Percent Change Calculator
Enter the original value and the new value, then press Calculate. Percent change measures the move from the original — the sign of the answer is the direction.
This free percent change calculator tells you how much a value has grown or shrunk, as a percentage of where it started. Enter the original value and the new value, press Calculate, and you get the percentage change with its sign, a plain sentence naming the direction — an increase or a decrease — the absolute change, the multiplier, and the complete working, rounded honestly to the precision your numbers actually justify. It covers percentage increase and percentage decrease in one tool, handles negative values properly, and there is not a single advertisement between you and the answer.
The calculator sits at the top of this page, already showing a solved example. Everything below explains the formula it runs, how to read each part of what it reports, and the places where percent change quietly misleads people — because with this particular formula, the arithmetic is rarely the hard part. The direction, the base, and the sign are where the mistakes live, and this page and this tool were built around all three.
What Is Percent Change?
Percent change measures the movement from one value to another, relative to where the movement started. A price that goes from 48 to 36, a salary that goes from 50,000 to 55,000, a population, a share price, a test score at two points in time — whenever one number comes before the other, percent change is the measure that describes the journey between them.
That word "before" is doing real work. Percent change assumes the two values have an order: an original, and what it became. The original is the base everything is measured against, which is why the same pair of numbers gives different answers depending on which one you start from — a point we will return to, because it surprises almost everyone the first time. In British and Indian usage the same quantity is written percentage change; if you arrived here looking for a percentage change calculator, this is the same tool under the other spelling.
The Percent Change Formula
For an original value and a new value:
percent change = (new − original) ÷ |original| × 100
| Term | What it is | Why it is there |
|---|---|---|
| new − original | The change itself, in your own units | No absolute value on top — the sign of the answer is the direction |
| |original| | The size of the starting value | The change is measured from where it began; the absolute value keeps the sign honest when the start is negative |
| × 100 | Ratio converted to a percentage | −0.25 is easier to discuss as −25% |
Two design decisions in that formula deserve a sentence each, because they are exactly where hand calculations go wrong. There is no absolute value in the numerator: a positive answer means the value rose and a negative answer means it fell, and stripping the sign throws that information away. And the denominator is the original value, always — not the new one, not the average. Measuring the move from anywhere other than its starting point answers a different question.
How to Calculate Percent Change Step by Step
Take a price that falls from 48 to 36 — the example the calculator above opens with.
Step 1 — subtract, original from new. 36 − 48 = −12. Keep the sign; it is not a nuisance to be discarded but the direction of the story. Negative: the price fell.
Step 2 — divide by the original. −12 ÷ 48 = −0.25. The change is now expressed relative to where it started.
Step 3 — scale to a percentage. −0.25 × 100 = −25%. The price dropped by a quarter of its original value: a 25% decrease.
Notice what did not happen: nobody divided by 36, and nobody threw the minus sign away and then tried to remember afterwards which way the price had moved. The calculator's step-by-step panel prints this exact sequence with your own numbers, the fraction stacked the way you would write it on paper, and finishes with one step most tools skip: since both values here carry two significant figures, −25% is also the honest figure for a report — no string of decimal places pretending to a precision the inputs never had.
Percentage Increase and Percentage Decrease
These are not two formulas; they are the two signs of one formula. When the new value is larger, the answer comes out positive and you have a percentage increase — 50,000 to 55,000 is +10%. When the new value is smaller, the answer comes out negative and you have a percentage decrease — 250 to 175 is −30%. The calculator above computes both with the same two boxes and says which one you have in words, so there is no separate tool to find and no sign convention to remember.
What genuinely surprises people is that the two directions are not mirror images. An increase of 25% is not cancelled by a decrease of 25%. Take 100, raise it 20% to 120, then lower it 20%: you land on 96, not 100, because the second move was measured from a bigger base. The percentage that actually undoes a change is always a different number:
| A rise of… | …is undone by a fall of |
|---|---|
| +10% | −9.09% |
| +20% | −16.67% |
| +25% | −20% |
| +50% | −33.33% |
| +100% | −50% |
This asymmetry is why a stock that halves must then double just to break even, and why "the market fell 10%, then recovered 10%" describes a loss. The calculator above computes the undoing percentage for every calculation you run — you will find it under More detail as "To undo this change" — and its Reverse button lets you feel the asymmetry directly: 48 to 36 reads −25%, one tap reverses it, and 36 to 48 reads +33.33%.
How to Use This Percent Change Calculator
The tool is deliberately plain, but several of its behaviours are worth knowing because they are not what other calculators do.
Enter the original value, then the new value. The order matters here — unlike percent difference, this measure has a direction — and the labels say which box is which. Both boxes accept decimals, negative numbers, thousands separators such as 50,000, a trailing per-cent sign, and scientific notation in any of the forms 1.5e3, 1.5E3, 1.5×10^3 or 1.5*10^3. When the page first loads, a solved example is already sitting there; your first keystroke clears it.
Press Calculate. The answer deliberately waits for you rather than flickering while you type. On a phone, pressing Calculate also closes the keyboard and brings the result band into view, and the Enter key does the same job.
Read the answer band. The large number carries its sign — +10% or −25% — and the sentence underneath says the same thing in words: "48 → 36 is a decrease of 25%." Below that sit the absolute change in your own units and the multiplier, the ×0.75 view of the same move that spreadsheet users and investors often prefer.
Open More detail for the rest. Behind that button are the "To undo this change" reading discussed above, the answer rounded to the significant figures your inputs justify, and — when both of your inputs are themselves percentages — the change expressed in percentage points.
Use Reverse deliberately. The button between the boxes swaps original and new. It exists partly for the obvious reason — you typed them the wrong way round — and partly as a teaching instrument: the answer after reversing is never just the old answer with its sign flipped, and one tap makes that lesson stick better than a paragraph.
Try the examples. The four chips each demonstrate something: a clean price drop, a salary rise whose bare trailing zeros trigger the calculator's precision note, a change between two negative values, and a change between two percentages.
What This Percent Change Calculator Does Differently
Every feature on this page exists because of a specific way percent change goes wrong in practice.
It keeps the sign, and says the direction out loud. Plenty of tools hand you a bare number and leave you to remember which way things moved. This one shows +10% or −25% and writes the sentence underneath: an increase, or a decrease, of that much. A number with a direction attached is worth more than a number alone, especially when it is going into a report someone else will read.
It shows what would undo the change. This is the reading almost nobody offers, and it is the one that prevents real financial mistakes: a 25% rise is reversed by a 20% fall, not another 25%. You will find it on every calculation under More detail. If you have ever wondered why a portfolio that dropped 30% needs a 42.86% gain to get back to level, that row answers it directly.
It handles negative starting values correctly, and explains the sign. A value moving from −10 to −25 has got worse, and this calculator reports −150%. Divide by −10 instead of |−10| and the two minus signs cancel, silently reporting a positive change for a value that fell — the classic trap with this formula. When your original value is negative, the working panel adds a step explaining exactly why the absolute value is there.
It rounds like a scientist. Two two-figure values give a two-figure answer, not thirteen decimal places borrowed from a floating-point unit. And when an input's precision is genuinely ambiguous — a bare 50,000, whose trailing zeros may or may not be significant — the calculator says so and shows you how to write it unambiguously rather than guessing on your behalf. The companion sig fig calculator is built on the same principle.
It catches the percentage-points trap. Type two percentages into the boxes — 4% and 5%, say — and a notice appears explaining that the gap between them is one percentage point even though the relative change is 25%. Both numbers are correct and they mean different things; conflating them is one of the most common quantitative errors in published writing, and it happens because no calculator ever mentions it.
It refuses honestly when the mathematics breaks. Percent change from zero is undefined — nothing has no size to be measured against, so "infinite growth" is not a result, it is a category error. Instead of printing a meaningless number, the calculator explains the problem and hands you the absolute change to report instead.
Percent Change With Negative Numbers
Negative values are where most percent change calculators either produce nonsense or refuse to try, so it is worth setting out how this one behaves and why.
Both values negative. A balance moving from −10 to −25 has fallen by 15, and 15 is 150% of the starting magnitude, so the answer is −150%. The direction is what a human would call it: things got worse. This works because the formula divides by |original|, not by original.
The value crosses zero. A business going from −25 to +25 shows +200%: it climbed by 50, which is twice the size of where it started. Changes beyond ±100% are entirely legitimate here — the value passed through nothing and came out the other side — and the calculator adds a step to the working saying so, because a reader seeing 200% for the first time reasonably wonders whether something has gone wrong.
The value falls to exactly zero. That is exactly −100%, and it is the floor for any value that stays non-negative. You cannot lose more than all of something. A decrease can only pass −100% by going negative, which is precisely why a −150% headline should make you check whether you are looking at profits rather than revenue.
The original value is zero. Undefined, and this calculator says so rather than inventing a figure. When something goes from 0 to 50, the honest statements are "it increased by 50" or "it went from nothing to 50" — percentage growth from zero has no meaning, however often reports claim otherwise.
Percent Change vs Percentage Points
The single most common misreading of a percent change involves values that are already percentages. If an interest rate moves from 4% to 5%, two different true statements are available, and choosing the wrong one misleads your reader by a factor of twenty-five.
The arithmetic gap is 1 percentage point, usually abbreviated pp. The percent change is +25%, because 1 is a quarter of the original 4. Neither is wrong; they answer different questions. Say "the rate rose one percentage point" when you mean the gap, and "the rate rose 25%" when you mean the relative move. Writing "the rate rose 1%" — which is what most people say — is the one formulation that means neither.
This calculator watches for the situation: type a per-cent sign on both inputs and it reports the change in percentage points alongside the percentage, and explains the distinction on the spot. For the record, the same care applies to unemployment figures, tax rates, market share, battery percentage and exam pass rates — anywhere the quantity being compared is itself a percentage.
Worked Examples
| Original | New | Percent change | What it shows |
|---|---|---|---|
| 48 | 36 | −25% | a price cut of a quarter |
| 36 | 48 | +33.33% | the same pair reversed — not +25% |
| 50,000 | 55,000 | +10% | a salary rise; trailing zeros flagged as ambiguous |
| 250 | 175 | −30% | a straightforward decrease |
| −10 | −25 | −150% | both negative — the sign stays honest |
| −25 | 25 | +200% | crossed zero; beyond 100% is legitimate |
| 50 | 0 | −100% | the floor: everything is gone |
| 4% | 5% | +25% | …but only 1 percentage point |
Frequently Asked Questions
How do you calculate percent change?
What is the percent change formula?
How do I calculate percentage increase?
How do I calculate percentage decrease?
Can percent change be negative?
How do you calculate percent change with negative numbers?
What if the original value is zero?
Can percent change be more than 100%?
Why does a 25% increase need only a 20% decrease to undo it?
What is the difference between percent change and percentage points?
How do I calculate percent change in Excel or Google Sheets?
=(B2-A2)/ABS(A2) with the cell formatted as a percentage, or =(B2-A2)/ABS(A2)*100 for a plain number, where A2 is the original value. The ABS is what keeps the sign correct if your original value can be negative; most published templates omit it.What is the difference between percent change and percent difference?
Is percentage change the same as percent change?
Is this percent change calculator free?
Percent change is the measure that describes a journey: it starts where the value started, keeps the sign so the direction survives, and refuses to pretend that a rise and a fall of the same percentage cancel out. Divide by the original, keep the minus sign when there is one, watch for percentage points when your values are already percentages, and remember that nothing can fall more than 100% without going negative. The percent change calculator at the top of this page will hold you to all of it — and when the two numbers you are comparing are peers rather than a before and an after, the percent difference calculator is the right tool instead. The whole free toolkit lives on the Monkza calculators page.