Maths calculator · Free · No sign-up
Percentage Change Calculator
Percentage change is (new − old) ÷ old × 100. From 2.1% to 1.8% that is −0.3 ÷ 2.1 = −14.29%, a decrease of 14.29%. Because both values are percentages, the plain gap is 0.3 percentage points, a different figure. This calculator gives both, plus the percent difference.
Percent change, points, difference.
- The change: new minus old = 1.8% − 2.1% = −0.3 percentage points.
- Divide by the old value: −0.3 ÷ 2.1 = −0.(142857).
- Multiply by 100: −14.(285714)%, −14.29% to 2 decimal places, a decrease.
- Both values are percentages, so the plain gap is 0.3 percentage points: a different figure from the 14.29% change.
| Result | Value |
|---|---|
| Percentage change | −14.29% |
| Change in percentage points | −0.3 points |
| Percent difference (no direction) | 15.38% |
| New ÷ old | 0.8571 |
| The change back, new to old | +16.67% |
The figures above are an example (infection rates of 2.1% and 1.8%): put in your own. Set the values to percentages when they are rates, shares or interest, and the gap is given in percentage points too. Worked out exactly in this browser and kept there; nothing is sent anywhere.
Type the old and new values to get the percentage change, the change in percentage points when the values are rates, the direction-free percent difference and the change back. The working shows each step.
Percentage change is the difference between a new and an old value as a percentage of the old one. A percentage point is the plain difference between two percentages; percent difference compares two values without treating either as the start.
- No sign-up
- Nothing uploaded
- Shows every step
- Works offline
- Exact, no rounding errors
Key facts
| Detail | Answer |
|---|---|
| Gives | Percent change, percentage points, percent difference, change back |
| Example | 2.1% to 1.8%: −14.29%, or −0.3 percentage points |
| Formula | (new − old) ÷ |old| × 100 |
| Percent difference | |a − b| ÷ average of a and b × 100 |
| Refuses | A change from 0, with the plain change given instead |
| Where your numbers are kept | This browser only |
How to calculate percentage change
Subtract, divide by the old value, multiply by 100, and name the unit.
Enter the old value
The starting figure, before the change.
Enter the new value
The figure after it.
Say what the values are
Plain numbers, or percentages such as rates and shares.
Subtract old from new
The difference, in the values’ own units or in percentage points.
Divide by the old value and multiply by 100
That is the percentage change, with its sign.
Quote it with its unit
Percent for the relative change, points for the plain gap between rates.
Who uses a percentage change calculator
Anyone reporting how much something moved, and who wants the right unit on it.
Journalists and analysts
A rate’s move in points and in percent, side by side.
Investors
A price change, and the rise needed to win it back. An exchange rate moves the same way, and the currency converter gives the day’s rate both ways.
Teachers
Pass rates from one year to the next.
Marketers
Conversion rates before and after a change.
Students
Percent change and percent difference kept apart.
Clubs and coaches
Season figures compared with last season’s.
Percent or percentage points: 2% to 3% is +1 point and +50%
When the two values are themselves percentages, “the change” can mean two different numbers, and news reports, papers and adverts regularly print one while meaning the other. Interest rates rising from 2% to 3% have risen by 1 percentage point, which is a 50% increase in the rate. Both are correct; only the unit tells the reader which.
| From, to | Percentage points | Percent change | Percent difference |
|---|---|---|---|
| 2.1% to 1.8% | −0.3 points | −14.29% | 15.38% |
| 2% to 3% | +1 point | +50% | 40% |
| 10% to 12% | +2 points | +20% | 18.18% |
| 40% to 44% | +4 points | +10% | 9.52% |
| 0.5% to 1% | +0.5 points | +100% | 66.67% |
| 60% to 30% | −30 points | −50% | 66.67% |
The first row is the example in the EU’s official data portal guide on percentages versus percentage points: a study found covid-19 infection rates of 2.1% without masks and 1.8% with them. One side quoted “a 0.3% difference”; the other quoted a 14% reduction. The guide’s point is that the first should have been called 0.3 percentage points, since (2.1 − 1.8) ÷ 2.1 is the 14% relative change. Small base rates make the two figures diverge most, which is why a risk going from 1 in 1,000 to 2 in 1,000 can be sold as “doubled”.
Percent change, percent difference and percent error
Percent change has a direction: it is measured from the old value to the new one, so it needs to know which came first. Percent difference does not. It compares two values neither of which is the reference, by dividing the gap by their average.
| Measure | Formula | Use it when | Example |
|---|---|---|---|
| Percent change | (new − old) ÷ |old| × 100 | Before and after; a known starting point | 80 to 100: +25%; 100 to 80: −20% |
| Percent difference | |a − b| ÷ ((a + b) ÷ 2) × 100 | Two measurements of equal standing | 80 and 100: 22.22% either way |
| Percentage points | new % − old % | Both values are already percentages | 2% to 3%: +1 point |
| Percent error | |measured − true| ÷ |true| × 100 | One value is the accepted true value | Measured 2.85, true 2.70: 5.56% |
The US NIST style guide for scientific writing, Special Publication 811, section 7.10.2, makes the same warning from the other side: a sentence such as “the two values differ by 0.05 %” does not say whether that is a relative difference or a difference in a quantity that is itself a percentage, so it asks writers to say which. The calculator gives all three at once, labelled, so the right one can be quoted. For a measurement against a known value use the percent error calculator.
Why down 20% needs up 25% to get back
A change and its reverse are not the same size in percent. Up from 80 to 100 is +25%; back from 100 to 80 is −20%. The gap is the same 20, but it is measured against a different starting value each time. The calculator always shows the change back, because quoting it the wrong way round is one of the commonest misreadings of a chart.
| A change of | Needs this to return |
|---|---|
| +10% | −9.09% |
| +20% | −16.67% |
| +25% | −20% |
| +50% | −33.33% |
| +100% | −50% |
| −10% | +11.11% |
| −50% | +100% |
| −90% | +900% |
The bottom rows matter for anything that has fallen a long way: a share price down 90% must rise 900% to recover. The rule is that a change of c (as a decimal) is reversed by −c ÷ (1 + c). Old values that are negative (a loss becoming a profit) are divided by their size, as most textbooks do, and the calculator says so in its working; a change from 0 has no percentage and is refused, with the plain change given instead.
What this calculator does not do
This calculator compares two numbers. It does not average several changes, annualise growth over years, adjust for inflation or test whether a change is statistically meaningful. A change in a percentage taken from a small sample can be noise: 4 of 10 becoming 6 of 10 is +20 points and +50%, and proves very little. The yes/no counter shows how wide that uncertainty is for a tally.
Rounding is half away from zero, to the places you choose; the exact value, with any repeating digits in brackets, stays in the working, so −14.29% is shown as −14.(285714)% before it is rounded. To type values with a % sign, set “The values are” to percentages; plain numbers are refused with a % sign so a rate is never mistaken for a count.
This calculator or an answer-only one
What this page does that a typical answer-only widget does not.
| This page | A typical calculator | |
|---|---|---|
| Percentage points | Given when values are rates | Usually missing |
| Percent difference | Beside the change, labelled | A separate tool, or confused with change |
| Change back | Always shown | Not shown |
| Shows the working | Every step | Answer only |
| Exact arithmetic | No floating-point drift | Floating point |
| Your numbers leave the browser | Never | Varies |
More calculators
Every calculator on the site runs in your browser, needs no sign-up, and sends nothing anywhere.
Percentages7
Percent of a number, increase, change and error, and percentages to and from fractions and decimals.
Percent error calculator
Measured against accepted, signed or absolute, for one result or the mean of several trials.
Open percent error calculator →Percent to decimal
12.5% = 0.125 and 0.5% = 0.005, with the fraction, per mille and basis points.
Open percent to decimal →Decimal to percent
0.875 = 87.5%, and repeating decimals such as 0.(3) = 33.(3)% converted exactly.
Open decimal to percent →Fraction to percent
A fraction, mixed number or score such as 17 out of 20 as a percent, repeats marked.
Open fraction to percent →Percent to fraction
Any percent as a fraction in lowest terms: 37.5% = 3/8, 33 1/3% = 1/3, and why 33% is not.
Open percent to fraction →Percentage calculator
What is P% of a number, X is what % of Y, and X is P% of what, with the working and exact answers.
Open percentage calculator →Percentage increase calculator
The increase from one number to another, a number plus P%, and the original before an increase.
Open percentage increase calculator →
All 18 calculators, by category: Percentages (8) · Fractions & decimals (3) · Statistics & random (1) · Health & fitness (1) · Counting & sport (5)
Frequently asked questions
How do you calculate percentage change?
Subtract the old value from the new one, divide by the old value and multiply by 100. From 50 to 75: 25 ÷ 50 = 0.5, a change of +50%. A negative result is a decrease: from 75 to 50 is −25 ÷ 75 = −33.33%, a fall of a third.
What is the difference between percent and percentage points?
Percentage points are the plain gap between two percentages; percent is the change relative to the starting value. A rate going from 2% to 3% rises by 1 percentage point, which is a 50% increase in the rate. Use points for the gap and percent for the relative change, and say which.
What is the difference between percent change and percent difference?
Percent change measures from an old value to a new one, so it has a direction. Percent difference compares two values of equal standing by dividing the gap by their average, so it is the same either way round: 80 and 100 differ by 22.22%, while 80 to 100 is a 25% change.
Why is a fall from 100 to 80 a 20% decrease but the rise back a 25% increase?
Each percentage is measured against its own starting value. The gap is 20 both times, but 20 is a fifth of 100 and a quarter of 80. A change c is reversed by −c ÷ (1 + c), so a 50% fall needs a 100% rise to recover.
How do I calculate percentage decrease?
Use the same formula: (new − old) ÷ old × 100, and read the minus sign as a decrease. From 1.8 to 1.2 is −0.6 ÷ 1.8 = −33.33%, a decrease of 33.33%. A decrease of a positive value can never exceed 100%. The calculator names it as a decrease.
Can percentage change be calculated from zero?
No. Dividing by an old value of 0 has no answer, so any rise from 0 is undefined in percent. The calculator refuses it and gives the plain change instead. Quote that, or measure from a different baseline that is not zero.
How is percentage change calculated with negative numbers?
Most textbooks divide by the size of the old value, ignoring its sign, so a change from −10 to 5 is +15 ÷ 10 = +150%. The calculator does that and says so in the working, but percentages of a negative base are easy to misread: give the plain change too.
Is a change from 10% to 12% a 2% increase?
It is a 2 percentage point increase and a 20% increase in the rate. Calling it “a 2% increase” is ambiguous, and some readers take it to mean 10.2%. Set the values to percentages in the calculator and it gives both figures, labelled.
Related guides
Longer answers to the questions behind the numbers.
- Surveys
How many people do you need to survey?
Why 385 answers a city and 45 answers a club, and the margin each sample size buys.
- Writing
How long is a chapter?
Every chapter of 27 public-domain novels, counted. The median is 2,733 words, and fewer than half sit inside the usual 2,000 to 4,000.
- Surveys
How to tally survey responses by hand
A worked tally of 60 paper forms, from the sheet to the percentages. Blank answers, two boxes ticked, tick-all questions, write-ins, and the check that proves the count.
- Haematology
How to calculate the absolute neutrophil count (ANC)
The formula with bands, the two units and the ×10 shortcut, five worked examples, the absolute lymphocyte count, and why CTCAE grade 4 no longer means below 500.
- Basketball
How to keep basketball stats by hand
The NCAA statisticians' definitions of shots, rebounds, assists, steals and turnovers, one stat per volunteer, and the two sums that prove a hand-kept sheet.
- Counting
How to count votes at a meeting
Majority means more than half of the votes cast, not 50% plus one, and an abstention is not a vote. The four voting methods, two-teller counting, and a tellers' report worked with numbers.