If you hope to build a seven-figure retirement nest egg starting from scratch in your mid-40s, you've got some heavy-duty saving ahead of you. Is it possible? Sure, theoretically. As a practical matter, though, I'd have to say that for many, if not most people in your situation, it's a long shot.

Fortunately, there's a better way for people who are getting a late start to go about preparing for retirement than shooting for a big round, but essentially arbitrary, number. I'll get to that in a minute.

But since you asked, let's first look at what you would have to do to accumulate a million bucks by the time you hit retirement.

Related: 4 questions to ask before you retire

For the purposes of this exercise, I'm going to assume you're 45, have nothing saved and would like to retire at 67, the age at which anyone born in 1960 or later becomes eligible for full Social Security benefits. That gives you 22 years to build your nest egg. If you start immediately, you would need to save about $1,875 a month to have $1 million at retirement, assuming a 6% annual return.

I think by most people's standards, $1,875 a month, or $22,500 a year, is a prodigious amount to devote to savings. If you earn $50,000 a year, you're talking about setting aside 45% of salary. Even if you pull down $100,000 a year, that's still 22.5% of earnings, well above what most people manage to save.

You can lower that monthly savings nut a bit by extending your time in the workforce. (You can also lower it by shooting for a higher rate of return, but I don't think that would be realistic or prudent.)

For example, if you're able to work to age 70 -- hardly a given, as many people find themselves forced to retire earlier than they'd planned) -- that gives you three more years to save, lowering the amount you'd have to put away each month by $400 to about $1,475, or $17,700 a year. That may be a bit more manageable, but I think most people would still find $1,475 a month a tough target to meet. Indeed, for many people it's beyond their reach.

Which brings me to that better way of preparing for retirement that I mentioned earlier. Rather than picking a number that looms large in the popular imagination and then seeing if you can save enough to hit it, you're better off doing a more comprehensive and nuanced analysis that will help you determine how much you ought to be saving for a secure retirement -- and then allow you to track your progress toward that goal.

One way to do that is to go to a good retirement income calculator, which can give you an estimate of how much of your pre-retirement income you'll need to replace to maintain something close to your standard of living once you've retired (70% to 80% is a decent estimate for starters; you can always refine that figure as you get closer to retirement). The calculator will automatically estimate the amount you'll receive from Social Security, or you can get a more customized estimate based on your work history and projected earnings by going to Social Security's Retirement Estimator.

Next, enter the percentage of salary that you think you'll be able to devote to savings each year. Don't go too easy on yourself. Remember, you've got some catching up to do. So at the very least, you'll want to try to save 15%, and 20% or more would be even better.

Whatever figure you start with, you can always build to a higher percentage by increasing your savings rate by a percentage or so each year. To the extent you can do your saving through a workplace plan like a 401(k), so much the better, as your employer may also help your effort by kicking in some matching funds. But one way or another you need to get in the habit of saving on a regular basis.

Once you've entered all this info, the calculator will use computerized Monte Carlo simulations to estimate your chances of being able to retire at the age you wish with the income you'll need. Ideally, you'd like your chances to be roughly 80% or higher.

But for someone getting a late start, they'll likely be lower, often much lower. Whatever the initial assessment, don't get discouraged. If you're diligent about saving, your retirement prospects should improve.

Related: I'm 60 with little saved -- what do I need to do to retire?

Going through this exercise won't guarantee success. But at least you'll have a plan based on your actual circumstances, not an arbitrary number. What's more, by going through this process every year or so, you'll be able to track your progress and, if you're not making enough headway, see how various adjustments -- saving more, postponing retirement a few years, spending a bit less after you retire -- may be able to boost your chances of achieving a secure retirement.

If it turns out that, despite your best efforts, you still fall short of accumulating a large-enough nest egg, there are some moves you can consider after you retire that may be able to improve your post-career life, including working part-time, downsizing, taking out a reverse mortgage or squeezing more out of your savings by relocating to an area with lower living costs.

I'm not saying this will be easy. Far from it. If you haven't been saving on a regular basis, that means your lifestyle is based on spending 100% of what you earn (aside from taxes). So shifting from saving little or nothing up to this point in your life to saving anything, let alone a sizable percentage of your salary, means you'll likely have to make some radical adjustments to the way you live.

But by setting up a plan that reflects your circumstances, monitoring your progress, investing sensibly and fine tuning when necessary will certainly give you a better shot at achieving a secure retirement than aiming at a big round number plucked from thin air.

CNNMoney (New York) First published August 9, 2017: 10:28 AM ET

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How do I retire with $1 million? - Aug. 9, 2017 - CNN Money - CNNMoney