ROI Calculator

What the figure measures, and what it leaves out

Return on investment is the net change divided by what was put in, expressed as a percentage. The arithmetic is settled; the inputs are not. Whether a cost figure includes transaction charges, ongoing platform charges, tax already paid, or time spent managing the holding is a choice made before the calculation starts, and two people can arrive at different percentages for the same holding without either being wrong. The figure this page produces is whatever those two entered numbers make it, so the comparison only holds where both sides are drawn on the same basis: either both gross of costs, or both net of them.

Reading the result rows

The headline states the net change as a share of what was put in. The cash row gives the same change in currency, labelled as a gain or a loss according to its direction and as no net change where the two sides match. Value Multiple is the final value divided by the cost, so a 50% return reads as 1.50 and a total loss as 0.00, the same relationship in a unit that stays readable at large returns, where a percentage runs into the hundreds. The last row states the change as a share of the final value rather than the cost, which is a different number and a commonly confused one: a 50% return is a 33.33% share of the final figure. It appears only where there is a net change and the final value is above zero; the Sources and Methodology section sets out why each of the other three cases is left out.

The time dimension the figure does not carry

There is no holding period in this calculation, so a 30% return earned over one year and one earned over five both read 30%. Annualising is what separates them: the same 30% is 9.14% a year over three years, 5.39% over five, and 2.66% over ten. A single total can therefore describe anything from 30% a year to 2.66% a year, depending only on the period behind it, which is why a percentage quoted without one cannot be set against a percentage that has one. The CAGR Calculator does the annualisation directly from a start value, an end value and a number of years.

Three measures that share the name

Simple return, which is what this page computes, is the net change over the cost with no reference to time, and it fits one-off cases with a clean start and end. Annualised return, commonly called compound annual growth rate, is the yearly rate that compounds to the same total, and it is what a multi-year holding is usually described by. Money-weighted return, calculated as an internal rate of return, accounts for when each amount went in and came out, which is the measure for a holding built up through several contributions rather than one. Where a figure is quoted as a return without saying which of the three it is, it is usually the first, and short of a total loss the gap between the first and the other two widens with the period held.

Costs that fall outside the two figures

The cost input is whatever is entered, so anything not put into it is not in the result. Transaction charges on the way in and out, ongoing platform or management charges, and tax on the gain where it applies all sit outside the calculation unless they have already been folded into the two figures. Their combined size varies by asset, by market and by the account the holding sits in, and on a long hold in a taxable account they can move the figure materially rather than marginally. There are two places a charge can go, and they do not generally give the same answer. Both reduce the net change by the same amount, so the numerator is identical either way; what differs is that adding the charge to the cost also enlarges the denominator. Which way the two figures then diverge follows the sign of the net change after the charge. While it is positive, adding to the cost gives the lower percentage: on a 10,000 cost ending at 15,000, a 1,000 charge netted off the value reads 40.00% and added to the cost reads 36.36%. Once a charge takes the net change below zero, the larger denominator makes the result less negative instead, so adding to the cost gives the higher percentage. Where the charge exactly cancels the change, the numerator is zero and both treatments read zero, which is the one case where the choice makes no difference. Convention puts acquisition charges into the cost and nets ongoing charges off the value; what neither treatment allows is doing both, which counts the charge twice.

Total against annualised

A total return and an annualised one are not comparable figures, and most published benchmarks are quoted annualised. Short of a total loss, a multi-year total is larger in magnitude than the yearly rate behind it, so it overstates a gain and overstates a loss in the same way, since a 30% five-year total is 5.39% a year, and a 30% five-year loss is 6.89% a year. At a total loss the two coincide, since −100% over the period is −100% a year over any period. Past that point the relationship breaks rather than continuing: the growth factor turns negative, so an even number of periods has no real annual equivalent and an odd number has one only in the sense of a multiplier that flips sign each year, which is not a growth rate anything can be compared against. Converting one side before comparing is what makes the two describe the same thing.

Where a simple return is the whole answer

There are cases where no annualisation is wanted. A one-off project with a defined start and end, a piece of equipment measured against the savings it produced, a piece of work whose payoff arrived in a known window: in these the before-and-after comparison is the question, and dividing it across years adds nothing. This calculator produces that comparison from a cost and a final value, and nothing else enters it.

Which returns get calculated

A set of returns collected after the fact tends not to be a complete record, because the ones that went badly are less often worked out and less often kept. A portfolio figure that covers every position ever held, including those closed at a loss, is a different quantity from the return on the positions still open, and it is usually the lower of the two. The distinction matters when a single position's figure is used to describe an overall record, since the two answer different questions.

Applying the figure to non-financial cases

The same division is often applied to education, training, marketing and health spending. The arithmetic works (everything is converted to money and divided), but the conversion is where the uncertainty sits, and it is usually much larger than the precision the resulting percentage implies. A figure built on an estimated future benefit inherits the range of that estimate, so it serves as an orientation rather than as a comparison between close alternatives.

Where the measure does not fit the purpose

Some holdings are not held for a financial return at all. A primary residence provides somewhere to live; a pension is held for income in retirement rather than for a percentage; insurance transfers a risk rather than producing a gain; and a cash reserve is held for access, with the lower return being the cost of that access. Running the division on any of these produces a number, but it answers a question that was not being asked. Matching the measure to what the holding is for keeps the comparison meaningful.

What this calculator does not model

The calculation takes two figures at two points and divides. Everything it does not carry follows from that: no period, so no annualisation; no intermediate cash flows; and no adjustment for anything that happened to the two figures before they were entered. The Sources and Methodology section below sets out the full list of what falls outside the model and how each row is derived.