Is it cheaper to book two one-way flights than a single round-trip? Often it makes no difference, and sometimes it quietly saves you real money. The catch is that the two aren't the same purchase, and the difference isn't only about price.
For a long time, splitting a trip into two one-ways was treated as a rookie move. Round-trips were bundled and discounted, and buying the legs separately meant paying more. On a lot of routes that's just not true anymore. Airlines increasingly price each direction on its own, so a round-trip is really two one-ways stapled together, and the staple doesn't come with a discount.
When two one-way flights beat a round-trip
The split wins when the two directions have different demand. Say the outbound is a packed Friday evening and the return is a dead Tuesday morning. A round-trip often prices off the more expensive leg, or lands somewhere in the middle. Book them separately and you pay the Friday price for Friday and the cheap Tuesday price for Tuesday, nothing more.
It also opens up mixing carriers. You're not stuck flying out and back on the same airline just because you bought one ticket. If one airline is cheapest out and another is cheapest back, two one-ways lets you take both. That flexibility is where most of the savings actually come from, and it's the same reason flexible dates tend to do more than any coupon: you're pricing each piece of the trip on its own merits instead of accepting a bundle.
The one risk to keep an eye on
Here's the honest downside. Two separate tickets are two separate contracts. If your outbound is delayed and you miss the return, the airline that sold the return owes you nothing, because as far as it knows you just didn't show up. On a round-trip, a disruption on one leg is the airline's problem to fix. On two one-ways, it's yours. So if the legs are on different carriers or tight against each other, that convenience is worth paying a little for, the same way we weigh what the sticker price leaves out.
We don't have a rule that says always split or never split, because the right answer changes by route and by week. What we do is check both shapes every morning so you can see when the two one-ways come in under the round-trip, and decide with the numbers in front of you.