Investment return (ROI) calculator

Example: 10,000 EUR grows to 13,000 EUR in three years

The initial investment is 10,000 EUR, the final value 13,000 EUR and the term 3 years. Profit is 13,000 − 10,000 = 3,000 EUR. The return (ROI) is 3,000 ÷ 10,000 = 30%.

The annualised return (CAGR) is not 30 ÷ 3 = 10%. The calculator takes (13,000 ÷ 10,000) to the power of 1/3 minus 1, which is the cube root of 1.3 minus 1, giving 9.14% a year. Check: 10,000 × 1.0914 = 10,914 EUR at the end of year one, 11,912 EUR after year two and 13,000 EUR after year three. Each year's return is earned on an amount that has already grown, which is why 9.14% a year is enough to reach 30%.

The same logic runs the other way. If an investment grows 10% two years in a row, 10,000 EUR becomes 12,100 EUR. The ROI is 21%, not 20%, but the CAGR is exactly 10%.

Same profit, different period

ROI ignores time; CAGR includes it. That is why the same ROI can mean very different outcomes. In every example below the amount grows by 30%.

• 10,000 EUR → 13,000 EUR in one year: ROI 30%, CAGR 30%.
• 10,000 EUR → 13,000 EUR in three years: ROI 30%, CAGR 9.14%.
• 10,000 EUR → 13,000 EUR in six years: ROI 30%, CAGR 4.47%.
• 2,000 EUR → 2,600 EUR in half a year (term 0.5): ROI 30%, CAGR 69%. Annualising a short period assumes the same pace lasts a full year, which is rarely realistic.

Losses, and why they are harder to win back

If the final value is below the initial one, the profit and both percentages turn negative. A 5,000 EUR investment worth 4,200 EUR two years later gives a profit of −800 EUR, an ROI of −16% and a CAGR of −8.35% a year. 10,000 EUR → 9,000 EUR over three years gives an ROI of −10% and a CAGR of −3.45% a year.

Loss and gain percentages are not symmetrical. To get back to 5,000 EUR after a 16% fall, 4,200 EUR has to grow by 19.05%. A 50% fall needs a 100% rise to restore the original amount. So one year at +16% does not cancel a previous year at −16%.

What to enter as the initial and final value

The result is only as good as the inputs. The biggest error usually comes from leaving costs out of the initial value, or income received along the way out of the final value.

• Costs belong in the calculation. If you bought for 10,000 EUR and paid a 50 EUR transaction fee, the initial investment is 10,050 EUR. If selling costs another 50 EUR, the final value is 12,950 EUR. Result: profit 2,900 EUR, ROI 28.86% and CAGR 8.82%, not 30% and 9.14%.
• Income paid out has to be added back. If the investment is worth 13,000 EUR and you received 400 EUR in dividends along the way that you did not reinvest, enter 13,400 EUR as the final value. The ROI is then 34% and the CAGR 10.25%.
• Contributions made along the way break the calculation. The calculator assumes one amount at the start and one value at the end. If you added money during the period, comparing the final value with the first deposit is not a return, because part of the growth is your own added money.
• The period has to be the actual one. If you held the investment for 2 years and 6 months, enter 2.5, not 3 or 2.

What ROI and CAGR do not show

CAGR is a smoothed average. 10,000 EUR → 20,000 EUR over seven years gives a CAGR of 10.41%, but it does not tell you whether the value rose steadily or halved along the way and recovered. Neither figure says anything about volatility, and therefore risk.

The result is nominal. Inflation, taxes and ongoing fees that have not been taken off the final value reduce the real return. When comparing two investments, CAGR is a better basis than ROI because it accounts for the length of the period: 150% over ten years (8,000 EUR → 20,000 EUR) is 9.60% a year, less than 30% in a single year.