Average Return Calculator
Calculate the compound annual growth rate and average return on any investment.
Year-by-Year Running Value
| Year | Annual Return | Gain / Loss on £1,000 | Running Value | Cumulative Return |
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Arithmetic vs Geometric Mean
Arithmetic mean (simple average)
Add all annual returns and divide by the number of years. Easy to calculate but can overstate actual compound returns when there is volatility. A 50% gain followed by a 50% loss gives an arithmetic mean of 0%, but you actually lost 25%.
Geometric mean (CAGR)
The compound annual growth rate that would produce the same cumulative result. Formula: CAGR = (End ÷ Start)^(1/n) – 1. This is the more accurate measure of investment performance because it accounts for compounding and volatility. To project future growth using your CAGR, try the investment calculator.
Why they differ
The greater the volatility of returns, the larger the gap between arithmetic and geometric mean. The geometric mean is always ≤ the arithmetic mean. The difference is approximately: Geo ≈ Arith – (σ² / 2), where σ² is the variance of returns. The compound interest calculator shows how consistent returns grow without volatility drag.
Which should I use?
Use geometric mean (CAGR) to evaluate actual past performance — it tells you what rate of return would have produced your real result. Use arithmetic mean only for estimating expected future returns when individual period returns are independent. To compare annualised returns across completed investments, try the ROI calculator.
Worked example
An investment grows from £10,000 to £18,000 over 8 years. CAGR = (18,000 ÷ 10,000)^(1/8) − 1 = 7.63% per year. The arithmetic mean of any equivalent annual returns would be slightly higher due to volatility drag — for a consistent return, both measures would be identical.
Frequently Asked Questions
What is CAGR (compound annual growth rate)?
CAGR is the geometric mean annual growth rate of an investment over multiple years. Formula: CAGR = (End ÷ Start)^(1/years) − 1. It represents the steady rate at which an investment would have grown to produce the actual cumulative result — useful for comparing investments held over different periods.
What is the difference between arithmetic and geometric mean returns?
The arithmetic mean simply averages all annual returns. The geometric mean (CAGR) accounts for compounding. A 50% gain followed by a 50% loss gives an arithmetic mean of 0%, but you actually lost 25% — the geometric mean correctly shows the negative result. For actual past performance, always use CAGR.
What is a good average return on investment?
The S&P 500 has historically returned approximately 10% per year nominally (around 7% after inflation). A 'good' return depends on the asset class, time period, and risk taken. Always compare returns on a like-for-like basis using the same time period and accounting for fees and inflation.
Why does volatility reduce actual returns?
This is volatility drag. The geometric mean is always less than or equal to the arithmetic mean, with the gap growing with volatility. Approximately: Geometric ≈ Arithmetic − (variance/2). A portfolio returning 30% one year and −20% the next has an arithmetic mean of 5% but a CAGR of only about 2.5%.
Evidence & Methodology
How This Page Is Grounded
Method
Reports the arithmetic mean of periodic returns and the geometric mean from compounded growth across all periods.
Important limitation: Past average returns do not predict future results; the arithmetic mean does not represent compounded wealth growth.
Primary Sources
- Annual return Investor.gov — U.S. Securities and Exchange Commission
- Investing: an introduction MoneyHelper
Quality Checks
Checked with identical returns, mixed gains and losses, and a total-loss boundary case.
See how sources are selected and corrections are handled in our Editorial & Calculation Methodology, and which automated checks this page has to pass in How We Test.