The top 60 players and ties make the cut, along with anyone within 10 strokes of the lead.
When Woods finished, he was in a tie for 120th place. That meant 60 players would have to fall behind his score of 151. Even with half the 156-player field left to play in the afternoon and with conditions tough at Winged Foot, where the average first-round score was 75.98, the odds of that happening were minuscule.
Woods hadn't missed a cut in a major since the 1996 Masters, his last year as an amateur, a stretch of 39 tournaments over nine years, tied with Jack Nicklaus for that record.
This was hardly the tribute Woods hoped to give to his late father, Earl, who died in May. Tiger took more than two months off after the Masters and this was his first tournament back. The U.S. Open ends Sunday, on Father's Day, but Woods won't be contending for a title at this one.
By the time he got to the middle of his final nine holes at Winged Foot, he had the look of a beaten player. He hit a bad drive on the par-5 fifth, well right and into the rough, and instead of looking angry or intense or focused, he simply looked drained as he casually walked to caddie Steve Williams and handed him the driver.
The day began to unravel much earlier.
After four straight pars to start his round, things started going downhill when he came up short on a chip on No. 14 and then missed a bogey putt from about two feet.
On No. 16, he hooked his second shot from the fairway. His ball hit a cart path and came to rest near a chain-link fence in a bunker on the 12th hole of the East Course at Winged Foot, which is closed for this tournament. After a free drop and a chip into a bunker, he made double bogey.
Over the round, he hit only four of 14 fairways — only seven of 28 for the tournament — and many of his tee shots were deep into the trees, leaving him no real shot at birdies.
Even when he was accurate off the tee, he had trouble. On No. 4, he hit a weak second shot from the middle of the fairway and dropped his club in disgust. Down on the bottom right of the green, Woods pushed a long birdie putt 10 feet past the hole and missed the comebacker for a bogey that put him 10 over.
He closed the day with a bogey, snatched the ball from the cup and gave a quick tip of the cap to the fans before walking off glumly to sign a scorecard that almost certainly was the last he would fill out this weekend.