Percentage Increase Calculator — Calculate Percent Growth Online

Percentage increase = ((new − old) / old) × 100. Worked example: old = 50, new = 65 → (65 − 50) / 50 × 100 = 15 / 50 × 100 = 30%. The result is signed: a new value smaller than the old gives a negative "increase" (mathematically a decrease — the dedicated percentage-decrease calculator returns a positive number in that case for cleaner UX). Common reference cases: salary raise from $50,000 to $54,000 = 8%; stock price $100 → $112 = 12%; monthly visitors 1,000 → 1,500 = 50%; grocery bill $400 → $480 = 20%. Foundational from ISO 80000-1:2022 percentage definition.

CAGR = (end / start)^(1/years) − 1, the constant interanual growth rate that would compound from start to end over the given number of years. It is NOT equal to the simple arithmetic average of yearly percentage growths (which overstates due to Jensen's inequality on geometric vs arithmetic means). Worked example: $1,000 → $2,000 over 7 years → CAGR = (2000/1000)^(1/7) − 1 = 2^(1/7) − 1 = 0.1041 = 10.41% per year, NOT (100% / 7) = 14.3%. Use CAGR for any multi-period growth comparison: portfolio returns, revenue growth across years, population growth, subscriber base. Brealey, Myers, Allen & Edmans Principles of Corporate Finance 15th edition (2025) introduces CAGR in the time-value-of-money chapter; CFA Level I Quantitative Methods covers the geometric-vs-arithmetic distinction.

The US Bureau of Labor Statistics (BLS) reports headline inflation as the 12-month percentage change in the CPI-U (Consumer Price Index for All Urban Consumers) basket, weighted by household expenditure surveys. CPI methodology is documented at BLS Handbook of Methods CPI section (bls.gov/opub/hom/cpi, current methodology updated through 2024 indexes). Eurostat publishes the parallel HICP (Harmonised Index of Consumer Prices); the European Central Bank targets 2% YoY HICP inflation symmetric (since the July 2021 strategy review). "Headline" CPI includes food and energy; "core" CPI excludes them for less volatility. Monthly releases report both the latest 1-month change (annualised) and the rolling 12-month YoY for trend comparison. Personal Consumption Expenditures (PCE) is the Fed's preferred measure for the dual-mandate inflation goal, also reported as YoY %.

"Doubling" means the new value equals 2× the old, which is an INCREASE of 1× the old, which is 100% (since +100% means "add 100% of the original"). Going from 1 to 2 is +100% (1 became 2). +200% would mean tripling (1 became 3, an increase of 2× the original), and "100% increase" = 200% of original ≠ 200% increase. Common confusion: many people read "a 200% increase" as doubling, when it's actually tripling. Quick check: "X% increase" → new = old × (1 + X/100). A 100% increase: new = old × 2 (doubling). A 200% increase: new = old × 3 (tripling). A 50% increase: new = old × 1.5. The relationship is multiplicative on the original, not on the new.

Division by zero is undefined in mathematics, so percentage increase from 0 has no meaningful value (the formula ((new − 0) / 0) × 100 is mathematically infinite or undefined depending on convention). The calculator surfaces a friendly message instead of returning Infinity or NaN. Conceptually, this case represents "creating something from nothing" — a startup going from $0 revenue to $1M can't be expressed as a percentage increase (it's a categorical transition, not a relative one). Practical workarounds: report the absolute number ("+$1M revenue from a zero base"); use a different framing ("first year of revenue"); or pick a small non-zero baseline if mathematically defensible. The same edge case applies in CPI / GDP reporting when a series starts mid-period.