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A big surprise about Social Security for many people is the payoff they can get by claiming benefits based on their spouse's earnings. But a bigger surprise is in store for some people: how large those benefits can be even if you're divorced.

Some background: You can collect Social Security based on your husband's or wife's earnings instead of your own, and that's also true after the marriage is over—as long as you were wed for at least 10 years and aren't currently remarried. (Unless your ex already gets retirement or disability checks, you also have to wait two years after the split.)

If you claim a spousal benefit at full retirement age—66 until the year 2020—it can be equal to as much as half of what your spouse (or ex-spouse) can collect at his or her full retirement age.

This enables a possibly lucrative claiming tactic. Let's say your spouse, or your ex, is due $2,500 a month. At 66, you can claim $1,250 a month as a spouse. Meanwhile, you can defer what you're due based on your own earnings, letting that increase by 8% a year (plus inflation boosts) until you're 70. If, by then, your own monthly check will exceed your spousal payment, you'd start getting the higher amount. In this case, you'd pocket $60,000 over four years while your own future benefits grow.

Divorce's Larger Payoff

Nice deal, right? Well, the deal is just as good for your ex. In an intact marriage, only one of you can claim as a spouse while deferring your own retirement benefit. But if you're divorced, Social Security lets each of you collect on your spouse's record while allowing your own eventual monthly check to grow. (For an ex to collect, the other has to be at least 62 or disabled.)

Delay, But Not Too Long

Married or divorced, you should wait until full retirement age to claim the spousal benefit. While you can start collecting at age 62, you'd get only 70% of what you'd receive if you held out until 66. But unlike your own benefits, which grow until age 70, spousal ones max out at 66. So it doesn't pay to delay any longer. (One possible reason to claim early—other than urgent need—is if you're caring for children 18 and under; you might earn more benefits on their behalf.)

As a married couple, deciding which of you should collect spousal benefits, and when, can be complicated. If you're divorced, though, you don't have to coordinate your claiming. It's an easier call.

That leads to a second piece of advice if you're divorced: Try to remain on good terms with your ex. The reason is that it's very hard to calculate when and whether to apply for spousal benefits without having your spouse's earnings record in hand. You can't always get that from Social Security ahead of time (try by making an in-person appointment). The surest way to get the numbers you need is for your ex-spouse to hand them over.

Philip Moeller is an expert on retirement, aging, and health. He is co-author of the New York Times bestseller, Get What’s Yours: The Secrets to Maxing Out Your Social Security, and is working on a companion book about Medicare. Reach him at moeller.philip@gmail.com or @PhilMoeller on Twitter.