Percent Change Calculator

How percent change is calculated

Percent change compares a new value with an old value, using the old value as the base. The difference is new minus old. The percent is that difference divided by the old value, times 100. In symbols: ((new − old) ÷ old) × 100. A positive result is an increase. A negative result is a decrease. A result of zero means the two values are the same.

The panel shows three things: the percent rounded to three decimal places, the direction (increase, decrease, or no change), and the raw difference rounded to six decimal places. The difference is in the same units as the values you typed. Dollars stay dollars. Pounds stay pounds. The percent has no unit.

The base is always the old value, the first box. Swapping the boxes answers a different question. A move from 80 to 100 is (100 − 80) ÷ 80 = 0.25, a 25 percent increase. A move from 100 back to 80 is (80 − 100) ÷ 100 = −0.20, a 20 percent decrease. The return trip is not a 25 percent decrease, because the base changed. A 25 percent decrease from 100 would land at 75, not at 80. This is the single fact that causes most percent-change mistakes.

If the old value is exactly zero, the division cannot be done. The page still shows the direction and the difference, labels the percent undefined, and warns you. A jump from 0 to 1,000 has a difference of 1,000 and no percent. People sometimes call that "infinite" growth. The honest statement is that percent change is undefined when you start from zero.

Worked examples

Example 1: A raise, and why the reverse is a different percent

Old salary 80,000, new salary 100,000. Difference = 20,000. Percent = 20,000 ÷ 80,000 × 100 = 25 percent increase. If the salary later returns from 100,000 to 80,000, the percent is 20,000 ÷ 100,000 × 100 = 20 percent decrease. Both statements describe the same $20,000. They use different bases. When someone says "they gave 25 percent and then took 25 percent back," the second cut is larger than the first raise, and you do not land where you started.

Example 2: A price that fell

Old price 120, new price 90. Difference = −30. Percent = −30 ÷ 120 × 100 = −25, a 25 percent decrease. That is the same question as "what percent off is this?" when you know both prices. If you know the original price and the discount percent and want the sale price, use the Percent Off Calculator instead. Percent off starts from one price and a percent. Percent change starts from two prices.

Example 3: Two steps, and why you cannot add the percents

A value goes from 50 to 80, then from 80 to 100. First step: (80 − 50) ÷ 50 = 60 percent increase. Second step: (100 − 80) ÷ 80 = 25 percent increase. From the original 50 to the final 100 is (100 − 50) ÷ 50 = 100 percent increase. The 60 and the 25 do not add to 100, because they were taken against different bases. To get the overall change, enter the first old value and the last new value. To understand the path, run each step separately.

Example 4: Starting from zero

Old value 0, new value 1000. The difference is 1,000 and the direction is an increase. The percent is undefined, and the page says so. If last quarter's revenue was truly zero, report the dollar change and skip the percent. If the old value was small but not zero, say 10 growing to 1,000, the percent is 9,900 percent, which is arithmetically correct and easy to misread in a headline. Show the dollar difference beside any enormous percent.

When to use this

Use it whenever you have two measurements of the same thing and you want the change as a percent of the starting measurement. A raise, a rent increase, a price cut where both tags are visible, a month of revenue against the previous month, a weight against a starting weight, a bill that grew after a fee. The BMI Calculator and a scale give you the weights. This page turns two of those weights into a percent if you want one.

It is the wrong tool for a discount you already know as a percent, for a tip you want to add, or for a fraction you want to rewrite. Those are the percent-off calculator, the Tip Calculator, and the Fraction, Decimal, and Percent Converter. Percent change can be negative. A tip percent and a "percent off" are not signed that way.

Reading the result in context

A percent without the base is a weak summary. A 50 percent increase from 2 to 3 is one extra unit. A 50 percent increase from 2,000 to 3,000 is a thousand units. The panel's difference line is there so you can say both. In a budget, the dollars decide whether you care. The percent decides whether the move is large relative to where you started.

Year-over-year comparisons need the same definition in both periods. Revenue that includes a new product line, a weight that switched from clothed to unclothed, or a headcount that switched from full-time-only to full-time-plus-contractors will show a percent that mixes a real change with a change in the ruler. Align the definitions, then calculate.

Average change across several periods is a different question. This page handles one pair. If you have a list of values and want a typical value, the Average and Median Calculator is the next step. If you are splitting a change across people or ingredients in a fixed proportion, that is a ratio.

Common mistakes

• Dividing by the new value. The base is the old value. (new − old) ÷ new is a different ratio. From 80 to 100, dividing the $20 gain by 100 yields 20 percent, and the increase was 25 percent of the start.
• Expecting a decrease to undo an increase of the same percent. Twenty-five percent up from 80 is 100. Twenty-five percent down from 100 is 75.
• Adding percents from different steps. Each step has its own base. Chain them by using the original and the final value for the overall percent.
• Putting the later number in the old box. The first field is the starting point. Swapping them flips the sign and changes the percent.
• Forcing a percent when the old value is zero. Use the difference. The percent is undefined.
• Comparing percents whose bases differ and calling the larger percent the larger effect. Check the difference column before you rank them.
• Mixing units between the two boxes. Old in feet and new in inches produces a percent about a foot-to-inch conversion, not a real change. Convert first with the Length Converter or the matching measurement tool.

Limitations

One pair of numbers. No series, no compounding schedule, no inflation adjustment, and no "percent of the percent." The percent rounds to three decimals and the difference to six. Very large magnitudes can still be awkward to read in a text field, but the formula itself is the ordinary one. The page does not know whether your two numbers are comparable. A percent from a tiny base is allowed and can look sensational. Read it next to the difference. Negative old values are accepted mathematically (a change from −10 to −5 is an increase relative to −10) and are easy to misread. For ordinary prices, counts, and measurements, use positive bases.

FAQ

Is percent change the same as percent off?

Only in the special case where the new value is lower and you divide the drop by the original price. A drop from 120 to 90 is 25 percent off and a 25 percent decrease. Percent off as a shopping tool usually starts from the original and the discount percent. This page starts from the two values.

How do I get the new value if I know the percent?

New = old × (1 + percent ÷ 100). A 25 percent increase on 80 is 80 × 1.25 = 100. A 20 percent decrease on 100 is 100 × 0.80 = 80. This page runs the formula in the other direction.

Why is the reverse of a 25 percent increase a 20 percent decrease?

Because each percent uses its own starting value. The $20 raise was 25 percent of 80. The same $20 cut is 20 percent of 100. The dollars match. The percents do not, and they should not.

What should I report when we grew from zero?

Report the new level and the difference. Leave the percent out, which is what the warning is telling you. A percent needs a non-zero base.

Can I use this for a grade or a GPA?

You can compare two scores, such as 82 and 91, and get the percent change between those two numbers. A GPA on a 4-point scale is a different calculation. Use the GPA Calculator for credit-weighted grade points.

Related calculators

• Percent Off Calculator when you have a price and a discount percent
• Fraction, Decimal, and Percent Converter
• Tip Calculator
• Average and Median Calculator
• Ratio Calculator
• Unit Price Calculator to compare package sizes after a price change