How to Calculate Percentage Change
Percentage change measures relative increase or decrease from an original value to a new value.
Quick answer
Percentage change = ((New Value − Old Value) ÷ Old Value) × 100. A positive result is a percent increase; negative is a decrease. Always divide by the original (old) value, not the new one, unless you intentionally want percentage difference relative to a different baseline.
Overview
Percentage change appears everywhere in personal finance and business analysis: stock and portfolio returns, sale prices, inflation comparisons, revenue growth, and fitness progress photos translated into scale numbers. Using the correct baseline prevents misleading headlines—a drop from $100 to $80 is a 20% decrease, but recovering from $80 back to $100 is a 25% increase because the denominator changed. Mastering the formula and its edge cases keeps dashboards, spreadsheets, and mental math honest when communicating movement between two points in time.
The standard percentage change formula
Subtract the old value from the new value to get absolute change. Divide that difference by the old value to express change relative to where you started. Multiply by 100 to convert the decimal to a percentage readable in reports and charts.
Example: price rises from $40 to $50. Difference is $10. $10 ÷ $40 = 0.25 → 25% increase. The same $10 move from $50 down to $40 is $10 ÷ $50 = 20% decrease. Direction and baseline both matter for interpretation.
Percent increase and decrease are not symmetric
A 50% loss requires a 100% gain to break even because the post-loss baseline is smaller. Investors and analysts who forget this symmetry mis-set recovery expectations after drawdowns. Always re-anchor to the current baseline when projecting required bounce-back.
Reporting conventions often color decreases red and increases green, but cross-category comparisons need consistent time windows. Month-over-month and year-over-year percentage changes answer different questions and should be labeled explicitly in dashboards.
Single-period change vs compounded multi-period growth
Percentage change between two endpoints is one calculation. Average annual growth over many years uses geometric (CAGR) logic, not arithmetic averaging of yearly percentage changes. Quoting simple percentage change across five years without CAGR can overstate or understate typical yearly experience.
When analyzing investment statements, distinguish total return percentage change from annualized return. Compound interest calculators help bridge from lump-sum growth assumptions to annualized rates when contributions vary over time.
Zeros, negatives, and small bases
Percentage change from zero is undefined mathematically because division by zero is invalid. From a small near-zero baseline, large percentage swings may be technically correct but misleading—absolute change often tells a clearer story for early-stage metrics.
When values cross from negative to positive, percentage change is rarely meaningful for communication; use absolute dollar improvement instead. Financial analysts sometimes use basis points (hundredths of a percent) when discussing rate moves on already-small percentages like bond yields.
Everyday applications in finance and budgeting
Track grocery, rent, or utility bill changes month to month with the standard formula to see which categories drive budget drift. Compare sale discounts by treating shelf price as old value and checkout price as new value—verify whether tax or unit size changed before attributing full move to discount.
Business users calculate revenue or expense line percentage changes in variance analysis. Pair percentage change with absolute dollar variance so stakeholders see both relative momentum and materiality to the bottom line.
Examples
Stock price move
Shares rise from $28 to $35: (($35 − $28) ÷ $28) × 100 ≈ 25% increase. If they fall back to $28 from $35, change is −20%, not −25%.
Salary raise evaluation
Income increases from $55,000 to $60,500: $5,500 ÷ $55,000 ≈ 10% raise—useful for comparing to inflation or market benchmarks in the same year.
Budget category spike
Dining spend goes from $320 to $416 monthly: 30% increase signals a lifestyle or pricing shift worth investigating in absolute dollars ($96) as well as percent.
Common mistakes and edge cases
- Dividing by the new value instead of the original when calculating change.
- Assuming a 20% drop and 20% rise return to the same number.
- Averaging multiple percentage changes arithmetically across years instead of using CAGR.
- Quoting huge percentage gains from a negligible starting baseline without context.
Related resources
- What Is Compound Interest?Compound interest earns returns on both your principal and previously accumulated interest, accelerating growth over time.
- Simple vs Compound Interest ExplainedSimple interest applies only to principal; compound interest reinvests earned interest so balances grow faster over time.
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Last reviewed: 2026-05-23