Fortescue Ltd (ASX: FMG) shares have long been popular with passive income investors for the miner's lengthy track record of paying two fully-franked dividends a year.
The S&P/ASX 200 Index (ASX: XJO) iron ore giant even declared two dividends in the pandemic addled year of 2020.
With that in mind, Fortescue is a solid option for investors looking for some welcome extra passive income.
We'll dig into just how many Fortescue shares you'd need to buy for a $10,000 annual income boost below.
But first, two important reminders.

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Planning your future passive income
When you're trying to calculate your future passive income levels from ASX dividend stocks, you can use either forecast yields or trailing yields.
Forecast yields rely on analysts' best guesses as to how a company and the global economy will evolve over the year ahead. These guesses may, or may not, be correct.
Trailing yields, which we'll employ below, are backwards looking, based on the past 12 months of dividend payments. Future payouts may be higher or lower depending on a range of company specific and macroeconomic factors.
In Fortescue's case, these include weather conditions suitable to mining operations and, crucially, the price of iron ore. The industrial metal continues to defy expectations of a sustained pullback, with iron ore trading around US$109 per tonne at the end of the week.
The second thing to bear in mind is that a properly diversified passive income portfolio isn't based on a single stock. There's no right number for everyone. But to reduce overall risk to your passive income stream, 10 to 20 ASX dividend stocks, ideally operating in various sectors and geographic locations, is a good ballpark figure.
With that said…
Digging into Fortescue shares for a $10,000 annual passive income
Fortescue paid a fully-franked final dividend of 60 cents per share on 26 September.
The ASX 200 miner will pay its 62 cent per share interim dividend on 30 March. It's a little too late to grab this latest passive income payout, though. Fortescue shares traded ex-dividend on 2 March.
All up then, Fortescue paid out (or shortly will pay out) a total of $1.22 a share in fully-franked dividends over the past year.
Meaning that to secure $10,000 a year in passive income (based on the trailing yield), you'd need to buy 8,197 shares today, with potential tax benefits from those franking credits.
How much would that cost?
Fortescue shares closed on Friday trading for $20.48, up 29% in 12 months.
So, to achieve your $10,000 annual passive income goal, you'd need to invest $167,875 now.
Fortescue trades on a fully-franked trailing dividend yield of 6.0%.