Percentage increase, percentage decrease and percentage change sound like three different calculations. They are really one formula read three ways — and the base you divide by decides everything. Get the base right and the rest is arithmetic; get it wrong and a careful calculation still gives you the wrong answer with total confidence.
The short answer
Percentage change measures how much a value has moved compared with where it started:
Percentage change = (new value − old value) ÷ old value × 100
The sign of the answer tells you which word applies. A positive result is a percentage increase. A negative result is a percentage decrease. Zero means nothing changed. “Increase” and “decrease” are not separate formulas — they are the two possible directions of one formula.
So a price rising from $80 to $100 is (100 − 80) ÷ 80 × 100 = 25% — a 25% increase. A price falling from $100 to $80 is (80 − 100) ÷ 100 × 100 = −20% — a 20% decrease. The same two numbers give different percentages depending on direction. That is not an error. It is the first thing to understand about percentage change.
Two different jobs
Before you calculate anything, work out which of two jobs you are doing. They look alike, but they start from different knowns.
Job A: you know the old value and the new value, and you want the percent. A shop price went from $80 to $100 — by what percent did it rise? This is percentage change, and the formula above is the one to use.
Job B: you know the old value and a percent, and you want the new value. A price of $80 rises by 10% — what is the new price? A $500 item is reduced by 30% — what does it cost now? This is applying a percent, and it uses a different arrangement of the same maths, shown below.
Mixing up Job A and Job B is the most common source of percentage confusion: the arithmetic will still produce a number, it just will not answer the question you asked.
Job A worked: percentage increase
An increase means the new value is larger than the old one, so (new − old) is positive:
- $80 → $100: (100 − 80) ÷ 80 × 100 = 20 ÷ 80 × 100 = 25% increase.
- $50 → $65: (65 − 50) ÷ 50 × 100 = 15 ÷ 50 × 100 = 30% increase.
- $120 → $150: (150 − 120) ÷ 120 × 100 = 30 ÷ 120 × 100 = 25% increase.
The pattern is the same every time: find the difference, divide by the old value (never the new one), multiply by 100. Dividing by the new value is the classic mistake — for $80 → $100 it would give 20 ÷ 100 × 100 = 20%, understating the rise because it measures the $20 gain against the larger, later figure instead of the figure you started from.
An increase can be more than 100%. That simply means the value more than doubled: $100 → $250 is a 150% increase. A percentage over 100% is not a mistake; it is what doubling-plus looks like.
Job A worked: percentage decrease
A decrease means the new value is smaller than the old one, so (new − old) is negative. In everyday speech we drop the minus sign and say “a 20% decrease” rather than “minus 20%”, but the maths is identical:
- $100 → $80: (80 − 100) ÷ 100 × 100 = 20% decrease.
- $200 → $150: (150 − 200) ÷ 200 × 100 = 25% decrease.
- $500 → $350: (350 − 500) ÷ 500 × 100 = 30% decrease.
A decrease, unlike an increase, has a hard floor. A 100% decrease removes the entire value and leaves zero; anything beyond 100% would push the value below zero, which is not what a decrease means for a price, a quantity or a score. That is why the site’s Percentage Decrease Calculator rejects decrease percentages above 100.
Job B worked: increase or decrease a value by a percent
When the percent is given and the new value is what you want, use the multiplier form:
- Increase a value by a percent: new value = original × (1 + percent ÷ 100)
- Decrease a value by a percent: new value = original × (1 − percent ÷ 100)
Worked examples:
- Increase $80 by 10%: 80 × (1 + 0.10) = 80 × 1.10 = $88. The increase itself is $8, and $80 + $8 = $88 — the multiplier just does both steps at once.
- Decrease $500 by 30%: 500 × (1 − 0.30) = 500 × 0.70 = $350.
- Increase 150 by 20%: 150 × 1.20 = 180. Decrease 150 by 20%: 150 × 0.80 = 120.
Why the same pair gives two different percentages
Percentage change is not symmetric. Going from $80 to $100 is a 25% increase, but coming back from $100 to $80 is only a 20% decrease, even though the dollar difference is $20 in both directions. The reason is the base: on the way up, the $20 gain is measured against $80 (20 ÷ 80 = 25%); on the way down, the $20 loss is measured against $100 (20 ÷ 100 = 20%). Any time a percentage looks inconsistent in reverse, check the base first — the two percentages were measured against two different starting values, so they should differ.
The same asymmetry explains why reversals do not cancel: $100 up 50% is $150, and $150 down 50% is $75 — you end $25 below where you began, because the fall was applied to the larger figure.
Three traps to avoid
Trap 1: percentage points vs percent. When a figure is already a percentage, a change in it can be described two ways, and they are not interchangeable. A rate rising from 3% to 5% has risen by 2 percentage points — the simple subtraction, 5 − 3 = 2. But in relative terms it has risen by (5 − 3) ÷ 3 × 100 = 66.7%. If someone says “up 2%”, ask whether they mean 2 percentage points or 2% relative to the old rate: here, the difference is between a small nudge and a two-thirds jump.
Trap 2: percentage change vs percentage difference. Percentage change has a direction — it goes from an old value to a new one, and its base is the old value. Percentage difference has no direction: it compares two values that are simply different, and its base is their average, |new − old| ÷ ((new + old) ÷ 2) × 100. For 80 and 100, the percentage difference is 20 ÷ 90 × 100 = 22.2% — neither the 25% increase nor the 20% decrease. Use percentage change when there is a before and an after. Use percentage difference only when the two values are independent comparisons with no natural starting point, such as two competing prices side by side. The site’s percentage tools calculate percentage change, not percentage difference, so for a difference figure, use the average-based formula above by hand.
Trap 3: reversals that do not cancel. Never assume that applying a percent and then applying the same percent in reverse restores the original, because each step applies to a different base. A rise of X% needs a smaller fall to return to the start, and a fall of X% needs a larger rise to recover.
The zero problem
Percentage change is measured against the old value, so it cannot be calculated when the old value is zero: the formula asks you to divide by zero, which has no defined answer. A value going from 0 to anything is not a “100% increase” in any useful sense — there is no starting size for the change to be a percentage of. The site’s general Percentage Calculator handles this honestly: when the old value is zero, it shows an error instead of inventing a figure. If you meet a zero starting value in real work, describe the change in plain numbers instead (“from 0 to 40 sales”).
Which tool for which question
The site has three percentage tools, and the right one depends on which job you named at the start:
- You know the old and new values and want the percent? Use the Percentage Calculator. It answers three everyday percentage questions at once — a percent of a number, one number as a percent of another, and the percentage change between two numbers — and shows all three results, so use only the result that matches your question. Its own sample uses the inputs 150, 200 and 20, and it flags an error rather than a figure when the old value is zero.
- You know the old value and an increase percent and want the new value? Use the Percentage Increase Calculator. Enter the original value and the increase percentage, and it returns both the increase amount and the new, larger value. One limit to know: a single calculation covers one step only, so growth that repeats over several periods needs the calculation run again for each period.
- You know the old value and a decrease percent and want the new value? Use the Percentage Decrease Calculator. Enter the original value and the decrease percentage, and it returns both the decrease amount and the new, reduced value. Its limit is the one described above: a decrease percentage above 100 is rejected, because a 100% decrease already reaches zero.
All three live in the Calculators category, and you can browse all free tools for related checks. If percentages in pricing are your interest, the companion explainer on markup vs margin covers the other pair of percentage figures readers most often mix up: a markup is added to cost, a margin is taken from the selling price, and the two percentages for the same item are never the same number.
The worked explanations at SkillsYouNeed and Calculator.io use the same definitions.
Frequently asked questions
Can a percentage decrease be more than 100%? No, for an ordinary price, quantity or score. A 100% decrease removes the whole value and leaves zero; anything beyond that would go negative, which is why the Percentage Decrease Calculator rejects it. Percentage increases, by contrast, have no ceiling.
Why is $80 → $100 a 25% increase, but $100 → $80 only a 20% decrease? Because the base changes: the $20 difference is measured against $80 on the way up and against $100 on the way down. The dollar change is identical; the percentage differs because the starting point differs.
Is a rise of 2 percentage points the same as a 2% rise? No. A rate moving from 3% to 5% rises by 2 percentage points, but that is a 66.7% rise relative to the old rate. Always check whether a quoted change is in points or in percent.
What if the old value is zero? Then percentage change is undefined — you cannot divide by zero. Describe the change in plain numbers instead, and expect the general Percentage Calculator to show an error rather than a percentage.
Which calculator should I use? Match the tool to your question. Old and new values, want the percent: the general Percentage Calculator. Old value plus an increase percent, want the new value: the Percentage Increase Calculator. Old value plus a decrease percent, want the new value: the Percentage Decrease Calculator. “By what percent did it change?” is Job A; “what is it after a 20% rise?” is Job B.
One formula, three readings
Percentage increase, percentage decrease and percentage change are not three calculations to memorize separately. They are one formula — (new − old) ÷ old × 100 — read three ways: positive means up, negative means down, and the base is always where you started. Name your job, divide by the old value, and read the sign. Everything else — percentage points, percentage difference, reversals that do not cancel — falls into place once that habit is set.
Next time a percentage figure looks surprising, check which value was used as the base, check whether points or percent was meant, and run the calculation through the Percentage Calculator, using the result that matches the question you actually asked.
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