Percent change calculator

Percent change always compares the difference with the old, starting value:

percent change = (new − old) / |old| × 100

A positive result is an increase and a negative result is a decrease. The calculator writes out each step: first the difference, then the division by the old value, then the multiplication by 100. That makes the answer easy to check, and easy to copy into homework or a report.

Two edge cases are handled on purpose:

• A negative starting value. If a company goes from a loss of −$40,000 to a profit of $10,000, dividing by a negative number would flip the sign and call an improvement a decrease. Using the absolute value of the old number in the denominator keeps the direction right: (10,000 − (−40,000)) / 40,000 × 100 = +125%.
• A starting value of zero. There is no percent change from zero, because you can't divide by zero. Going from 0 to 50 is an increase of 50 units, but not of any percentage. The calculator says so instead of printing a meaningless number.

A concert ticket went from $250 to $300.

1. Difference: 300 − 250 = 50.
2. Divide by the old value: 50 / 250 = 0.2.
3. Multiply by 100: 0.2 × 100 = +20%.

Now reverse it. If the price drops back from $300 to $250, the change is (250 − 300) / 300 × 100 = −16.67%. The same $50 is a bigger share of $250 than of $300, so the increase and the decrease are not the same size. This asymmetry is the most common source of confusion with percentages, and it is why it matters which number you treat as the starting point.

Your rent is $1,200 a month and the landlord announces a 15% increase.

• The increase: 1,200 × 15 / 100 = $180.
• The new rent: 1,200 × 1.15 = $1,380.

A decrease works the same way with subtraction: 15% off $1,200 is 1,200 × 0.85 = $1,020. The second part of the calculator shows both results at once, with the multiplier written out, so you can see that "increase by 15%" means "multiply by 1.15".

To go backwards, from the new rent to the old, divide instead of subtracting: 1,380 / 1.15 = 1,200. Taking 15% off $1,380 would give $1,173, not $1,200, because the 15% would be measured from the larger number.

A frequent mistake is to add two percentage changes together. If a stock rises 10% and then falls 10%, you don't end up where you started:

100 × 1.10 × 0.90 = 99, a total change of −1%.

The second change applies to the new, larger amount. To combine several changes, multiply the multipliers (1.10 × 0.90 = 0.99) and subtract 1. The same rule explains inflation: two years of 5% price increases are not 10% but 1.05 × 1.05 − 1 = 10.25% in total. Over many years the gap gets large, which is the same effect that makes compound interest grow faster than simple interest.

Change 1	Change 2	Naive sum	Actual total
+10%	−10%	0%	−1%
+50%	−50%	0%	−25%
+20%	+20%	+40%	+44%
−30%	+30%	0%	−9%

The bigger the individual changes, the further the naive sum is from the truth. A 50% loss needs a 100% gain to get back to even.

When a rate itself is a percentage, be careful with the wording. If a mortgage rate rises from 4% to 5%, that is a rise of 1 percentage point, but a 25% increase in the rate: (5 − 4) / 4 × 100 = 25%.

Old rate	New rate	Change in points	Percent change
4%	5%	+1 point	+25%
10%	8%	−2 points	−20%
50%	55%	+5 points	+10%

News reports, financial disclosures and polling results mix these up all the time. This calculator gives the percent change between the two numbers you enter; to get the change in percentage points, subtract one rate from the other.

Use percent change when there is a clear before and after: last year's sales and this year's, an old price and a new one, your weight in January and in June. The old value is the reference point.

Use percentage difference when the two numbers are on equal footing and neither is the starting point, such as two stores' prices for the same item or two lab measurements. That formula divides by the average of the two numbers, so the order doesn't matter.

Use percent error when one value is the accepted, true value and the other is a measurement you're checking against it.

All three are one click away from this page if you need them.

• 10% of a number: move the decimal point one place left (1,380 → 138).
• 5%: half of 10%. 20%: double 10%. 25%: a quarter. 50%: half.
• Doubling is a +100% change, halving is −50%, and tripling is +200%, not +300%.
• Undoing a rise: after a 20% increase, you need a 1 − 1 / 1.2 = 16.67% decrease to get back.

The calculator also shows the multiplier (for example 1.2×) and what share of the old value the new one is, which is often the quickest way to explain a change to someone else. The numbers you type are saved in the page link, so the Share button sends exactly this calculation.