Percentage Change Calculator — % Change Between Two Numbers

Use percentage-change when you don't yet know the direction (or when you want a single tool that handles both directions). Use the dedicated % increase or % decrease tools when you know the direction in advance and want the result framed positively in that direction (e.g., "25% off" reads more naturally than "−25% change" in retail context). The math is the same family — ((new − old) / |old|) × 100 — but the sign convention differs: percentage-change returns + or − to indicate direction, percentage-increase always assumes new > old (negative result hints at direction error), percentage-decrease returns positive numbers for actual drops. Same input → consistent magnitude across all three tools.

A loss followed by an equal-percentage gain is NOT a wash, because each percentage applies to a different base. If a $100 stock loses 10%, it becomes $90; a 10% gain on $90 is $99, NOT back to $100. To recover from a loss of L (as a fraction), you need a gain of L / (1 − L). Worked: L = 0.10 → gain = 0.10 / 0.90 = 0.1111 = 11.11%. L = 0.20 → 25%. L = 0.50 → 100%. L = 0.75 → 300%. The asymmetry compounds the deeper the loss — a 50% drawdown requires a full doubling to recover, a 90% drawdown requires a 10×. CFA Institute curriculum uses this formula in portfolio-drawdown analysis; Brealey, Myers, Allen & Edmans Principles of Corporate Finance (15th ed, 2025) introduces it in the risk-and-return chapter.

For sub-percent moves — interest rates, bond yields, credit spreads, FX moves smaller than 1% — financial industry convention is basis points (1 bp = 0.01%). The Bank for International Settlements (BIS) reporting standards use bp throughout; central-bank rate decisions are quoted in bp ("ECB +25 bp", "Fed cut 50 bp"); 10y Treasury yield is "4.50% ± 5 bp" not "0.05%". The reason is precision and unambiguity: "the rate moved 0.25%" can mean either +0.25 percentage points (absolute) OR a 0.25% relative change (tiny). "25 bp" unambiguously means 0.25 percentage points absolute. For non-financial percentages and moves of 1% or more, percentage change is the natural unit.

Without Math.abs, going from −10 to −5 calculates as ((−5) − (−10)) / (−10) × 100 = 5 / (−10) × 100 = −50%, which inverts the intuitive reading. The natural-language statement "the value rose by 5 from −10" matches a +50% reading, not −50%. Putting Math.abs around the denominator (((new − old) / |old|) × 100) preserves the sign of the numerator so that the percentage's sign tells direction (+ = rose, − = fell) regardless of whether the base is positive, negative, or zero. Spreadsheet implementations of percent change typically apply the same `abs()` convention to handle negative bases. Without abs, negative-base inputs produce mathematically valid but everyday-counter-intuitive results that confuse most users.

SEC Form 10-K (annual) and 10-Q (quarterly) filings include comparative period data — quarterly results vs the same quarter prior year (Q3 2024 vs Q3 2023), and full-year vs full-year — calculated as ((current − prior) / prior) × 100. The "year-over-year" (YoY) framing isolates seasonal effects (a retailer's Q4 vs Q4, a SaaS company's Q1 vs Q1) and is the dominant comparison metric in earnings releases and investor presentations. Constant-currency reporting strips out FX moves to show "underlying" YoY change. CPI inflation is also reported as 12-month rolling YoY % change in the BLS All Items basket; ECB inflation target is 2% YoY symmetric (since July 2021 strategy review).