Percent Change Calculator (Increase, Decrease & Percent Error)

A percent change calculator measures how much a value rose or fell compared with where it started: percent change = (new − old) ÷ |old| × 100. From 80 to 92 the change is 12, and 12 ÷ 80 = 0.15, so the value rose by 15%. Going back from 92 to 80 is a 13.04% decrease, because the starting value is different.

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How to use the percent change calculator

1. Pick what you need: Percent change (old to new), Reverse (find the new or the original value), Points vs percent (a change in a rate), Successive changes, Annualized change over several years, or Percent error.
2. Type your numbers. Commas, decimals, negative values and percent signs are fine.
3. Read the answer and the labels Increase or Decrease, then the extra figures: the amount of change, the multiplier, the reverse change and the percent difference. Open Show steps to see the working with your own numbers.

This page is only about change. To find a percent of a number or what percent one number is of another, use the percentage calculator.

Percent change formula

Percent change = (new value − old value) ÷ |old value| × 100

• new − old is the actual change. It is positive for an increase and negative for a decrease.
• |old value| is the starting value, the base you compare with. The absolute value bars only matter when the starting value is negative.
• Multiplying by 100 turns the decimal into a percent.

Percent change from 0 is undefined, because you cannot divide by zero. In that case, report the actual change instead (for example, “sales went from 0 to 40 units”).

Percent increase and percent decrease examples

Example 1, a price drop. A jacket goes from $50 to $35. Change = 35 − 50 = −15. Then −15 ÷ 50 = −0.30, so the price fell by 30%.

Example 2, a population increase. A town grows from 1,250 to 1,300 people. Change = 50, and 50 ÷ 1,250 = 0.04, a 4% increase.

Example 3, a negative starting value. A company’s profit goes from −20 to 10 (thousand dollars). Change = 10 − (−20) = 30. Divide by |−20| = 20: 30 ÷ 20 = 1.5, a 150% increase. Dividing by −20 instead would give −150%, which wrongly reads as a decrease. With negative values, quote the actual change too, because percents can mislead.

Reverse percent change: finding the original or new value

To find the new value, multiply by 1 + p/100 for an increase or 1 − p/100 for a decrease: 250 increased by 20% is 250 × 1.2 = 300.

To find the original value, divide instead. A shirt costs $48 after a 20% discount, so 48 = original × 0.8 and the original price was 48 ÷ 0.8 = $60. Adding 20% to $48 gives $57.60, which is wrong: the 20% was taken off $60, not off $48.

Percentage points vs percent

When the numbers are already percentages, there are two kinds of change. An interest rate that rises from 4% to 5% rose by 1 percentage point (5 − 4). As a percent change it rose by 25% (1 ÷ 4 × 100). Both are correct, but they answer different questions. News reports about rates, polls and unemployment should use percentage points for the plain difference. One percentage point equals 100 basis points.

Successive percent changes

Percent changes in a row multiply; they do not add. Turn each one into a multiplier, multiply, then convert back:

• +25%, then −20%, then +10%: 1.25 × 0.8 × 1.1 = 1.1, a total change of +10%, not +15%.
• +50%, then −50%: 1.5 × 0.5 = 0.75, a total change of −25%. A rise and a fall of the same percent always leave you below where you started.

Annualized percent change

For a change over several years, the annualized rate is the steady yearly change that produces the same total: (end ÷ start)^1/years − 1. A salary that grows from 50,000 to 80,000 in 5 years changed by 60% in total. The annualized change is 1.6^1/5 − 1 ≈ 9.86% per year, not 60 ÷ 5 = 12%, because each year’s raise builds on the last one. For investments, the same idea is called the compound annual growth rate; the CAGR calculator covers it in more detail.

Percent change vs percent difference vs percent error

For 80 and 92, the percent change is 15%, but the percent difference is 12 ÷ 86 ≈ 13.95%. A measured 9.6 m/s² against the accepted 9.81 m/s² has a percent error of 0.21 ÷ 9.81 ≈ 2.14%.

Percent change reference table

Each change has a multiplier, and undoing it takes a different percent.

Common mistakes with percent change

• Dividing by the new value. Always divide by the starting value. 80 to 92 is 12 ÷ 80, not 12 ÷ 92.
• Adding successive percents. +10% and then +10% is +21%, not +20%.
• Mixing up points and percent. A rate going from 2% to 3% is up 1 point, but 50% in relative terms.
• Undoing a change with the same percent. After a 25% rise, a 25% cut does not get you back; you need a 20% cut.
• Rounding too early. Keep full decimals until the last step, then round the percent.
• Not checking. Multiply the old value by the multiplier; you should get the new value. Estimate first, too: 80 to 92 is a bit more than 10%, so 15% is reasonable.

Percent change practice quiz: 10 questions

Test yourself with 10 multiple-choice questions. Choose an answer and press Submit to see if you are right and why. Your score appears at the end.

Frequently asked questions

How is percentage change calculated?

Subtract the old value from the new value, divide by the old value, and multiply by 100. From 40 to 50: (50 − 40) ÷ 40 × 100 = 25%. A positive answer is an increase; a negative answer is a decrease.

How do you find the percentage decrease?

Use the same formula, or the shortcut (old − new) ÷ old × 100 to get a positive number. From 50 to 35: 15 ÷ 50 × 100 = a 30% decrease.

Is percent change new minus old?

Yes. The top of the fraction is new minus old, so increases come out positive. The bottom is always the old value. Old minus new gives the same size with the opposite sign.

How do you calculate percent change year over year?

Compare each year with the year before it: (this year − last year) ÷ last year × 100. Revenue of 2.4 million last year and 2.7 million this year is a 12.5% year-over-year increase. For an average over several years, use the annualized change instead of averaging the yearly percents.

What is the percentage difference between two numbers?

Percentage difference compares two values when neither is the starting point: divide the gap by their average. For 80 and 92 it is 12 ÷ 86 × 100 ≈ 13.95%. The calculator shows it next to the percent change.

How do you calculate percentage change without a calculator?

Write the change over the old value as a fraction and simplify it to a denominator of 100. From 80 to 92: 12/80 = 3/20 = 15/100, so 15%. Halves, quarters, fifths and tenths are worth memorizing: 1/4 = 25%, 1/5 = 20%, 1/8 = 12.5%.

Related calculators

• Percentage calculator: percent of a number, what percent, find the whole
• Percent error calculator: measurement error in more detail
• CAGR calculator: compound annual growth rate
• Discount, tax and tip calculator: sale prices and totals
• Fraction, decimal and percent converter
• Average rate of change calculator: change per unit of time