ROI Calculator
Return on investment without the usual self-deception: gain against cost, and — when you give it a holding period — the annualised rate computed geometrically, not by dividing. Plus doubling time, by the exact logarithm and by the rule of 72 so you can see how good the shortcut is.
The honest annualisation
The only defensible way to compare returns across different periods is the geometric rate: (final ÷ initial)^(1/years) − 1. It answers the precise question 'what constant yearly rate would have produced this outcome' — and it is always below the arithmetic shortcut, which is why the shortcut survives in marketing.
Doubling time is the same mathematics reflected: ln 2 divided by ln(1 + rate). The rule of 72 approximates that logarithm well enough for coffee-break arithmetic, and printing both side by side keeps the approximation honest.
Frequently asked questions
Why is 100% over 5 years not 20% a year?
Because returns compound: money that doubled in five years grew 14.87% a year — each year's growth built on the last. Dividing by years pretends the gains sat idle, and it overstates every multi-year investment; the gap widens the longer the period.
What does ROI leave out?
Time, risk and cash flows. Twenty percent is excellent in one year, poor in ten — which is what the annualised line fixes. It also cannot see deposits and withdrawals along the way; for a portfolio with flows, money-weighted return is the honest measure.
How accurate is the rule of 72?
Within a few percent for the rates people actually meet — at 10% it says 7.2 years against a true 7.27. It drifts at extremes, which is why the exact logarithm is printed beside it: the rule is for mental arithmetic, the log for the decision.
Should ROI be compared before or after costs?
After, always: fees, taxes and spreads come out of the final value, not the headline. A 12% gross return with a 2% annual fee is a 10% investment — run the calculator on what actually lands in the account and comparisons across options become meaningful.
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