How to Calculate Percentage Change, Increase and Decrease

To calculate percentage change, subtract the old value from the new value, divide by the old value, and multiply by 100. If a gallon of milk goes from $3.20 to $3.68, the change is (3.68 − 3.20) ÷ 3.20 × 100 = 15%. A positive answer is a percentage increase; a negative answer is a percentage decrease. The same formula handles both.

The percentage change formula

The old value, also called the starting or reference value, always goes in the denominator. That single rule explains almost every confusing result you will meet with percentages, because the size of a change depends on where you start measuring from.

The vertical bars around old mean “absolute value.” They only matter when the starting value is negative, which is covered below.

Steps

1. Write down the old (starting) value and the new (ending) value.
2. Subtract: new − old. This is the absolute change.
3. Divide the absolute change by the old value.
4. Multiply by 100 and add a percent sign.

Worked examples

A percentage increase

A small business had 1,000 customers last year and 1,250 this year.

A percentage decrease

The next year, the customer count falls from 1,250 back to 1,000.

Notice the asymmetry. The business gained 25% and then lost 20%, and ended exactly where it started. The two percentages differ because the first change is measured from 1,000 and the second from 1,250. You can check either direction quickly with the percentage increase calculator or the percentage decrease calculator.

Why gains and losses do not cancel

Because each change uses a different base, a loss always needs a larger gain to recover, and the gap widens fast.

This is why investors say a 50% loss needs a 100% gain to break even. A $100 position that falls to $50 must double to return to $100.

Successive percentage changes

When several changes happen one after another, do not add the percentages. Convert each change to a multiplier and multiply them together:

A price that rises 10% and then falls 10% ends at 1.10 × 0.90 = 0.99 of where it started, a net 1% decrease, not zero.

Average change per period

A value that grows from 200 to 288 over two years increased by 44% in total. The average yearly increase is not 22%. Use the compound growth formula:

Here (288 ÷ 200)^1/2 − 1 = 1.2 − 1 = 20% per year. Check: 200 × 1.2 = 240, and 240 × 1.2 = 288. This is the compound annual growth rate, and the CAGR calculator works it out for any number of years.

Reversing a percentage change

If you know the new value and the percentage change, divide by the multiplier to find the original:

A shirt costs $92 after a 15% price increase. The old price was 92 ÷ 1.15 = $80. Subtracting 15% of $92 would give $78.20, which is wrong because the 15% was calculated on $80, not $92.

Percent vs percentage points

When the values you are comparing are themselves percentages, there are two ways to describe the change, and they give very different numbers.

• Percentage points are the simple difference. A mortgage rate that moves from 4% to 5% rose by 1 percentage point.
• Percent is the relative change. The same move is (5 − 4) ÷ 4 = a 25% increase.

Both statements are true, but they answer different questions. Reports on interest rates, unemployment and polling should use percentage points for the difference between two rates. If a headline says a rate “rose 25%,” check whether it went from 4% to 5% or from 4% to 29%.

Negative and zero starting values

Starting from zero. Percentage change from 0 is undefined because you cannot divide by zero. Going from 0 to 12 sales is not an “infinite percent” increase; just report the absolute change.

Negative starting values. Dividing by the absolute value of the old number keeps the sign meaningful. A company whose loss shrinks from −$50,000 to −$30,000 improved by (−30,000 − (−50,000)) ÷ 50,000 = +40%. Without the absolute value, the formula would report −40% for an improvement. Many analysts simply avoid percentages when the sign flips from loss to profit and report the dollar change instead.

Percentage change vs related measures

For two prices of $40 and $50 at different stores, there is no “old” price, so the percentage difference calculator divides the $10 gap by the $45 average: about 22.2%. In a lab, the percent error calculator measures how far a result landed from the accepted value.

Percentage change in a spreadsheet

With the old value in A2 and the new value in B2, enter =(B2-A2)/A2 and format the cell as a percentage. For 3.20 and 3.68 the cell shows 15%. To guard against a zero starting value, wrap it: =IF(A2=0,"n/a",(B2-A2)/ABS(A2)). The ABS also handles negative starting values the way described above.

To apply a percentage change instead of measuring one, multiply: =A2*(1+C2) raises the value in A2 by the rate in C2, and a negative rate in C2 lowers it.

Practice problems

1. A town’s population grew from 48,000 to 52,800. What was the percentage change? (52,800 − 48,000) ÷ 48,000 = 10% increase.
2. A laptop’s price fell from $1,150 to $920. (920 − 1,150) ÷ 1,150 = 20% decrease.
3. After a 20% markdown a lamp costs $56. What was the original price? 56 ÷ 0.80 = $70.

More problems with full solutions are on the percentage change word problems page.

For the basic part, whole and rate formulas that sit underneath all of these, see how to calculate a percentage. To skip the arithmetic entirely, the percentage change calculator shows the absolute change, the percent change and the multiplier together.