Percentage change tells you how much a value grew or shrank compared with where it started. It is the number behind price rises, salary increases, grade improvements and investment returns. This guide shows the formula, works through real examples step by step, and covers the mistakes that make percentage changes come out wrong.
Percentage change compares the size of a change with the value you started from. The formula is:
Percentage change = ((new value − old value) ÷ old value) × 100
The old value is the starting value, before the change. The new value is the value after the change. Subtracting the old value from the new value gives the change itself. Dividing by the old value expresses that change as a fraction of the starting point, and multiplying by 100 turns the fraction into a percentage.
The sign carries the meaning. A positive result means the value increased. A negative result means it decreased. A result of 0 means the value did not change at all. The size of the percentage only makes sense relative to the starting value, which is why the same $10 rise is 10 percent on a $100 item and only 1 percent on a $1,000 item.
A jacket was priced at $45 last season and costs $60 now. What is the percentage change?
The price increased by about 33.3 percent. You can run the same numbers in the percentage change calculator and see the identical working.
A website had 240 visitors a day in March and 180 visitors a day in April. What is the percentage change?
Traffic fell by 25 percent. The negative sign is the decrease, so the answer is usually stated as a 25 percent decrease rather than negative 25 percent.
When the values themselves are percentages, two different measures get confused. If an interest rate rises from 5 percent to 7 percent, the rate rose by 2 percentage points. The percentage change is different. The change is 2, the old value is 5, and 2 ÷ 5 × 100 = 40 percent. The rate rose by 2 percentage points, which is a 40 percent increase in the rate.
News reports mix these up often, and the difference matters. Use percentage points when you describe the simple gap between two percentages. Use percentage change when you describe how much a value grew or shrank relative to its own starting point.
Dividing by the new value. The most common error is using the new value as the base. In the jacket example, dividing $15 by $60 gives 25 percent, which is wrong. The base is always the value you started from, the old value.
Averaging percentages. Percentages with different bases cannot be added or averaged directly. If a price falls 50 percent and then rises 50 percent, it does not return to the start. A $100 item falls to $50, and a 50 percent rise on $50 only brings it back to $75.
Confusing percent of with percentage change. Finding 20 percent of $80 answers a different question, and the percentage calculator handles that one. Percentage change needs both an old and a new value. A discount is a percentage decrease applied to a price, so discount questions belong to percentage change.
Starting from zero. If the old value is 0, the formula divides by zero and the percentage change is undefined. Growth from nothing cannot be expressed as a percentage, so describe it in absolute terms instead, for example sales grew from $0 to $500.
Subtract the old value from the new value, divide by the old value, and format the cell as a percentage. If the old value is in cell A2 and the new value is in B2, the formula is =(B2-A2)/A2. The cell shows the same result this page works out by hand.
Yes, for increases. A value that doubles has risen by 100 percent, and a value that triples has risen by 200 percent. Decreases are capped the other way. A positive value cannot fall by more than 100 percent, because a 100 percent fall brings it to zero.
Percentage change uses the old value as the base, because one value came first. Percent difference is used when neither value is the starting point, and it uses the average of the two values as the base instead. For before and after questions, percentage change is the right tool.
Because the base changes. Going from 80 to 100 is a 25 percent increase, but going from 100 back to 80 is a 20 percent decrease. The change is 20 in both directions, while the starting value is different, so the percentages differ.
Work out the percentage increase or decrease between two values, with the steps shown.
Use calculatorFind what percent of a number is, or what percent one number is of another.
Use calculatorCalculate sale prices and total savings from any discount percentage.
Use calculator