Percentage change:
how much a number rose or fell

What percentage change means

Percentage change tells you how large an increase or decrease is relative to a starting value. That makes it useful for comparing prices, website traffic, salaries, exam scores and electricity bills, even when the original amounts are very different.

A move from 100 to 120 is a rise of 20 units and 20%. A move from 1,000 to 1,020 is also 20 units, but only 2%. The starting value is what gives the number its meaning.

The same logic lets you compare things measured in different sizes. A ₹5 rise on a ₹50 item and a ₹500 rise on a ₹5,000 item are both 10%, even though one is a hundred times larger in rupees. Percentage change removes the size of the thing and keeps only the proportion.

In everyday life you meet it in salary hikes, inflation, a year of fund returns, marks and discounts. In all of them the question is how much a number changed compared with where it started.

A positive result is an increase and a negative result is a decrease. If you only care about drops, such as price cuts, the percentage decrease guide narrows this down to that single case.

Percentage change formula and steps

1. 1Subtract the old value from the new value.
2. 2Divide that difference by the old value.
3. 3Multiply by 100.
4. 4Keep the plus or minus sign so the direction is clear.

A quick sense-check before you trust a result: a new value exactly double the old is +100%, one that is half the old is −50%, and an unchanged value is 0%. If your answer sits far from what those landmarks suggest, re-check which number you divided by.

Some people prefer to work with the ratio: new ÷ old, minus 1. For 800 and 920 that is 1.15 − 1 = 0.15, or 15%. It is the same calculation, and the ratio 1.15 is also the multiplier you would use to project the next period.

Always subtract in the order new minus old. Reversing it flips the sign and tells the reader the opposite story.

Worked examples: a price rise and a traffic drop

A product costs ₹800 and later costs ₹920. The difference is ₹120, and dividing by the original ₹800 gives 0.15.

Now suppose monthly website visitors fall from 25,000 to 20,000. The difference is −5,000, and relative to the original 25,000 that is a 20% decrease.

In both cases the denominator is the figure you started from. You never divide by the final number.

Try it with your own pair of numbers before moving on. Marks rising from 60 to 75 is (75 − 60) ÷ 60 = 25%, but falling from 75 back to 60 is only 20%, because the base is now 75. If the answer is above 100%, the new value must be more than double the old.

The two examples have the same shape, but one rises and one falls. In a spreadsheet you can write the formula once as (B − A) ÷ A and copy it down a whole column of before-and-after pairs, so every row is calculated the same way.

Percentage points vs percentage change

When two figures are themselves percentages, the gap between them is measured in percentage points. The relative change is a separate number, and the table shows why you must say which one you mean.

A 15% rise does not reverse with a 15% fall, because the second change is taken from a different base. In the last row, the 20% fall is calculated on ₹120, not ₹100, which leaves you below where you started.

Reports that mix up points and percent can both be right and still mislead: a rate that moves from 4% to 5% rose one point, or 25% in relative terms.

When you read a headline number, ask two questions: percent of what, and compared with when? "Prices fell 10%" means little without the base and the period, and the number cannot be checked.

The same care applies to several periods. Yearly changes of +10%, −10% and +10% do not net to +10%: 1.10 × 0.90 × 1.10 = 1.089, which is +8.9%.

When the starting value is zero or negative

Division by zero is not allowed, so the ordinary formula cannot be used when the starting value is zero. Say the amount rose from zero to the new figure and quote the absolute change instead.

Small bases exaggerate changes. A shop that sold 2 items last week and 6 this week has grown 200%, while one that sold 2,000 and then 2,400 has grown 20%. The first number looks dramatic but reflects four extra sales. Quote the absolute figures whenever the base is small.

Negative starting values need care too. A business that goes from a loss of ₹50,000 to a profit of ₹30,000 improved by ₹80,000, yet the formula returns −160%, a negative number for a gain. Describe such swings in rupees.

How to report a percentage change clearly

• Label the baseline: last month, last year or the previous price.
• Show both the original and updated values when readers must judge scale.
• Use the original value as the denominator for conventional percentage change.
• Add the absolute change when the base is small, so a large percentage is not mistaken for a large move.
• State whether a claim is a percentage-point movement or relative growth.

If you are comparing two figures with no natural before and after, such as two cities' populations, the percentage difference guide covers a method that does not privilege either figure.

A good reporting line has four parts: the old value, the new value, the percentage change with its sign, and the period. For example: "Visitors fell from 25,000 to 20,000, a 20% decrease month on month." It is short, checkable and hard to misread.