Percentage change reports how far a value moved relative to where it started. A price rising from 20 to 25 is a 25% increase, and one falling from 80 to 60 is a 25% decrease. The formula is ((new − original) ÷ original) × 100, and the usual way to get it wrong is dividing by the new value instead of the original one.

Key Takeaways

From 20 to 25, ((25-20)/20)×100 = 25: a 25% increase.

From 80 to 60, ((60-80)/80)×100 = -25: a 25% decrease, with the sign carrying the direction.

The denominator is always the original value, never the new one.

A rise from 4% to 5% is 1 percentage point but a 25% change: the two measures answer different questions.

What percentage change means

Percentage change is the size of a move measured against the starting point. The formula is ((new − original) ÷ original) × 100. When the value rises the answer is positive, when it falls it is negative, and when nothing moves it is zero. Because the reference is always the starting value, two changes from different starting points are directly comparable.

The formula, with worked examples

A percentage increase

A price moves from 20 to 25. Plug in: ((25 − 20) ÷ 20) × 100 = (5 ÷ 20) × 100 = 25. That is a 25% increase. Type ((25-20)/20)*100 → = 25, and the same arithmetic appears in the percentage calculator.

A percentage decrease

A price drops from 80 to 60. ((60 − 80) ÷ 80) × 100 = (−20 ÷ 80) × 100 = −25. The negative sign reports a 25% decrease. Type ((60-80)/80)*100 → = -25. Do not strip the sign and read it as an increase; the sign is half the information.

A smaller rise

Units sold go from 200 to 220. ((220 − 200) ÷ 200) × 100 = 10, a 10% increase. Small moves hide their relative size well: 20 extra units on a base of 200 is one tenth of the base, exactly the 10% the formula reports.

The most common mistake: the wrong denominator

Divide by the original value, always. A move from 20 to 25 is 25% of 20 but only 20% of 25, so dividing by the new value shrinks every increase and inflates every decrease. The guard against it is to say the question in words first: compared with where it started, 5 more is a quarter of 20, so 25%. If the reference is not the same in both directions, the two legs of a round trip will not cancel.

Percentage change versus percentage points

These two measures answer different questions, and both are correct. A rate that climbs from 4% to 5% moves by 1 percentage point. Measured against its starting value it rises ((5 − 4) ÷ 4) × 100 = 25%. Financial writing usually states which one it means, because the two labels lead to very different sentences about the same event. Percentage points report the raw gap; percentage change reports the gap relative to where you began.

Working the other way: from a change to a new value

Sometimes you already know the change and need the new value. A 10% increase on 8 is 8 + (10/100) × 8, and 8+(10/100)*8 → = 8.8. To reverse a percentage change, divide rather than subtract: a 20% increase takes 100 to 120, so you undo it with 120 ÷ 1.2 = 100. Subtracting gives 120 × 0.8 = 96, which is not the starting value, because 20% of 120 is larger than 20% of 100.

Compound changes do not add up

Two percentage changes in a row do not combine by addition. A rise of 10% followed by another 10% leaves 100 at 121, not 120, so the total move is 21%, not 20%. Type 1001.11.1 → = 121 to see it. The second 10% is applied to the larger base, the same wrong-denominator effect compounding on itself. Whenever a figure is quoted as a series of changes, multiply the factors rather than adding the percentages.

The percentages guide covers the base concept of percent, and changes over time are exactly what the statistics calculator is built to summarize.

Frequently asked questions

Why is the denominator always the original value?

Because percentage change reports how far the value moved relative to where it started, and the reference has to stay fixed or comparisons stop meaning anything. Dividing by the new value measures a different thing and gives a different answer in nearly every case.

What does a negative percentage change mean?

It is a decrease. The number reads the same as a positive one: -25 is a drop of 25%. Keep the sign through the arithmetic and interpret it at the end.

Why is a move from 4% to 5% both a 1 point rise and a 25% rise?

Because the two measures count different things. Percentage points subtract the rates directly, 5 minus 4. Percentage change divides that difference by the starting rate, 1 divided by 4. Both statements are accurate labels for the same move.

How do I undo a percentage change?

Divide by the factor instead of subtracting. A 20% increase takes 100 to 120, so reverse it with 120 ÷ 1.2 = 100. Subtracting 20% gives 120 × 0.8 = 96, not 100, because the percentage is applied to the larger number on the way back.