Percentage Change Calculator

Type a starting value and an ending value and the calculator returns the percentage change between them along with the raw difference. Growth shows as a positive percentage, decline as a negative one, and the inputs accept any numbers — prices, weights, page views, test scores. Results update as you type and nothing is sent to a server.

The formula and a worked example

Percentage change is relative change: the gap between the two values, measured against the value you started from. The plain difference on its own cannot tell you whether a move is large, because a rise of 60 means one thing on a base of 240 and something else entirely on a base of 24,000. Dividing by the starting value strips the scale out and leaves a pure ratio, and multiplying by 100 turns that ratio into a percentage.

change = (v_to − v_from) ÷ v_from × 100%

With the defaults, 240 to 300, the difference is 60 and the change is 60 ÷ 240 = 0.25, shown as 25.00%. This is the same relative-change formula the US Bureau of Labor Statistics uses to report monthly CPI movements and the one behind the percentage next to every stock quote. Watch the denominator: it is always the starting value, the reference point the move is measured against. From 240 to 300 is a 25% increase, but from 300 back to 240 is a 20% decrease, because the base changed under you. If the starting value is zero the formula divides by zero, so the calculator reports an error instead of a number.

From Roman auctions to the percent sign

Percentages are older than the decimal point. In ancient Rome, before positional decimals existed, quantities were often reckoned in fractions with a denominator of 100, and taxes were levied the same way. Augustus imposed a one-hundredth duty on goods sold at auction, the centesima rerum venalium, so calculating what was owed on a sale amounted to computing a percentage. The Latin phrase per centum, "by the hundred," is where the word comes from.

The habit spread with trade rather than with mathematics. As coinage and credit grew through the Middle Ages, working to a base of 100 became convenient enough that arithmetic manuals of the late fifteenth and early sixteenth centuries treated it as routine, folding it into lessons on profit and loss, interest, and the Rule of Three, the proportion method every apprentice merchant learned. By the seventeenth century it was standard to quote interest rates in hundredths, much as they are quoted now.

The symbol arrived later and almost by accident. Italian clerks wrote per cento, "for a hundred," and abbreviated it heavily: an arithmetic text of 1339 shortens the phrase toward "per 100," with the per collapsed into a single p carrying a crossed descender. No dedicated percentage symbol is known before 1425, when a scribe working on an Italian manuscript wrote the contraction pc followed by a tiny loop standing for the masculine ordinal ending heard in primo and secondo. By 1650 that loop had flattened into a horizontal fraction bar, and in texts printed in the 1680s the per has dropped away altogether, leaving a mark that reads as two zeros stacked around a line. The diagonal-stroke form of the modern % is comparatively recent: the historian of mathematics David Eugene Smith, writing in 1925, described the solidus version as modern.

Percentage change vs percentage points

When both values are themselves percentages, the two ways of describing the move give very different figures. A mortgage rate going from 4% to 5% has risen 1 percentage point but 25 percent. Central banks — the Federal Reserve, the Bank of England, the ECB, the Bank of Canada, the Reserve Bank of Australia — avoid the ambiguity by quoting moves in basis points, where one basis point is a hundredth of a percentage point and 100 basis points equal 1 percentage point. The unit comes from interest-rate trading, where the "basis" is the spread between two rates; because that spread is usually small it is quoted multiplied up by 10,000, so a full point of movement in the basis is one basis point. A 25 bp hike takes a 4.00% rate to 4.25%. If a headline says a rate "rose 25%", check whether it means points or percent before reacting.

Gains and losses are not symmetric

A 25% rise followed by a 25% fall does not return to the start. Take 240 up 25% and you get 300; take 300 down 25% and you land on 225. Each step uses its own base, and the second base is larger. The gain needed to recover a loss is always bigger than the loss itself:

This is the arithmetic behind the old trading line that a portfolio which halves must double just to break even.

Working the formula backwards

Two everyday questions invert the calculation. To find the ending value from a known percentage, multiply the start by one plus the change written as a decimal: 240 grown by 25% is 240 × 1.25 = 300, and 240 cut by 25% is 240 × 0.75 = 180. To recover the starting value from an ending value and a percentage, divide rather than subtract — a price of 300 that already includes a 25% markup came from 300 ÷ 1.25 = 240, not from 300 minus 25%, which would give 225. That second slip, taking the percentage back off the larger number, is one of the most common mistakes in pricing and tax, and it happens for the same reason gains and losses are asymmetric: the markup was measured against the smaller base.

Limits worth knowing

The formula assumes a positive starting value. It still returns a number when the base is negative — from −50 to −25 it reports −50% even though the value moved up — but the flipped sign makes such results misleading, so read them with care. For quantities that cross zero, quote the absolute difference instead. When neither value is the natural base, analysts often divide by the average of the two; that variant is called percent difference and is a different measure from the one on this page. Economists who need changes that add up cleanly across periods sometimes use log change, the natural logarithm of the ratio, which is symmetric — a rise and the fall that undoes it are equal and opposite — and closely matches ordinary percentage change for small moves.

Percentage figures describe arithmetic, not advice; always check what base a quoted change was measured against. See the site disclaimer.

Frequently asked questions

How do I calculate percentage change between two numbers?

Subtract the starting value from the ending value, divide by the starting value, and multiply by 100. Going from 240 to 300 gives (300 − 240) ÷ 240 = 0.25, which is a 25% increase. The order matters: the number you started with always goes in the denominator.

What is the difference between percentage change and percentage points?

Percentage points measure the raw gap between two percentages, while percentage change measures the relative move. A savings rate going from 4% to 5% has risen 1 percentage point but 25 percent, because 1 is a quarter of 4. News stories mix the two up often enough that it is worth checking which one a headline means.

Why does a 25% increase followed by a 25% decrease not get back to the start?

Because each step is measured against a different base. Take 240 up 25% and you reach 300; take 300 down 25% and you land on 225, not 240. Undoing a 25% rise actually requires a 20% fall, since 60 is a fifth of 300.

What does a negative percentage change mean?

It means the ending value is below the starting value. Going from 300 to 240 is a change of −20%, and the difference output shows −60. A change of −100% means the value fell all the way to zero.

Can percentage change be more than 100%?

Yes, any time a value more than doubles. Going from 240 to 600 is a change of +150%, and going from 20 to 100 is +400%. There is no upper limit on increases, but a decrease can never pass −100% unless the value turns negative.