About
About Geometric Mean Calculator
A free, browser-based tool for multiplicative averages — built by statisticians and finance analysts who needed a calculator that shows the formula, proves the math, and never sends your data to a server.
Geometric Mean Calculator exists because the most common averaging mistake in finance is using arithmetic mean for compound returns. Returns of 50% and -50% give AM = 0% but GM = -13.4%/yr — only GM reproduces the actual ending value ($1,000 x 1.5 x 0.5 = $750). This single error leads analysts to overstate expected wealth, miscompare fund performance, and violate GIPS reporting standards. Every calculation on this site runs in your browser via JavaScript, shows the step-by-step formula, and pairs each result with practical context for finance (CAGR, XIRR), statistics (AM-GM inequality, variance), geometry (altitude theorem), and education.
The site includes six specialized calculators — geometric mean, arithmetic mean, harmonic mean, variance & standard deviation, CAGR, and CAGR-to-XIRR — plus the geometric mean altitude theorem for right-triangle geometry. Each calculator shows the formula, works through a numeric example step by step, and explains when a different metric would be more accurate. Comparison guides cover GM vs AM, GM vs HM, CAGR vs GM, CAGR vs XIRR, mean-median-mode-range, and a decision-flow tool for choosing the correct average.