Calculate percentage increase, percentage decrease, absolute change, growth multiplier, reverse percentage change, and loss recovery between two values — plus a final-value planner, percentage-points mode, multi-period tracker, scenario comparison, and a CAGR companion. Every mode shows the formula, the steps, and a downloadable Excel workbook.
Use this calculator when you have an original value and a new value and want to know how much the value increased or decreased.
Educational tool — exact to the precision you choose. Verify figures that matter (invoices, investments, grades).
Percentage change = ((New value − Original value) ÷ Original value) × 100. From 100 to 125 that is (25 ÷ 100) × 100 = a 25% increase (multiplier 1.25×); from 100 to 80 it is (−20 ÷ 100) × 100 = a 20% decrease (0.80×). The result is undefined when the original value is zero.
Enter your values
Common percentage change examples
Basic Change
The reference point everything is measured against.
Results
Increase
Percentage change
25%
↑ increase
Absolute change
25
New − original (same units).
Growth multiplier
1.25×
New ÷ original = 1.25×.
New as % of original
125%
New ÷ original × 100.
The value increased from 100 to 125. The absolute change is 25, which is a 25% increase. The new value is 1.25× the original.
Formula
% Change = ((New − Original) ÷ Original) × 100
Absolute change = 125 − 100 = 25.
Divide by the original: 25 ÷ 100 = 0.25.
Multiply by 100: 25% (increase).
10 sheets — reverse change, final-value planner, loss recovery, multi-period tracker, scenarios, percentage-points, CAGR, formulas, and 25 practice questions.
Before / after
100 → 125
Original
100
New
125
Quick answers
How do you calculate percentage change?
Subtract the original from the new value, divide by the original, then multiply by 100: % Change = ((New − Original) ÷ Original) × 100. From 100 to 125 is (25 ÷ 100) × 100 = +25%.
How do I find the original value before the change?
Divide the final value by the multiplier: Original = Final ÷ (1 + change ÷ 100). 125 after a 25% increase came from 125 ÷ 1.25 = 100. You divide — you do not subtract the same percentage.
After a 50% loss, what gain do I need to break even?
A 50% loss from 100 leaves 50. Getting back from 50 to 100 means doubling — a 100% gain. A loss and an equal gain use different bases, so they never cancel out.
Percentage points vs percentage change
A rate moving from 3% to 5% is a 2 percentage-point rise, but a 66.67% relative increase (2 ÷ 3 × 100). Never call it "a 2% increase".
How to use this percentage change calculator
Pick a mode. Use the segmented control: basic change, reverse change, final value, a growth/decline planner, loss recovery, percentage points, a multi-period tracker, scenario comparison, or the CAGR companion. Basic change is the default before/after question.
Or tap a common example. The preset cards above the calculator load a ready-made example into the right mode — "100 → 125", "3% → 5%", "50% loss", "1,000 + 18%", and more.
Enter your values. Percentages are typed as you say them — 25 for 25%. For reverse and final-value modes, choose whether the percentage is an increase, a decrease, or a signed value, because −20% and a 20% decrease are the same but a 20% increase is not.
Read the result, formula, and steps. Each mode shows the headline result, supporting numbers, a direction badge, the exact formula, a plain-English interpretation, and a step-by-step you can show or hide.
Mind the edge cases. Change from zero is undefined; a negative starting value or values that cross zero raise a warning that steers you to the absolute change; a 100% loss cannot be recovered. The calculator surfaces these rather than hiding them.
Explore and export. Set the decimal precision, use the multi-period and scenario tables, then download the 10-sheet Excel workbook built from your current inputs.
Percentage change formula
Percentage change measures the relative move from an original value to a new value. The four core formulas:
Percentage change
((New − Original) ÷ Original) × 100
Positive = increase, negative = decrease, zero = no change.
For ordinary positive starting values this calculator uses the original value as the denominator and keeps the sign: ((New − Original) ÷ Original) × 100. We do not divide by |Original|. When the original is zero, percentage change is undefined (you cannot divide by zero). When the original is negative or the two values cross zero, the result is still computable but can be hard to interpret in everyday language — so the calculator shows a warning and points you to the absolute change rather than hiding the ambiguity.
Percentage increase vs percentage decrease
Both use the same formula; the sign tells you the direction. From 100 to 125 is a 25% increase; from 100 to 80 is a 20% decrease.
Crucially, 80 → 100 is not the mirror of 100 → 80. Going from 80 up to 100 is a 25% increase (20 ÷ 80), while going from 100 down to 80 is a 20% decrease (−20 ÷ 100) — different because each divides by its own starting value. That single fact is behind most percentage-change confusion.
Percentage change vs percentage difference
Percentage change and percentage difference sound alike and are constantly mixed up, but they answer different questions. Percentage change has a reference point: it measures how far a value moved from a known starting value, ((New − Original) ÷ Original) × 100. Because it divides by the original, swapping the two numbers changes the answer — 80 → 100 is +25%, while 100 → 80 is −20%.
Percentage difference has no "before". It compares two values on equal footing by dividing their absolute difference by their average: |A − B| ÷ ((A + B) ÷ 2) × 100. It is symmetric — swap the values and the answer is identical. Use percentage change when one value is clearly the starting point; use percentage difference when neither is privileged, such as comparing two independent measurements.
The percentage calculator includes a dedicated percentage-difference mode if that is the comparison you need.
Percentage point change vs percentage change
When the thing you are measuring is itself a percentage — an interest rate, an inflation rate, a conversion rate, an exam percentage, a profit margin, a market share — the language gets slippery.
If a rate moves from 3% to 5%, the percentage-point change is 2 points, but the relative percentage change is 66.67% (2 ÷ 3 × 100). They describe the same event in different units. The rule: a percentage point is the plain gap between two percentages; a percentage change measures that gap against the starting rate. Never write "the rate rose 2%" for a 3% → 5% move — that is two points, not a 2% relative change.
Why losses need bigger gains to recover
A loss and an equal gain do not cancel out, because they are measured on different bases. A 50% loss from 100 leaves 50; a 50% gain on 50 is only 25, taking you to 75 — not 100. To return from 50 to 100 you need to double — a 100% gain. The formula is Gain% = Loss% ÷ (100 − Loss%) × 100.
Loss
Value left from 100
Gain needed to recover
Recovery multiplier
10%
90
11.11%
1.1111×
20%
80
25%
1.25×
25%
75
33.33%
1.3333×
50%
50
100%
2.00×
75%
25
300%
4.00×
90%
10
900%
10.00×
The Loss Recovery mode shows the full table out to 95%. A 100% loss leaves nothing to grow from, so it cannot be recovered.
When percentage change can be misleading
The original value is zero
Percentage change divides by the original, and dividing by zero is undefined — there is no "percent of nothing". The calculator returns "Undefined" and points you to the absolute change instead of printing a misleading number.
A negative starting value
When the original is negative, the formula still computes, but the sign and size can defy everyday growth language — moving from −100 to −50 is an improvement, yet the formula reports −50%. A warning flags this so you read the absolute change in context.
Values that cross zero
A move from −100 to 50, or 50 to −100, crosses zero. The percentage can look enormous or carry a confusing sign. In these cases the absolute change (+150 or −150) communicates the situation far more clearly.
A very small original value
When the base is tiny, an ordinary absolute move turns into a huge percentage. A change from 0.5 to 1.5 is "+200%" — true, but the 1.0 absolute move is the more honest headline. Always read the percentage and the absolute change together.
Confusing points with percent
For rates, a 3% → 5% move is 2 percentage points but a 66.7% relative change. Quoting "2%" for that move is the single most common reporting error this page exists to prevent.
Reporting only the percentage
A 5% change on a small base is small; the same 5% on a large base can be enormous in absolute terms. A percentage without its absolute change tells only half the story.
When to use CAGR instead
Plain percentage change measures the total move between two values and ignores how long it took. When the time period matters, use the compound annual growth rate: CAGR = (New ÷ Original)^(1 ÷ Years) − 1.
100 to 200 is a 100% total increase. If that happened in one year, the CAGR is 100%. If it took five years, the CAGR is only about 14.87% per year — the same total move, a very different yearly rate. Use the total when time is irrelevant; use CAGR for investments, revenue, users, or population over multiple periods. The CAGR companion mode is a lightweight check, not a replacement for a full time-series analysis.
Worked examples
100 → 125. Absolute change 25; (25 ÷ 100) × 100 = +25%; multiplier 1.25×. The new value is 1.25 times the original.
Reverse +25%. A final value of 125 after a 25% increase came from 125 ÷ 1.25 = 100.
1,000 + 18%. Final value = 1,000 × 1.18 = 1,180; the change amount is 180.
3% → 5%. A 2 percentage-point rise, but a 66.67% relative increase.
50% loss. Value left 50; gain needed = 50 ÷ 50 × 100 = 100% to get back to 100.
100 → 200 over 5 years. Total change +100%; CAGR = (200 ÷ 100)^(1 ÷ 5) − 1 ≈ 14.87% per year.
Real-world uses
Prices, discounts & markdowns
See the percentage and money change when a price moves, and use the final-value mode to apply a planned markdown or markup.
Salary & raises
Turn a raise into a new salary (final value), or work back from an offer to the old figure (reverse change).
Revenue & profit
Measure revenue growth or a profit decline month over month, and the multi-period tracker for a whole quarter or year — with the absolute change beside the percentage.
Website traffic & conversion
Track traffic growth across periods, and use percentage points for conversion-rate moves so "2.0% → 2.4%" is read as +0.4 points (a 20% relative lift), not "+0.4%".
Interest, inflation & rates
The percentage-point mode keeps rate changes honest: a base-rate move from 3% to 5% is 2 points, not a 2% change.
Investments & long-term growth
Use plain percentage change for a single move, and the CAGR companion when the result is spread over several years.
Exam scores & measurements
Convert a score improvement to a percentage, or compare a reading against a baseline — watching for tiny bases that inflate the percentage.
Inventory & cost reduction
Plan a cost cut with the planner (required reduction and the target value), and track stock movements across periods.
Common mistakes
Dividing by the new value. Percentage change always divides by the original (starting) value, never the new one.
Reversing by subtracting the same %. To undo a 25% increase you divide by 1.25, not subtract 25%.
Treating a loss and equal gain as a wash. A 50% loss needs a 100% gain to recover.
Confusing points with percent. A 3% → 5% rate move is 2 points, not "a 2% increase".
Quoting % without the absolute change. 5% of a small base is tiny; 5% of a large base can be huge.
Using percentage change across different time spans. When the period matters, use CAGR.
Reading a percentage of zero or a negative base. These are undefined or misleading — the calculator warns you.
Which calculator should I use? For a slice of a number, reverse percentage, or a percentage difference, use the percentage calculator. For pricing from cost, the markup and profit margin calculators. For sales tax and VAT, the VAT calculator. For an investment return, the ROI calculator.
Frequently asked questions
What is percentage change?
Percentage change measures how much a value increased or decreased relative to the original value. It is the absolute change divided by the original, times 100: ((New − Original) ÷ Original) × 100.
How do I calculate percentage increase?
Use ((New − Original) ÷ Original) × 100. When the new value is larger the result is positive — an increase. From 100 to 125: (125 − 100) ÷ 100 × 100 = +25%.
How do I calculate percentage decrease?
The same formula, ((New − Original) ÷ Original) × 100. A negative result means a decrease. From 100 to 80: (80 − 100) ÷ 100 × 100 = −20%.
Why is percentage change from zero undefined?
Because the formula divides by the original value, and division by zero is undefined — there is no meaningful percentage of nothing. When the original is 0, report the absolute change or choose a non-zero baseline.
What is absolute change?
Absolute change is New value − Original value. It is the raw difference in the same units as your inputs (dollars, users, points), and it is the honest companion to the percentage — especially on small or zero bases.
What is a growth multiplier?
The growth multiplier is New ÷ Original. A multiplier of 1.25 means the new value is 1.25 times the original — a 25% increase; 0.80 means it shrank to 80% of the original — a 20% decrease.
How do I reverse a percentage change?
Divide the final value by the multiplier: Original = Final ÷ (1 + change% ÷ 100). For a decrease, divide by (1 − decrease% ÷ 100). 125 after a 25% increase came from 125 ÷ 1.25 = 100. You divide — you never subtract the same percentage.
Why does a 50% loss need a 100% gain to recover?
A 50% loss from 100 leaves 50. To get back from 50 to 100 you must double — a 100% gain. The gain is measured on the smaller remaining base, so a loss and an equal gain do not cancel out. The formula is Gain% = Loss% ÷ (100 − Loss%) × 100.
What is the difference between percentage change and percentage points?
Percentage points measure the plain arithmetic gap between two percentages (3% to 5% is 2 points). Percentage change measures that gap relative to the old percentage (2 ÷ 3 × 100 = 66.67%). They describe the same move in different language — be clear which one you mean.
What is the difference between percentage change and percentage difference?
Percentage change uses the original value as the denominator and has a direction. Percentage difference uses the average of the two values as the denominator and is symmetric. For the same pair they usually give different numbers, so they are not interchangeable.
Can percentage change be more than 100%?
Yes. If a value doubles, the increase is 100%; if it triples, 200%. A change above 100% simply means the new value is more than double the original.
Can percentage change be negative?
Yes. A negative percentage change means the value decreased — for example 200 to 150 is −25%. The minus sign is the direction; the number is the size of the fall.
Why can percentage change be misleading with negative numbers?
When the original value is negative, the formula still computes but the direction and magnitude can defy ordinary growth language — moving from −100 to −50 is an improvement yet reads as −50%. The same applies when values cross zero. In those cases the absolute change is the clearer figure, and the calculator warns you.
When should I use CAGR instead of percentage change?
Use plain percentage change for a single before/after move where time does not matter. Use CAGR — the compound annual growth rate, (New ÷ Original)^(1 ÷ Years) − 1 — when the change is spread over several years and you want the average yearly rate. 100 to 200 is a 100% total change, but over 5 years that is only ~14.87% per year.
Is this calculator suitable for finance or business decisions?
It is an educational calculator that shows every formula and step. It is accurate to the precision you choose, but you should verify results — and the appropriate formula and rounding — for professional, financial, legal, academic, or business-critical use.
Percentage increase vs decrease
Same formula. A positive result is an increase (100 → 125 = +25%); a negative result is a decrease (100 → 80 = −20%). The sign is the direction; the size is the magnitude.
Related calculators
These tools take specific percentage problems further:
Percentage CalculatorA complete percentage hub: X% of Y, what percent X is of Y, reverse percentage, increase/decrease, percentage change vs difference, discounts and tax/tip/commission — with steps, a scenario table, and a 7-sheet Excel workbook.
Markup CalculatorPrice from cost across 9 modes — markup, target margin, price analysis, profit target, reverse cost ceilings, ecommerce landed cost after fees, discount impact, quantity profit, and batch comparison, with a 10-sheet Excel pricing workbook.
Profit Margin CalculatorA full profitability cockpit — gross, contribution, operating, and net margin across simple, advanced, ecommerce, service, SaaS, and solve-for modes, with target pricing, discount impact, break-even, scenarios, SKU comparison, and a 17-sheet Excel workbook.
ROI CalculatorReturn on investment five ways — simple ROI, date-based ROI, net ROI after fees/taxes/income, a reverse target solver, and a two-investment comparison — with gain/loss, annualised ROI (CAGR), and a multi-sheet Excel report.
VAT/GST CalculatorAdd or remove VAT, GST, HST, or consumption tax from a price, solve tax-inclusive and tax-exclusive values, calculate mixed-rate invoices, and export a formula-backed XLSX workbook.
Standard Deviation CalculatorA full descriptive-statistics analyzer — sample & population SD, variance, mean, median, quartiles, IQR, MAD, CV, standard error, confidence interval, z-scores, outliers, the empirical rule, dataset comparison, charts, and a 12-tab Excel workbook. Paste data from any spreadsheet.
Sources & methodology
The calculator applies the standard percentage-change identities — change ÷ original × 100, the growth multiplier, reverse change (divide by the multiplier), the increase/decrease multipliers, loss recovery (Loss ÷ (100 − Loss) × 100), the percentage-point vs relative-change distinction, and CAGR — as published in the references below. It uses the original value as the denominator and surfaces the zero, negative-base, and crossing-zero edge cases rather than hiding them. The exported workbook reproduces the identical formulas as live, editable Excel formulas, validated cell-by-cell against this page's engine. Calculator Matters is an independent project, not affiliated with any source listed. Links open in a new tab.
Last reviewed: 14 June 2026. Formula and assumptions reviewed for accuracy. First published 13 June 2026.
Educational use disclaimer
This percentage change calculator and its Excel workbook are for education and everyday estimation only. They are not financial, tax, accounting, legal, or professional advice. Percentage change is undefined when the original value is zero, and it can be misleading when the original is negative or the two values cross zero — in those cases read the absolute change. CAGR assumes positive start and end values. Results are mathematically exact to the precision you choose, but only as correct as the numbers you enter and the formula your context requires. For graded coursework, investment decisions, or professional reports, confirm the required method and rounding with the appropriate source or professional.
Built and maintained by Calculator Matters, an independent calculator project. Formulas reviewed against the published sources above · Last reviewed 14 June 2026 · How we calculate · Found an error? [email protected]
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