Percentage Change Calculator

Find the percent increase or decrease from one value to another, the percent difference between two numbers, or add or subtract a percentage, with every step shown.

% change % difference Add/subtract %

Starting value

Final value

My values are percentages (rates)

Percent change

+25%

Increase from 80 to 100

Absolute change

+20

Multiplier (final ÷ starting)

×1.25

How it's calculated

Subtract the starting value from the final value: 100 − 80 = 20
Divide by the starting value: 20 ÷ 80 = 0.25
Multiply by 100: 0.25 × 100 = 25%

Updated: October 5, 2026

Percentage change calculator. Percent increase or decrease between two numbers, percent difference and adding a percentage.

This percentage change calculator turns a starting and a final value into the percent increase or decrease and the absolute change between them. Two other modes give the percent difference of two numbers, measured against their average, and a value increased or decreased by a percentage.

What percent change is, and the two related questions this page answers

Percent change is the difference between a final value and a starting value, divided by the size of the starting value and multiplied by 100. From 80 to 100 the difference is 20, and 20 ÷ 80 × 100 = 25, so the value rose 25%. A positive result is an increase and a negative one a decrease: going back from 100 to 80 is -20%, because the base is now 100.

The measure fits anything recorded twice, before and after: a price, a salary, a monthly bill, a test score, the population of a town. The U.S. Bureau of Labor Statistics follows the same three steps for the Consumer Price Index. In its worked example the index moves from 277.948 to 278.802, a rise of 0.854 index points; 0.854 ÷ 277.948 × 100 rounds to the 0.3% that BLS reports, and this calculator shows +0.31% because it keeps two decimals.

The pills at the top of the form switch between three questions about two numbers. % change, the default, gives the percent change from a starting value to a final value, the absolute change in the same units and, for a starting value above 0, the multiplier from one to the other. % difference compares two values with no before and after, such as two quotes for the same job, and divides their gap by their average, so the order of the two does not change the answer. Add/subtract % runs the other way, from a value and a percentage to the value after the change, such as a price with sales tax added.

In % change, the switch My values are percentages (rates) handles a change between two rates, such as interest rates or poll shares. The second card then becomes Change in percentage points, and Percent change keeps the relative figure, so both readings of the same move are on screen. Every result comes with its working in the How it's calculated fold, open when the page loads, so you can check a homework answer or a figure for a report line by line.

Two neighboring pages cover what this one leaves out: the percentage calculator for a part of a whole, such as 25% of 80 or what percent 20 is of 80, and the discount percentage calculator for the percent off between a price and a sale price. The article Same Two Numbers, Five Different Answers sorts out which of these questions a given pair of numbers is asking.

The percent change formula, with percent difference and adding a percentage

\text{Percent change} = \frac{V_{\text{final}} - V_{\text{start}}}{\left|V_{\text{start}}\right|} \times 100

$V_{\text{start}}$ = the starting value, the one you compare against, such as last year's price or the old salary
$V_{\text{final}}$ = the final value, the one the starting value moved to
$\left|V_{\text{start}}\right|$ = the size of the starting value, its distance from 0; for a positive start it is the starting value itself, and for a negative start it drops the minus sign

For a positive starting value the bars change nothing, and the formula is the familiar (new − old) ÷ old × 100. They matter for a negative start. From -25 to 25 the value rose by 50, and dividing by 25, the size of -25, gives +200%; dividing by -25 itself would report -200%, a decrease for a value that went up. The percent change formulas published by CalculatorSoup and Omni Calculator divide by the absolute value too, so a result checked against either of them agrees with this page. Wikipedia's article on relative change adds the other boundary: the change is not defined when the reference value is 0, and the Percent change card shows a dash in that case.

Percent difference takes the average of the two sizes as its base, so swapping the values leaves the result unchanged:

\text{Percent difference} = \frac{|A - B|}{(|A| + |B|)/2} \times 100

For 20 and 30 the gap is 10 and the average is 25, so the percent difference is 10 ÷ 25 × 100 = 40%. The absolute values inside the average follow Wikipedia's relative difference, which stays defined for negative numbers and equals 0 when both values are 0. The formulas on calculator.net and Omni Calculator write the average as (V1 + V2) / 2, which matches this page for positive values; for -4 and -6 that version gives -40%, while this page gives 40%, subtitled Compared with the average of their sizes, 5. CalculatorSoup's percent difference calculator accepts only numbers greater than 0.

Adding or subtracting a percentage runs percent change backward:

\text{New value} = V \pm |V| \times \frac{p}{100}

With V = 80 and p = 25 the new value is 80 + 20 = 100. Taking the percentage of the size keeps the two directions consistent for negatives as well: -50 increased by 10% is -45, and from -50 to -45 is a +10% change.

For two rates, the change in percentage points is the plain difference, final rate minus starting rate, and the relative change is the percent change between them. Wikipedia's Percentage point article gives the example of 40% rising to 44%: an increase of 4 percentage points, which is a 10% relative increase.

How to use it: checking a rent increase

A tenant's rent goes from 1,450 to 1,595 a month, and the renewal letter says next year brings another 10%.

1. The page opens on % change, with 80 in Starting value and 100 in Final value. The large card reads Percent change +25%, subtitled Increase from 80 to 100, and the two smaller cards read Absolute change +20 and Multiplier (final ÷ starting) ×1.25.

2. Type 1450 in Starting value and 1595 in Final value. There is no Calculate button: the cards follow each keystroke and settle on +10%, +145 and ×1.1. The fields keep what you typed, while the cards and steps print larger numbers with thousands separators, as in 1,595.

3. The How it's calculated fold is already open under the cards, rewritten for these numbers: 1,595 − 1,450 = 145, then 145 ÷ 1,450 = 0.1, then 0.1 × 100 = 10%.

4. For next year, pick Add/subtract %, type 1595 in Starting value and 10 in Percentage, and leave Increase selected. New value reads 1,754.5, subtitled 1,595 increased by 10%, and Change reads +159.5. The page does not round to cents, because its values carry no unit: that rent is 1,754.50 a month.

5. The copy button next to the large card copies its figure as displayed, such as +10%, for a spreadsheet or a message. The page address holds every value that differs from the defaults, so a copied link reopens the same numbers, and an address with no query opens 80 and 100.

Worked examples: pay, shares, rates, losses, quotes and sales tax

A raise from 52,000 to 55,120, measured against prices that rose 3%

In % change, a starting value of 52000 and a final value of 55120 give Percent change +6%, Absolute change +3,120 and Multiplier ×1.06. Suppose prices rose 3% over the same year. The raise in buying power is the ratio of the two multipliers, 1.06 ÷ 1.03 = 1.0291, about +2.91%, a little under the 3 points that 6 − 3 suggests.

The page gets there without the division: enter 103 as the starting value and 106 as the final value, and Percent change reads +2.91%. A raise that trails prices comes out negative the same way: a 2% raise against 3% inflation, 103 to 102, reads -0.97%.

A share that falls 50% and then gains 50%

A share bought at 100 drops to 50. % change reads -50% with a multiplier of ×0.5. From 50 it climbs to 75, which reads +50% and ×1.5. The two percentages look as if they cancel, yet from 100 to 75 the page reads -25% and ×0.75: multipliers chain by multiplication, 0.5 × 1.5 = 0.75, and percentages do not add. Getting from 50 back to 100 takes +100%, a doubling.

A mortgage rate from 6% to 7.5%: percentage points and percent

Turn on My values are percentages (rates), and the fields become Starting rate (%) and Final rate (%). Type 6 and 7.5 as plain numbers; these fields take no % sign. The second card turns into Change in percentage points and reads +1.5 pp, while Percent change reads +25%, subtitled Increase from 6% to 7.5%. A note under the cards reads: "From 6% to 7.5% is a rise of 1.5 percentage points: a 25% relative increase."

A headline saying rates rose 1.5% is counting percentage points. The +25% is what happens to the interest charged on the same balance, a quarter more each year.

A loss that turns into a profit: percent change across zero

A small business lost 60 thousand last year and earned 50 thousand this year. In % change, -60 to 50 reads +183.33%, with an absolute change of +110 and no Multiplier card, and a note appears under the cards: "The starting value is negative, so the change is divided by its size, 60. Across zero, percent changes can mislead; analysts often report them as not meaningful."

A second business that lost 10 and also earned 50 shows +600% (-10 to 50, absolute change +60), the bigger percentage for the smaller turnaround. Jon Acampora of Excel Campus uses this same pair to show how the ABS formula misleads, and suggests printing "--" in a spreadsheet when either value is 0 or below. The absolute changes, +110 against +60, rank the two businesses in the right order. A loss that deepens is a decrease on this page: -20 to -45 reads -125%.

Two quotes for the same job: percent difference

Two contractors quote 1,800 and 2,200 for the same kitchen, and neither quote came first. In % difference, Value A 1800 and Value B 2200 give Percent difference 20%, subtitled Compared with their average, 2,000, and Absolute difference 400. The note under the cards adds the two directional readings: "Percent change depends on direction: from 1,800 to 2,200 is +22.22%, from 2,200 to 1,800 is -18.18%."

The higher quote is 22.22% above the lower, the lower is 18.18% below the higher, and 20% is the figure that takes neither as the base.

Sales tax and a tip with Add/subtract %

An item priced 19.99 with 7.5% sales tax: in Add/subtract %, Starting value 19.99 with Increase selected and Percentage 7.5 gives New value 21.48925 and Change +1.49925. The page keeps every decimal, so round to 21.49 yourself.

An 18% tip on a 64 check works the same way, 64 × 18 ÷ 100 = 11.52, for a total of 75.52. Decrease takes a percentage off instead: 80 decreased by 15% is 68, with a Change of -12.

Common percent changes, their multipliers and the change that undoes each

Percent change	From 100 to	Multiplier	Change back to 100
+5%	105	×1.05	-4.76%
+10%	110	×1.1	-9.09%
+20%	120	×1.2	-16.67%
+25%	125	×1.25	-20%
+50%	150	×1.5	-33.33%
+100%	200	×2	-50%
+200%	300	×3	-66.67%
-10%	90	×0.9	+11.11%
-20%	80	×0.8	+25%
-25%	75	×0.75	+33.33%
-50%	50	×0.5	+100%
-75%	25	×0.25	+300%
-90%	10	×0.1	+900%

Which figure to report: percent change, percent difference, points or the plain change

Percent change is the figure for anything with a first value and a later one, such as last quarter's sales against this quarter's. The starting value is the base, so name it in the sentence, as in "up 15% from 40", and a reader can rebuild the figure.

Two values on an equal footing, such as two stores' prices for the same item, call for percent difference. The result is unsigned and the same in either order. If one of the two is an accepted or true value, the figure a lab report asks for is percent error, the size of the change measured from that true value; in % change, put the true value in Starting value and drop the sign.

A change in a rate, such as an unemployment rate or a poll share, is best given in percentage points. Wikipedia's Relative change article recommends points whenever the variable is itself a percentage, to keep relative and absolute change apart. A relative figure can sit next to it as long as it is labeled as one.

The absolute change is the safer figure when the starting value is 0, negative or small. A percent from 0 does not exist, a percent across zero can rank a small turnaround above a large one, and a jump from 2 cases to 5 reads +150% while describing three cases. The Absolute change card stays on the page in all three situations.

To chain changes, multiply the multipliers. A 6% raise is ×1.06, and two years of it are 1.06 × 1.06 = 1.1236, a total of +12.36%. For the same rate compounding over many periods, the compound interest calculator does the repeated multiplication and shows where it ends up.

Mistakes that produce the wrong percentage

Dividing by the final value. The base is the starting value. From 80 to 100, dividing the gap of 20 by 100 gives 20%, which is the decrease from 100 to 80; the increase from 80 is 20 ÷ 80 = 25%.
Undoing a percentage with the same percentage. Adding 40% back to a jacket that costs 60 after 40% off gives 84 (Add/subtract %: 60 increased by 40%), and the jacket cost 100 before the sale. The 40% was a share of that original price, 60 ÷ 0.6 = 100, so the climb back from 60 to 100 is +66.67%.
Treating "percent of" as percent change. 25 is 25% of 100, a part of a whole. Going from 25 to 100 is a +300% change. Both statements use the same two numbers and answer different questions; the percentage calculator handles the part-of-a-whole one.
Taking the percent change of a temperature. Celsius and Fahrenheit put their zero at an arbitrary point, so ratios between readings carry no meaning; Wikipedia's Level of measurement article gives the example that 20 °C is not twice as hot as 10 °C. From 10 °C to 20 °C the page would print +100%, and the same two days in Fahrenheit, 50 °F to 68 °F, give +36%. Report a temperature change in degrees.
Using percent difference for a before-and-after. A price that went from 200 to 260 rose 30%. % difference on the same pair returns 26.09%, the gap of 60 divided by the average, 230, which describes two prices side by side and understates the increase.

Percent change questions

How do you calculate the percentage increase or decrease between two numbers?

Subtract the old number from the new one, divide by the old number and multiply by 100. From 40 to 46: 46 − 40 = 6, 6 ÷ 40 = 0.15, and 0.15 × 100 = 15%. A negative result is a decrease: 46 to 40 is -13.04%.

Why is 80 to 100 a 25% increase but 100 to 80 only a 20% decrease?

Each percentage is measured against its own starting point. The gap is 20 both ways, and 20 is a quarter of 80 but a fifth of 100. For positive values, any increase is bigger in percent than the decrease that reverses it: +50% is undone by -33.33%, and +100% by -50%. In % difference, the note under the cards shows both directions for a pair of values.

Is percent difference the same as percent change?

No. Percent change has a direction and divides by the starting value; percent difference has none and divides by the average of the two values. For 80 and 100 the percent difference is 22.22% in either order, while the percent change is +25% one way and -20% the other. Percent difference is the one for two numbers where neither came first.

Is a rise from 3% to 5% a 2% increase or a 66.67% increase?

It is a rise of 2 percentage points (5 − 3) and a 66.67% relative increase (2 ÷ 3). Calling it a 2% increase mixes the two up: 2% of 3% would be only 0.06 points. With My values are percentages (rates) turned on, the page shows +2 pp on the Change in percentage points card and +66.67% as the percent change.

How do you calculate percent change with negative numbers?

Divide the change by the size of the starting value, its absolute value, so the sign of the result still matches the direction. Wikipedia's relative change article shows the trap with -10 to -6: dividing by -10 gives -40% for a value that rose, and dividing by 10 gives +40%. A loss that deepens from -20 to -45 is -25 ÷ 20 = -125%, a decrease. The page uses this rule and adds a note under the cards whenever the starting value is negative.

What is the percent change from 0?

There is none, because dividing by a starting value of 0 is undefined. The Percent change card shows a dash, subtitled Undefined: the starting value is 0, and the Absolute change card still reports the move, +50 for 0 to 50. Report that number, or the new value alone.

What does a 200% increase mean, and is "three times more" the same thing?

A 200% increase triples a value: 100 to 300 reads +200%, with a multiplier of ×3. A 100% increase doubles it, and 100 to 250 is +150%, or ×2.5. "Three times more" can be read as ×3 or as the original plus 300%, which is ×4. Bill Walsh, then a multiplatform editor at The Washington Post, advised in a Vocabulary.com article writing "three times as much" instead; quoting the multiplier or the percent avoids the question.

Can a percentage decrease be more than 100%?

Only if the value crosses zero. From 100 to -20 is -120%, and in Add/subtract %, 200 decreased by 120% leaves -40, with the note "A decrease of more than 100% takes the value past zero." A price or a count cannot go below 0, so for those -100% is the floor: the value has fallen to nothing.

How do I find the original number before a percentage increase?

Divide the new number by its multiplier, 1 plus the percentage as a decimal. A price of 100 after a 25% increase started at 100 ÷ 1.25 = 80, and 68 after a 15% decrease started at 68 ÷ 0.85 = 80. The page has no reverse mode, but Add/subtract % confirms the answer: 80 increased by 25% returns 100.

Can I add or average percent changes from several years?

Not by adding them. A value that rises 10% and then falls 10% goes 100 → 110 → 99, a net -1%, though the two percentages sum to 0. For a run of years, multiply the yearly multipliers (here 1.1 × 0.9 = 0.99) and subtract 1, or enter the first and the last value in % change. The average yearly rate behind a multi-year change is a compound rate, the kind the compound interest calculator works with.

When is the percent difference 100% or 200%?

Percent difference is 100% when one value is three times the other: 10 and 30 differ by 20, which equals their average. It reaches 200%, its ceiling, when one value is 0 or the two have opposite signs, as with 0 and 10 or -5 and 5, and the page adds a note under the cards saying so.

What is the Excel or Google Sheets formula for percent change?

With the old value in A2 and the new one in B2, =(B2-A2)/ABS(A2) returns the change as a decimal; format the cell as a percentage to read 25% for 80 and 100. The ABS keeps the sign right when the old value is negative, which is the rule this page follows, so the two agree. For percent difference, use =ABS(A2-B2)/((ABS(A2)+ABS(B2))/2). Both formulas return #DIV/0! when the divisor is 0.

How should I report a percent change in a report or a slide?

Give the direction, the base and the size: "sales rose 12%, from 2,500 to 2,800 units" lets a reader check the figure, and "up 12%" alone does not say from where. For rates, write percentage points. The copy button next to the result copies the signed figure, such as +12%, ready to paste into a spreadsheet or a slide.

How many decimals does the result show, and is it rounded?

Percents show up to two decimals with no trailing zeros, such as +25% or +183.33%. A change below 0.01% keeps two significant figures, so 1,000,000 to 1,000,001 reads +0.0001% and a real change never shows as 0%; below 0.000001%, or at a billion percent and above, the page switches to E-notation. Other numbers keep the decimals your inputs imply, up to ten: 19.99 plus 7.5% shows 21.48925, with no rounding to cents.

Why doesn't the Multiplier card appear?

The card shows final ÷ starting, and it appears in % change only when the starting value is above 0. For a starting value of 0 the ratio does not exist, and for a negative one it misleads: from -25 to 25 the ratio is -1 although the value rose. The Percent change and Absolute change cards still show in both cases.

Is this percentage change calculator free, and can I share or embed a result?

Yes, it is free and needs no account. The page address keeps every value that differs from the defaults, such as ?a=3&b=5&rates=true for a rate going from 3% to 5%, so a copied link reopens the same numbers. The same calculator can be embedded on another site.

Sources & References

Content verified by the Smart Calculators Team