Percentage Change Calculator

How to read your result

The formula always divides by the ORIGINAL value, never the new one, and the sign tells you the direction — positive is an increase, negative is a decrease. This has one sharp consequence: 80 to 100 is a 25% increase, but 100 to 80 is a 20% decrease — not the mirror image, because each move divides by its own starting point. If what you're measuring is itself a percentage (an interest rate, a conversion rate, a margin), keep percentage points and percentage change separate: a rate moving from 3% to 5% is a 2 percentage-point rise but a 66.67% relative increase — never call that "a 2% increase." And percentage change is not percentage difference: change has a direction and a starting point; difference is symmetric and compares two values against their average — the percentage calculatorhas a dedicated difference mode if that's what you need.

Percentage change formula

Worked example

100 → 125. Absolute change 25; (25 ÷ 100) × 100 = +25%; multiplier 1.25×. Reversing it: 125 ÷ 1.25 = 100 — you divide by the multiplier, you never subtract the same percentage back off.

A 50% loss needs a 100% gain to recover. A 50% loss from 100 leaves 50. A 50% gain on that 50 is only 25, taking you to 75 — not back to 100. To return from 50 to 100 you must double: Gain% = 50 ÷ (100 − 50) × 100 = 100%. The loss and the recovery gain are measured on different bases, so they never cancel out at the same percentage.

Time matters for compounding. 100 to 200 is a 100% total change regardless of how long it took. Over 1 year that IS a 100% annual rate; spread over 5 years the annualised rate (CAGR) is only about 14.87% per year — the CAGR companion mode handles this conversion.

Assumptions

• Percentage change uses the original (starting) value as the denominator and keeps the sign — never the new value, and never |Original|.
• When the original is negative or the two values cross zero, the result is still computed but can defy everyday growth language; read the absolute change alongside it.
• CAGR assumes positive start and end values and a constant annual rate — real growth is rarely perfectly smooth.
• Percentages are entered as whole numbers (25 means 25%, not 0.25).
• Results are rounded only for display, to the number of decimals you select; the maths is carried at full precision.

Limitations

• Percentage change from an original value of zero is undefined — there is no percentage of nothing.
• A very small original value can turn an ordinary absolute move into a huge-looking percentage; always read the percentage and the absolute change together.
• Plain percentage change ignores time — use CAGR when the move happened over multiple years and the rate per year matters.
• This is an educational tool, not financial, tax, or professional advice.

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.

Frequently asked questions

Related calculators

These tools take specific percentage problems further:

• Percentage CalculatorSolve X% of Y, what percent X is of Y, reverse percentage, increase/decrease, discounts, and tax, tip, or commission.
• Markup CalculatorPrice from cost across nine modes — markup, target margin, reverse cost ceilings, and ecommerce landed cost after fees.
• Profit Margin CalculatorWork out gross, contribution, operating, and net margin, with target pricing, break-even, scenarios, and SKU comparison.
• VAT/GST CalculatorAdd or remove VAT, GST, or HST from a price, solve tax-inclusive and tax-exclusive values, and build mixed-rate invoices.
• Standard Deviation CalculatorSample and population standard deviation, plus variance, mean, median, quartiles, z-scores, outliers, and confidence intervals.
• Scientific CalculatorTrigonometry, logarithms, powers, roots, and factorials with correct order of operations, memory registers, history, and keyboard entry.

Read the guide

There is no dedicated percentage-change guide yet. For compound growth over time — the idea behind this calculator's CAGR companion — see How Compound Interest Works With Regular Contributions.