Percentage Increase Calculator

1. Pick your question: the percent change between two values, adding or removing a percent, the original before a change, or two rates in percentage points.
2. Enter the original and new values, or a value and a percent. Add the number of periods if you want an average yearly or monthly rate.
3. Read the percent change, the amount of change and the multiplier. The working line shows every step.

A percentage increase is the size of a rise expressed as a share of the starting value. It answers "by how much did this grow, relative to where it began?"

Percent means per hundred. NIST Special Publication 811 treats the % symbol as the number 0.01, so 10% is 0.10 of the original. A percent change therefore compares values of very different sizes on one scale: a 3,000 raise on a 30,000 salary and a 30,000 raise on a 300,000 salary are both 10%.

A percentage decrease is the same idea when the value falls, and it shows as a negative percent change. The measure is used for pay rises, price changes, sales growth, test scores and population counts. It is not the same as the percent off a price, which starts from a percent and finds the new price, although both use the same arithmetic.

Subtract the original value from the new value, divide by the original value, then multiply by 100. OpenStax Prealgebra teaches the same two steps: find the amount of increase, then find it as a percent of the original amount.

1. Find the change: new minus original. A negative change means a decrease.
2. Divide the change by the original value, not by the new one.
3. Multiply by 100 and add the % sign.
4. To apply a percent instead, multiply by 1 plus the percent as a decimal (or 1 minus it for a decrease).

Why Up and Down Are Not Symmetric

A rise of 50% multiplies by 1.5, and a fall of 50% multiplies by 0.5. Doing both leaves 1.5 x 0.5 = 0.75, which is a 25% loss overall. In the same way, a drop from 80 to 60 is -25%, but the climb back from 60 to 80 is +33.33%. The calculator shows this "undo" figure for every result.

Average Growth Over Several Periods

When a value changes over several years, the average compound rate is (new / original) raised to 1 / periods, minus 1. Growth from 100 to 150 over 3 years is 50% in total but 14.47% per year, not 16.67%. The guide to raise percentages uses the same steps for pay.

Salary: pay rises from 30,000 to 33,000. Change = 3,000. 3,000 / 30,000 x 100 = 10% increase. To undo it, a fall of 9.09% would be needed.

Sales: revenue grows from 100,000 to 150,000. Change = 50,000, so the increase is 50% and the multiplier is 1.5x. Over 3 years that is an average of 14.47% per year.

Price drop: an item falls from 80 to 60. (60 - 80) / 80 x 100 = -25%. Getting back to 80 takes a rise of 33.33%.

Reverse: a fare is 90 after a 20% rise. The original is 90 / 1.20 = 75, not 90 minus 20% of 90 (72).

Two rates: an interest rate moves from 4% to 5%. That is 1 percentage point, and a 25% relative increase in the rate.

The starting value decides the answer more than anything else, because it is the denominator.

Which Value Is the Original

Swapping the two values changes the result. 60 to 80 is +33.33%, while 80 to 60 is -25%. Always put the earlier or reference value first.

A Small or Zero Starting Value

A rise from 2 to 6 is 200%, which can sound dramatic for a small real change. A change from 0 has no percent at all, so the tool reports it as undefined.

Negative Starting Values

Profit moving from -50 to 25 has no clean percent meaning. The tool divides by the size of the start and flags the result so you read it with care.

Time Span

A 20% rise over 10 years and a 20% rise over 1 year are very different. Enter the number of periods to see the compound rate per period.

These three measures are often mixed up. Each suits a different question.

The Journalist's Resource tip sheet from the Harvard Kennedy School puts it simply: when you compare two percentages, the gap is in percentage points. A diagnosis rate that rises from 1% to 5% rose 4 points, which is a 400% relative increase, not 4%.

Pay Rises and Job Offers

Compare a new salary with the old one, or find what a 4% raise adds to your pay.

Prices and Inflation

Check how much a bill or product has gone up. For the general price level over time, use the inflation calculator alongside this one.

Business and Sales Figures

Report growth month on month or year on year. When a selling price is built up from cost, a markup calculator fits better, because markup is a percent of cost.

News and Statistics

Check whether a headline means percent or percentage points before you repeat it.

1. Dividing by the New Value

30,000 to 33,000 divided by 33,000 gives 9.09%, which is the decrease back, not the increase. The original always goes on the bottom.

2. Reversing a Percent by Subtracting It

A price of 90 after a 20% rise was 75, not 72. Divide by 1.20 instead.

3. Adding Percent Changes Together

+10% then -10% is not zero. 100 x 1.1 x 0.9 = 99, a 1% loss.

4. Calling a Points Change a Percent Change

A rate going from 4% to 5% rose 1 point, or 25%. Saying it rose 1% understates it.

5. Averaging Yearly Growth by Simple Division

50% over 3 years is 14.47% a year compounded, not 16.67%.

6. Ignoring a Tiny Base

A 300% jump from 1 to 4 may matter less than a 5% rise on a large base. Look at the amount as well as the percent.

The arithmetic is exact for any numbers you enter. The results are shown to 4 decimal places, with percents rounded to 2.

Subtract the old number from the new one, divide by the old number and multiply by 100. From 50 to 65 is 15 / 50 x 100 = 30%.

Use the same formula; the answer comes out negative. From 200 to 150 is -50 / 200 x 100 = -25%, a 25% decrease.

Multiply the number by 1 plus the percent as a decimal. Adding 15% to 240 is 240 x 1.15 = 276.

Divide the new price by 1 plus the percent as a decimal. 90 after a 20% rise was 90 / 1.20 = 75.

Percentage points are the plain gap between two percentages, while percent change is relative. A rate moving from 4% to 5% is up 1 point, or 25%.

Yes. Any value that more than doubles has risen by over 100%. From 20 to 70 is a 250% increase.

The rise is measured from the smaller, lower value. 100 falling to 50 needs 50 more, which is 100% of 50.

No. Dividing by zero is undefined, so there is no percent change from 0. Report the amount of change instead.

Enter the number of years in the periods field. The tool shows the compound rate, such as 14.47% a year for 100 to 150 over 3 years.

No. Percent change divides by the original value, while percent difference divides by the average of two values with no before or after.

No. The math runs in your browser and nothing is sent to us. Save keeps a result only in this browser.

• Percent increase and percent decrease (OpenStax Prealgebra 2e, section 6.2; find the amount of change, then divide by the original amount).
• Percent change vs percentage-point change (The Journalist's Resource, Shorenstein Center, Harvard Kennedy School).
• The % symbol as the number 0.01 (NIST Special Publication 811, section 7.10.2).