Percentage Change Calculator

How to use the percentage change calculator

The first calculator at the top, highlighted, answers “From A to B is a change of …%”. Type the old value first and the new value second; the result says how big the change is and whether it’s an increase (green) or a decrease (red). The second highlighted calculator gives the percentage difference between two values when neither is the “before”.

The percentage change formula

Percentage change = (new − old) ÷ |old| × 100

A positive result is an increase, a negative one a decrease. Examples:

Notice the last two rows: going up from 50 to 65 is +30%, but going back down from 65 to 50 is only −23.08%. The change is always measured against the starting value, and the starting values differ.

Order matters: which number is “old”?

Percentage change has a direction, so the order of the two numbers matters. The “old” value is your reference point: last month’s sales, the price before, the first measurement. Swap them and you get a different answer, as the table shows. If there is no natural before and after, for example comparing two shops’ prices on the same day, use percentage difference instead.

Percentage change vs percentage difference

• Percentage change compares a new value with an old one: (new − old) ÷ old. It has a direction (up or down).
• Percentage difference compares two values on equal terms: |A − B| ÷ the average of A and B. It’s always positive and gives the same answer in either order.

For 80 and 100: the change from 80 to 100 is +25%, from 100 to 80 is −20%, but the difference between them is 22.22% either way. Scientists and engineers often use the difference when comparing two measurements; businesses and news reports usually mean change.

Limits: decreases stop at 100%

A value can only fall by 100%, down to zero. Increases have no upper limit: from 10 to 50 is a 400% increase. This is why big falls need even bigger rises to recover. A share price that falls 50% needs a 100% rise to get back to where it was.

If the old value is zero, percentage change can’t be calculated (any increase from zero would be infinite), and the calculator says so instead of showing a meaningless number.

Changes involving negative numbers

With negative values, such as profits turning into losses or temperatures below zero, the formula divides by the size of the old value (|old|), so the direction stays meaningful. From −50 to −20 is a 60% increase, because −20 is higher than −50. Even so, percentage changes across zero, for example from a loss to a profit, are hard to interpret; in reports it’s often clearer to state the change in units as well.

Reporting a change clearly

• Give both numbers as well as the percentage: “sales fell 20.8%, from 1,200 to 950”.
• Say percentage points when the values are themselves percentages: a conversion rate going from 4% to 5% is a 1-point rise, or a 25% increase.
• Watch small bases. Going from 2 to 4 is a 100% increase, which sounds dramatic but is just 2 more.
• Round sensibly, usually to one decimal place.

For raises and adding a percentage to a number, see the percentage increase calculator.

Where percentage change is used

Shops use it for discounts and price changes, investors for share prices and portfolio returns, managers for sales and budgets month on month, scientists for measurements before and after an experiment, and anyone tracking a habit, such as weight, running times or spending. The calculation is always the same; what changes is choosing the right starting value. For the other everyday percentage questions, such as finding X% of a number, the main percentage calculator has a sentence for each.

Ask in plain words

• “Sales went from 1,200 to 950. What’s the percentage change?”
• “What’s the percentage difference between 80 and 100?”
• “My weight went from 82 kg to 76 kg. What percentage is that?”

Type it under the calculator or in the AI workspace. To compare growth over many years, try the compound interest calculator.