How to Calculate Percentage Change (Increase and Decrease)

What is percentage change?

Percentage change describes how far a value moved, measured as a share of where it started. It answers the question “by what percent did this go up or down?” The starting point is called the original, old, or base value. The later reading is the new value.

Because the result is scaled to the starting value, it lets you compare movements of very different sizes. A rent that rose from 1,000 to 1,050 and a bus fare that rose from 2.00 to 2.10 both increased by 5%, even though one rose by 50 and the other by 0.10.

The sign carries meaning. A positive percentage change is an increase, a negative one is a decrease, and zero means the value did not move.

What is the formula for percent increase and percent decrease?

There is only one formula, and it handles both directions: (new − original) ÷ original × 100. When the new value is larger, the top of the fraction is positive and you get a percent increase. When the new value is smaller, the top is negative and you get a percent decrease.

Some textbooks split it into two formulas. Percent increase is (new − original) ÷ original × 100, and percent decrease is (original − new) ÷ original × 100. The second version simply flips the subtraction so the answer comes out positive. Both describe the same movement, so pick whichever wording your class or report uses and stay consistent.

Notice the 40 to 90 row. A percentage increase can be larger than 100%, because the new value can be more than double the original. A percentage decrease of a positive quantity, on the other hand, stops at 100%, which means the value fell all the way to zero.

Why does a rise and an equal fall not cancel out?

The base changes between the two moves. A 25% rise from 80 lands on 100. A 25% fall from 100 lands on 75, not 80, because 25% of 100 is bigger than 25% of 80. To get from 100 back to 80 you need a 20% drop.

This is why a price that is cut by 50% and later raised by 50% ends up at 75% of where it began. If an investment loses 10% one year and gains 10% the next, it finishes slightly below its starting value. Whenever you chain two percentage changes, multiply the growth factors instead of adding the percentages. A 10% rise is a factor of 1.10, a 10% fall is a factor of 0.90, and 1.10 × 0.90 = 0.99, which is a 1% net fall.

What is the difference between percentage points and percentage change?

When the values you are comparing are already percentages, there are two honest ways to describe the move, and they give different numbers. If a pass rate goes from 40% to 50%, it rose by 10 percentage points. Measured as a percentage change, it rose by (50 − 40) ÷ 40 × 100 = 25%.

Both statements are true, but they answer different questions. Percentage points describe the plain gap between two rates. Percentage change describes how big that gap is relative to the starting rate. News reports about interest rates, polls and exam results use percentage points for exactly this reason, because “a 25% rise in the pass rate” can sound like something larger than it is.

The calculator works with whatever numbers you type. Enter 40 and 50 and it reports a 25% increase. If you want the points figure, read the Difference line instead, which shows 10.

Is percentage difference the same as percentage change?

Not quite. Percentage change has a direction: there is a before and an after, and you divide by the before. Percentage difference is used when neither value is the starting point, such as comparing the heights of two buildings or the prices at two shops on the same day.

A common definition of percentage difference divides the absolute gap by the average of the two values. For 80 and 100, the gap is 20 and the average is 90, so the percentage difference is about 22.2%. That sits between the 25% and 20% you get from the two possible percentage changes. This calculator computes percentage change only, so use it when one value clearly came first.

What happens when the original value is zero or negative?

Dividing by zero has no answer, so a change from 0 to any other number cannot be expressed as a percentage. Going from 0 sales to 15 sales is a gain of 15, not an infinite percent. The calculator rejects that case with a message, and it reports 0% when both values are 0. In a report, give the raw difference for anything that started at zero.

Negative starting values cause a different problem. The formula still divides by the original, so the sign of the result can contradict the direction of the move. A loss that shrinks from −50 to −25 improved by 25, yet the formula divides 25 by −50 and gives −50%. If you work with profits and losses, temperatures below zero, or account balances that can go negative, read the Difference line for the direction and explain the percentage separately, or measure against the absolute value of the original if your field accepts that convention.

How to calculate percentage change with the calculator

1. Type the original value. Enter the earlier, starting, or reference figure in the Original value box. Use plain digits and a decimal point, such as 1250 or 12.5. Commas and currency signs are not accepted, so 1,250 or $12.50 will show an error.
2. Type the new value. Enter the later reading in the New value box. It can be bigger, smaller, or the same as the original.
3. Press Calculate. The large line shows the size of the move and its direction, such as “25% increase”. The line below gives the signed change, such as −20%, and the plain difference between the two values.
4. Copy or reset. Use the copy button to copy the signed percentage for a spreadsheet or message. Reset clears both boxes so you can start another comparison. Nothing you type is sent anywhere, because the arithmetic runs in your browser.

Example

Tips and limitations

FAQ

Which number do I divide by when I work out a percentage change?

Divide by the original, earlier, or reference value. If you divide by the new value instead, you get a different answer, such as 20% instead of 25% for a move from 80 to 100.

Can a percentage increase be more than 100%?

Yes. Any new value more than double the original gives an increase above 100%. Going from 20 to 70 is a 250% increase.

Can a percentage decrease be more than 100%?

For a positive quantity that stays at zero or above, no. A 100% decrease means the value fell to zero. A larger figure only appears when the new value is negative, such as a balance going from 100 to −20.

How do I find the original value if I know the new value and the percent change?

Divide the new value by the growth factor. After a 25% rise to 100, the original was 100 ÷ 1.25 = 80. After a 20% fall to 80, the original was 80 ÷ 0.80 = 100.

How do I add a percentage increase to a number?

Multiply by one plus the rate. A 15% increase on 200 is 200 × 1.15 = 230. The Percentage Calculator can also find 15% of 200 for you, which you then add on.

Is a change from 2% to 3% a 1% increase or a 50% increase?

It is a rise of 1 percentage point and a 50% relative increase. Both are correct, so name the one you mean.

How do I calculate percentage change in Excel or Google Sheets?

With the original in A2 and the new value in B2, use =(B2-A2)/A2 and format the cell as a percentage. That is the same formula the calculator uses.

Why does my percentage change look wrong for negative numbers?

The formula divides by the original, so a negative original flips the sign. A loss shrinking from −50 to −25 shows −50% even though the value rose. Use the Difference line for direction in that case.

How do I compare growth over several years?

For the total change, compare the first and last values. Year-by-year changes do not add together, because each year starts from a new base.

Does the calculator round the result?

It shows up to six decimal places and drops trailing zeros. The Copy button copies the signed figure as displayed, such as 12.5% or -20%.

Sources and further reading

• Understand percent (OpenStax Prealgebra 2e)