How to calculate percentage change in your head

To calculate percentage change, take the new number, subtract the old number, divide by the old number, and multiply by 100. If the answer is positive, it went up by that percent. If it is negative, it went down.

Percent change = (new minus old) divided by old, times 100.

A worked example with round, hypothetical numbers: a coffee that cost 4 now costs 5. New minus old is 1. Divided by the old price, 4, that is 0.25. Times 100 is 25. The price rose 25 percent.

That is the whole formula. The rest of this post is three mental shortcuts that let you do it in your head in the store aisle, plus two common mistakes to avoid.

This is general education about arithmetic, not financial, investment or tax advice. For decisions about your own money, a qualified accountant or financial professional can look at your full situation.

Always divide by the old number

The old number is the starting point, so it is the thing you compare against. This matters more than it looks.

Take the coffee again. Going from 4 to 5 is a change of 1. Divided by 4, that is a 25 percent rise. Now suppose the price later drops from 5 back to 4. The change is still 1, but now the old number is 5, so the drop is 1 divided by 5, which is 20 percent.

Up 25 percent and down 20 percent bring you back to the same place. That surprises people, but it follows straight from the formula: the starting point changed, so the percent changed.

Shortcut 1: Build from 10 percent and 1 percent

Ten percent of any number is that number with the decimal point moved one place left. One percent is the decimal moved two places left. With those two pieces you can measure almost any change.

Hypothetical example: rent goes from 1,200 to 1,260 a month.

• The change is 60.
• Ten percent of the old rent, 1,200, is 120.
• 60 is half of 120, so the change is half of 10 percent.
• The rent rose 5 percent.

Another: a bill falls from 300 to 270. The change is 30. Ten percent of 300 is 30. So the bill fell exactly 10 percent.

Shortcut 2: Know a few friendly fractions

Many everyday changes are simple fractions of the old number. If you recognize the fraction, you know the percent.

• A change of one half of the old number is 50 percent.
• One quarter is 25 percent.
• One fifth is 20 percent.
• One tenth is 10 percent.
• One third is about 33 percent.
• Doubling is a 100 percent increase. Tripling is a 200 percent increase, not 300.
• Halving is a 50 percent decrease.

Hypothetical example: a streaming plan goes from 15 to 20 a month. The change is 5, and 5 is one third of 15. So the price rose by about 33 percent. You did not need to divide anything on paper.

Shortcut 3: Round to a friendly old number

When the old number is awkward, round it to something easy, get a quick answer, and remember that you rounded.

Hypothetical example: a grocery bill goes from 98 to 112. The change is 14. The old number, 98, is close to 100, and 14 out of 100 is 14 percent. Because 98 is a little less than 100, the true answer is a little more than 14 percent. The exact figure is 14 divided by 98, about 14.3 percent. For most everyday decisions, "about 14 percent" is plenty.

The rule of thumb: if you rounded the old number up, the real percent is slightly bigger than your estimate. If you rounded it down, the real percent is slightly smaller.

The other common mistake: percent versus percentage points

When the thing that changed is already a percentage, be careful with words. If an interest rate goes from 4 percent to 5 percent, it rose by 1 percentage point. As a percent change, though, it rose by 25 percent, because 1 divided by 4 is 0.25.

Both statements are true. They answer different questions. When you read about rates, check which one is meant.

Practice this week

The shortcuts only stick if you use them. Try this for a few days:

• Pick one price you pay regularly and compare it with what you paid last time.
• Find the change, then find 10 percent of the old price.
• Estimate the percent in your head before you check it on a calculator.
• Note whether you rounded up or down, and whether your estimate landed on the right side.

After a handful of tries, most everyday percent changes take a few seconds. You will spot a 20 percent price rise on the shelf before you reach the checkout, and that is the whole point of doing the arithmetic yourself.