Quadratic Equation Solver (ax² + bx + c = 0)
About Geometric Mean Calculator
The Geometric Mean & Compound Growth Rate (CAGR) Calculator computes the geometric mean ($GM = (\prod x_i)^{1/n} = \exp(\frac{1}{n} \sum \ln x_i)$) for compounding financial returns, investment portfolios, biological dilution series, and proportional indices.
How to Use Geometric Mean Calculator
Step 1
Enter positive numbers separated by commas, spaces, or newlines.
Step 2
Choose whether numbers represent raw values or investment percentage returns.
Step 3
Review computed geometric mean and compound annual return.
Step 4
Click "Copy GM Report".
Practical Use Cases for Geometric Mean Calculator
Compound Annual Growth Rate (CAGR) & Investment Portfolio Returns
Calculate true multi-year compound annual returns when annual percentage growth rates vary wildly ($+50\%, -30\%, +20\%$).
Microbiology Bacterial Culture Growth & Serial Dilutions
Compute central tendencies for exponential biological bacterial colony growth and logarithmic dilution factors.
Input & Output Examples
Calculating Compound Investment Multipliers
Multipliers: `1.10, 1.25, 0.85, 1.15` (10%, 25%, -15%, 15% annual returns)
Geometric Mean: `1.0776` (True Average Compound Return: `+7.76% per year`) | Arithmetic Mean: `8.75% (Overestimated)`
Key Features & Performance
- ✓Log-Sum Exponential Algorithm: prevents numeric arithmetic overflow when multiplying large datasets of numbers.
- ✓Compares Geometric Mean against Arithmetic Mean and Harmonic Mean ($HM \le GM \le AM$ inequality).
- ✓Supports raw growth rates, percentage yields, and financial investment series.
- ✓100% Client-Side mathematical engine.
- ✓1-Click Copy geometric mean report.
Key Terminology & Definitions
Geometric Mean ($GM$)
The $n$th root of the product of $n$ numbers, reflecting multiplicative and compounding central tendencies.
AM-GM-HM Inequality
A fundamental mathematical theorem stating that for any positive dataset, $\text{Harmonic Mean} \le \text{Geometric Mean} \le \text{Arithmetic Mean}$.