ≈ 8.4% a year. If you need a plain average of a list of numbers instead, the average calculator and our guide to mean, median and mode will help.

Common mistakes

• Dividing by the new value instead of the old one.
• Forgetting to multiply by 100, so the answer looks like 0.25 instead of 25%.
• Subtracting a percentage of the new value when reversing a change.
• Adding percentage changes together instead of multiplying the factors.
• Confusing percent with percentage points.

For more everyday examples, from tips to test scores, read percentages in everyday life.