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Geometric Mean Rate Of Return Calculator | Geometric return

Calculate the true average annual return of an investment portfolio using the geometric mean, which accounts for compounding. Unlike the arithmetic average, it reflects actual growth — essential for comparing fund and portfolio performance.

Last updated: June 2026 · Free · No sign-up required

Results

Enter values above and click Calculate to see your result instantly.

How the Geometric Mean Rate Of Return Calculator works

Under the hood, this calculator applies Geometric mean = [(1+r₁)(1+r₂)…(1+rₙ)]^(1/n) − 1, so the geometric mean rate of return calculator result you see is genuine math, not a lookup table.

The reference table below covers the most common geometric mean rate of return calculator cases at a glance, the methodology section breaks the calculation into verifiable steps, and the FAQ tackles the edge cases.

Quick reference

MethodWhat it answers
Arithmetic meanSimple average of yearly returns
Geometric meanCompounded average actually earned
CAGRGeometric return from start & end value
Why it differsVolatility drags compounded returns
UseCompare investments over time

info Geometric Mean Rate Of Return Calculator

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info Private by design

Everything runs locally in your browser. No uploads, no accounts, no tracking.

info Works everywhere

Fully responsive and mobile-friendly — calculate on any device, any time.

info Educational

Includes the formula and step-by-step explanation so you understand the math, not just the answer.

Interpretation guide

Return patternGeometric vs arithmetic
Steady returnsThe two are nearly equal
Volatile returnsGeometric is noticeably lower
A big loss yearGeometric mean falls sharply
Reported "average"Use geometric for honest results

lightbulb Worked example

Let's say you are using the Geometric Mean Rate Of Return Calculator. Calculates geometric mean rate of return using Geometric mean = [(1+r₁)(1+r₂)…(1+rₙ)]^(1/n) − 1, in real time in your browser. Enter the values that match your situation into the input fields and press calculate — using realistic numbers makes the result directly useful for you.

Result: The calculator instantly applies the formula Geometric mean = [(1+r₁)(1+r₂)…(1+rₙ)]^(1/n) − 1 and returns the result with appropriate precision.

What this means: Read the result in the context of what you are measuring. The step-by-step breakdown lets you confirm the math and understand which input most affects the outcome.

Formula & methodology

Formula: Geometric mean = [(1+r₁)(1+r₂)…(1+rₙ)]^(1/n) − 1

How the geometric mean return is calculated

The tool applies Geometric mean = [(1+r₁)(1+r₂)…(1+rₙ)]^(1/n) − 1, compounding each period's return and taking the nth root — the constant annual rate that reproduces the actual ending value of the investment.

Example: returns of +50% and −50% have an arithmetic mean of 0% but a geometric mean of √(1.5 × 0.5) − 1 ≈ −13.4%, matching the real loss: $100 → $150 → $75.

Reading the result: the geometric mean is always at or below the arithmetic mean, and the gap widens with volatility — it is the correct average for compounding returns, portfolio performance, and any series where each period builds on the previous one. The arithmetic mean overstates growth whenever returns vary.

Authoritative source: Wolfram MathWorld

Frequently asked questions

What is the geometric mean rate of return?
It is the average growth rate that compounds over multiple periods: Geometric mean = [(1+r₁)(1+r₂)…(1+rₙ)]^(1/n) − 1. Unlike the arithmetic average, it accounts for compounding, so it answers the question 'what constant annual return would produce the same final value?' It is the correct measure for comparing investment performance over time.
How is geometric mean different from arithmetic mean?
The arithmetic mean simply averages the yearly returns, while the geometric mean multiplies the growth factors and takes a root. The geometric mean is always lower when returns vary and is the correct measure for multi-year performance.
Is geometric mean the same as CAGR?
The Geometric Mean Rate Of Return Calculator is free, private, and accurate: it runs entirely in your browser (no uploads, no accounts), applies the standard calculation, and explains each step so you can verify the result. Calculates geometric mean rate of return using Geometric mean = [(1+r₁)(1+r₂)…(1+rₙ)]^(1/n) − 1, in real time in your browser. There is no limit on usage, and it works on any device.
Why is the geometric mean lower than the arithmetic mean?
The geometric mean multiplies the period growth factors and takes the nth root, which penalizes volatility: a +50% year followed by a −50% year has an arithmetic average of 0% but a geometric mean of about −13.4%, matching the actual loss of value. Because real returns are volatile, the geometric mean is always at or below the arithmetic mean.
When should I use the geometric mean?
Use the geometric mean whenever returns compound over time — multi-year investment performance, fund comparisons, and any series where each period builds on the previous one. It gives the constant annual rate that reproduces the actual ending value. Use the arithmetic mean only for non-compounding contexts, like average monthly sales that do not build on each other.
What does the Geometric Mean Rate Of Return Calculator do?
Calculates geometric mean rate of return using Geometric mean = [(1+r₁)(1+r₂)…(1+rₙ)]^(1/n) − 1, in real time in your browser. The calculator takes your inputs, applies the standard calculation, and returns a clear result so you can make an informed decision without doing the math by hand.
What formula does the Geometric Mean Rate Of Return Calculator use?
It applies Geometric mean = [(1+r₁)(1+r₂)…(1+rₙ)]^(1/n) − 1, where each rᵢ is a period return expressed as a decimal. Enter the annual returns and the tool compounds them, returning the average annual growth rate that reproduces the final portfolio value. For example, returns of 10% and −10% give a geometric mean of about −0.5% per year.
Is the Geometric Mean Rate Of Return Calculator free and private?
Yes — the Geometric Mean Rate Of Return Calculator. There is no sign-up, no paywall, no trial, and no limit on how many calculations you can run. CalcaTools covers its costs with non-intrusive display advertising, so the calculator itself never asks for payment or restricts any feature.
How accurate is the Geometric Mean Rate Of Return Calculator?
The Geometric Mean Rate Of Return Calculator applies the standard formula: Geometric mean = [(1+r₁)(1+r₂)…(1+rₙ)]^(1/n) − 1. It is tested against published worked examples before launch and uses native double-precision arithmetic, so results are accurate to typical precision for the values you enter — with no intermediate rounding that could distort the answer.

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