Percentage Increase Calculator
Two numbers in — the percent change, the multiplier, and the change that would undo it out.
Work out the percent increase or decrease from one value to another: the calculator subtracts the original from the new value, divides by the original and multiplies by 100, so 40 → 52 is a +30% increase. Switch to Standard to apply a percent change (40 changed by +30% = 52) or find the original value before a change (52 before a 30% rise was 40), Detailed for the symmetric percent difference and the percent-vs-percentage-point distinction, or Advanced to chain changes — +10% then −10% lands at −1%, not zero.
Exact arithmetic — every percent change here is computed from the formula, not estimated. Displayed percentages round to 2 decimal places.
The percent increase formula, step by step
Subtract, divide by the original, multiply by 100
Percent change = (new − original) ÷ original × 100. For 40 → 52: the change is 52 − 40 = 12; dividing by the original gives 12 ÷ 40 = 0.30; and ×100 makes it a 30% increase. The same formula handles decreases — the sign of the answer carries the direction, so 80 → 60 gives (60 − 80) ÷ 80 = −25%.
| From → to | Change | Percent change |
|---|---|---|
| 40 → 52 | +12 | +30% |
| 80 → 60 | −20 | −25% |
| 25 → 35 | +10 | +40% |
| 10 → 25 | +15 | +150% |
| 1,500 → 1,650 | +150 | +10% |
| 50 → 100 | +50 | +100% (doubling) |
The multiplier view
Every percent change is a multiplication in disguise: an n% increase multiplies the value by (1 + n ÷ 100). So +30% is ×1.30 (40 × 1.30 = 52), −25% is ×0.75 (80 × 0.75 = 60), +100% is ×2, and −50% is ×0.5. Multipliers are what make the harder jobs mechanical — applying, reversing and chaining changes are all single multiplications or divisions once you convert.
Divide by the original, not the new value. For 40 → 52, dividing the change by 52 gives 12 ÷ 52 ≈ 23.08% — a real number, but it answers a different question: it's the percent drop from 52 back down to 40. The calculator shows that reverse change on its own row so the two never get mixed up.
Applying a change and finding the original value
Applying a percent change
Multiply by (1 + p ÷ 100). A 30% raise on 40 is 40 × 1.30 = 52; a 25% cut on 80 is 80 × 0.75 = 60. Never add the percent to the number itself — +30% on 40 is 52, not 70. The Standard level's Apply a percent change mode does this, and accepts negative percentages for decreases.
Finding the original before a change
Reverse the multiplication: original = final ÷ (1 + p ÷ 100). A price of $69 after a 15% increase started at 69 ÷ 1.15 = $60 — and the check is 60 × 1.15 = 69. After a decrease, divide by (1 − p ÷ 100): a value of 39.6 after a 10% fall started at 39.6 ÷ 0.90 = 44.
| Task | Formula | Example |
|---|---|---|
| Apply +30% to 40 | 40 × 1.30 | 52 |
| Apply −25% to 80 | 80 × 0.75 | 60 |
| Original before +15%, ending at 69 | 69 ÷ 1.15 | 60 |
| Original before −10%, ending at 39.6 | 39.6 ÷ 0.90 | 44 |
The subtraction trap. Subtracting 15% from the $69 final gives 69 × 0.85 = $58.65 — wrong by $1.35, because the 15% was applied to the smaller original ($60), not to the final. Division undoes multiplication; subtraction doesn't. The same move back-calculates a pre-tax price: an $8.60 receipt with 7.5% sales tax was $8.60 ÷ 1.075 = $8.00 before tax.
Percent difference, percent change and percentage points
Three different questions
Percent change is directional — it measures a move from a baseline, dividing by the original. Percent difference is symmetric — it measures how far apart two values are when neither is the baseline, dividing the gap by their average. Percentage points compare two numbers that are already percentages, by plain subtraction.
| Measure | Question it answers | For 45 and 55 | For 4% and 5% |
|---|---|---|---|
| Percent change (A → B) | How much did it grow from A? | +22.22% | +25% |
| Percent change (B → A) | How much did it shrink from B? | −18.18% | −20% |
| Percent difference | How far apart, no baseline? | 20% | 22.22% |
| Percentage points | Gap between two rates | — (not rates) | +1 pp |
Rates need both readings
A mortgage rate moving from 6% to 7% rises 1 percentage point — and +16.67% in relative terms (1 ÷ 6). On a $400,000 loan that "one little point" is real money, which is why quoting only the relative figure ("rates jumped 16.67%") or only the points figure ("rates rose 1 point") each tell half the story. At the Detailed level, set the input kind to Percentages and the calculator prints both readings side by side.
Headline check. "Unemployment rose 50%" and "unemployment rose 2 percentage points" can describe the same event — a move from 4% to 6% is +2 pp and +50% relative. Neither is wrong; the small-sounding one and the alarming-sounding one are the same fact in different units.
Chained changes: why +10% then −10% is not zero
Multiply the multipliers
Successive percent changes multiply — they never add. +10% then −10% is 1.10 × 0.90 = ×0.99, a 1% overall loss: 100 rises to 110, then loses 10% of 110 (11), landing at 99. The order makes no difference, and pairing +p% with −p% always ends below the start, because the combined multiplier is 1 − (p ÷ 100)².
| Chain | Multipliers | Overall |
|---|---|---|
| +10% then −10% | 1.10 × 0.90 | ×0.99 → −1% |
| −20% then −10% | 0.80 × 0.90 | ×0.72 → −28% (not −30%) |
| +50% then −50% | 1.50 × 0.50 | ×0.75 → −25% |
| +100% then −50% | 2.00 × 0.50 | ×1.00 → 0% |
| +3%, three times | 1.03 × 1.03 × 1.03 | ×1.092727 → +9.27% (not +9%) |
Where this bites in real life
Stacked discounts: "20% off, plus an extra 10% off" is 28% off, not 30%. Market falls: a 50% drop needs a +100% recovery just to break even (÷0.5 = ×2). Annual raises: three 3% raises compound to +9.27%, slightly better than 9% — compounding works for you on gains. The Advanced level takes up to three changes and prints every intermediate value plus the single multiplier that summarizes the whole chain.
The recovery rule. To undo a −p% fall you need +p ÷ (1 − p ÷ 100)% back: a −20% fall needs +25% (0.80 × 1.25 = 1), and a −50% fall needs +100%. The deeper the hole, the disproportionately bigger the climb out.
❓ Frequently asked Frequently asked questions
What is the percent increase formula?
Percent increase = (new value − original value) ÷ original value × 100. For an increase from 40 to 52: the change is 52 − 40 = 12, dividing by the original gives 12 ÷ 40 = 0.30, and multiplying by 100 gives a 30% increase. The division is always by the original (starting) value — dividing by the new value instead gives 12 ÷ 52 ≈ 23.08%, which is a different number and a common mistake. If the result comes out negative, the change is a decrease.
How do I calculate a percent decrease?
Use the same formula — (new − original) ÷ original × 100 — and the sign takes care of the direction. From 80 to 60: (60 − 80) ÷ 80 = −20 ÷ 80 = −0.25, so a 25% decrease. Note the asymmetry: going back up from 60 to 80 is (80 − 60) ÷ 60 ≈ +33.33%, not +25%, because the base of the calculation has changed from 80 to 60. A decrease and the increase that undoes it are never the same percentage (except 0%).
Why does +10% then −10% leave me 1% worse off?
Because the second change applies to a new, larger base. Start with 100: +10% takes it to 110, but the −10% is now 10% of 110, which is 11 — so you land on 99, a 1% overall loss. In multiplier terms, 1.10 × 0.90 = 0.99. The order doesn't matter (0.90 × 1.10 is also 0.99), but the loss always wins when you pair +p% with −p%: the overall multiplier is 1 − (p ÷ 100)², which is below 1 for any p except 0. The Advanced level chains up to three changes and shows every step.
What is the difference between a percent and a percentage point?
Percentage points measure the plain difference between two percentages; percent measures the relative change. If an interest rate goes from 4% to 5%, it has risen by 1 percentage point (5 − 4 = 1) — but as a relative change it is (5 − 4) ÷ 4 = +25%. Both statements are true: a headline saying rates rose 25% and one saying they rose 1 point describe the same move. When comparing two percentages, quote points for the absolute move and percent for the relative one — and say which you mean.
What is the difference between percent difference and percent change?
Percent change is directional: it divides by the original value, so 45 → 55 is +22.22% while 55 → 45 is −18.18%. Percent difference is symmetric: it divides the gap by the average of the two values, so for 45 and 55 it is 10 ÷ 50 = 20% either way. Use percent change when one value is genuinely the before (a price rise, a population change) and percent difference when neither value is the baseline — comparing two lab measurements, two quotes, or two sensors. This calculator shows percent difference at the Detailed level.
Is doubling a 100% increase or a 200% increase?
Doubling is a 100% increase. Going from 50 to 100 adds 50, and 50 ÷ 50 = 1 = 100%. A 200% increase means the change equals twice the original — 50 would become 150, which is tripling. The general rule: an n% increase multiplies the value by (1 + n ÷ 100), so +100% is ×2 and +200% is ×3. The confusion usually comes from mixing up 'increased by 200%' with 'increased to 200% of the original' — the latter is just doubling.
How do I find the original value before a percent increase?
Divide the final value by (1 + increase ÷ 100). If a price is $69 after a 15% increase, the original was 69 ÷ 1.15 = $60 — check: 60 × 1.15 = 69. The tempting shortcut of subtracting 15% from $69 is wrong: 69 × 0.85 = $58.65, off by $1.35, because the 15% was charged on the smaller original, not on the final. For a value after a decrease, divide by (1 − decrease ÷ 100): something worth 39.6 after a 10% fall started at 39.6 ÷ 0.90 = 44.
Can something decrease by more than 100%?
Not if the quantity can't go below zero. A 100% decrease takes any value exactly to 0 — a price, a weight or a count can't fall further, so decreases beyond 100% are impossible for them. Quantities that can go negative (profits, temperatures, account balances) can show changes beyond −100%: a profit falling from $50,000 to −$25,000 is a 150% decrease. Increases have no cap in either case — from 10 to 25 is +150%, and from 10 to 100 is +900%.
What if the starting value is zero or negative?
Percent change from zero is undefined — the formula divides by the original value, and division by zero has no answer. Saying something grew infinitely from 0 to 5 isn't math; report the absolute change instead (+5). Negative baselines are ambiguous: from −10 to 10, the formula gives 20 ÷ −10 = −200% for what is clearly an improvement. Conventions differ (some use the absolute value of the base), so for zero or negative baselines, quote the values themselves or the change in percentage points rather than a percent change.
Where these figures come from
Percent-change arithmetic is standard mathematics, not a matter of published rates — every result on this page follows from the definition of a percentage and of relative change. The definitions and conventions referenced above come from these references:
- Definition of percent and percentage notation — Wolfram MathWorld — Percent.
- Relative change, percent change and percent difference (including the mean-denominator convention) — Wikipedia — Relative change.
- Percentage points vs percent — Wikipedia — Percentage point.
- Why successive changes multiply (compounding) — Wikipedia — Compound interest.
Last checked: July 2026. Mathematical definitions don't change, but usage does drift — the percent-difference denominator (average of the two values) is the convention most style guides and lab manuals use, and it's the one this calculator follows.
Select the question that matches what you're working on.
The headline is your percent change — the gap between the two values, measured against the original and signed for direction.
Plus means increase, minus means decrease — one formula covers both. 40 → 52 reads +30%; 80 → 60 reads −25%. If you expected a rise and see a minus sign, check which number you entered as the original.
+30% means 30% of 40 (the start), not of 52. That's why the reverse trip shows −23.08%, not −30% — the base changes when the direction does.
+30% and ×1.30 are the same fact. Applying, undoing and chaining changes are all one multiplication or division once you convert — undoing ×1.30 is ÷1.30.
Three habits prevent nearly every percent-change mistake.
"Up 25%" means nothing until you say from what. The same pair of numbers gives +22.22% one way and −18.18% the other (45 and 55) — direction is part of the answer.
10 → 25 is a +150% jump but only +15 in absolute terms. A huge percentage often just means a tiny starting value — check the absolute change before reacting.
When the two numbers are already percentages, a plain subtraction gives percentage points and the formula gives relative percent — a rate moving 4% → 5% is +1 pp and +25% at the same time. Headlines routinely pick whichever sounds bigger, so translate to the other unit before deciding whether a move is large. The Detailed level prints both.
The everyday jobs this tool is built for, and the fastest route to each.
Simple level: original and new value. Rent going $1,500 → $1,650 is +10%; a grocery item going $2.50 → $3.00 is +20%.
Standard level, find-the-original mode: a $69 price tag after a 15% increase started at $60 — division by 1.15, not subtraction of 15%.
Advanced level: −20% then −10% multiplies to −28%, not −30%; three 3% raises compound to +9.27%. Every step is shown.
Percent change feeds straight into these tools.
Chained percent growth, compounded over years — with interest.
Compound Interest →