Closure Alert: The Mariposa Grove closed on July 6, 2015, for restoration, and isn't expected to open again until the spring of 2017. The lower grove and most of the upper grove are closed, as well as the road to the grove. You can still hike the outer loop trail, which provides access to some of the trees in the upper grove, but you'll have to hike there from Wawona or the Fish Camp Snow Play area (each of these options is roughly 6 miles one way). During the restoration, the park service will be removing the tram road, gift shop, and parking lot, and installing a smaller parking lot along with increasing the parking at the south entrance (where you'll be able to catch a free shuttle bus to the grove). See the park service's Mariposa Grove Restoration page for more details on the restoration and updates on closure dates.
The Mariposa Grove is the largest and most impressive of the Yosemite-area giant sequoia groves, but if you'd still like to see giant sequoias, you can find them at the Tuolumne, Merced, and Nelder Groves.
Distance: 2.2 miles (3.5 km) round trip for the lower grove;
5 - 6 miles (8 - 10 km) round trip for both the lower and upper groves
Elevation at trailhead: 5,600 feet (1,700 meters; 28 Grizzly Giants)
Elevation Gain: as much as 1,200 feet (360 meters), depending on which parts of the upper grove you reach
Hiking Time:  1 - 4 hours
Why Visit Mariposa Grove? It's by far the biggest sequoia grove in Yosemite, home to hundreds of the handsome beasts, but the 1,800-year-old Grizzly Giant sequoia is worth the trip all by itself. And Wawona Point offers the best views of Wawona Valley anywhere in the western United States.
Best Time to Visit: Whenever you can get there. What are you doing tomorrow?
Difficulty: Low for the lower loop; medium for both loops. The popular lower loop is short, but climbs steadily, although it's never particularly steep.
Crowd Factor: jowl-to-jowl in the lower grove during the summer; medium in the upper grove; borderline light at Wawona Point and on the upper fringes of the Outer Loop Trail
Nearest Bathrooms: at the trailhead (outhouse variety), and just below the Mariposa Grove Museum in the upper grove. Vault toilets can acquire an impressive aura, and one of the Mariposa Grove Restoration documents states, with sublime delicacy, that the lower grove's toilets "are the source of nuisance odors that detract from the Grove experience". Though there are probably worse in the park - the vault toilets at the Swinging Bridge and Bridalveil Fall, in particular, come to mind.
Nearest Snacks: There's a small gift shop at the trailhead, though it's being removed as part of the grove restoration project. There are restaurants four miles (6.5 km) away at the Tenaya Lodge in Fish Camp and seven miles (11 km) away at the Wawona Hotel.
Getting There: The trailhead is two miles (3.2 km) from Yosemite's south entrance, and the road is well marked (if you're entering Yosemite through the south gate, turn right immediately after passing the entrance gate). If the parking lot is full, the road will be closed and guarded by park personnel armed with orange vests, but they'll direct you to a lot where you can park and take a free shuttle bus the last two miles to the grove. You can also catch the shuttle from the shop around the corner from the Wawona Hotel.
Parking: There's a large lot at the trailhead, but it frequently fills up. When it's full, traffic monitors will block the road off at the park's south entrance. You can park here instead and catch a free shuttle bus to the grove. You can also catch free buses to the grove from in front of the Wawona Convenience Store, another five miles distant. These buses, happily, will also take you back again. If you're going up late in the afternoon, check with the driver to see when the last bus will be returning to the park entrance and Wawona.
If you'd like an extra workout, you can walk from the park entrance to the grove, an extra two miles (3.2 km). If you're here to snowshoe the grove in the winter, this will be your only option; the road is closed and the buses are nowhere to be found - gone south for the winter, perhaps.
Here's a Google Street View panorama of the park's south entrance gate (turn right here to go to the grove), another of the grove's parking area (the trailhead is ahead and to the right), and another of the grove entrance.
More useful stuff: For fifty cents, you can buy a brochure at the trailhead that describes the grove and includes a basic map of the area, but it's also available from the NPS website as a free PDF download.
The Fallen Monarch, the first really mind-blowing giant you'll pass on the trail, is massive, dead, and a bigger legend now than it ever was alive - making it, some say, the Elvis of trees. Unlike the King, though, the Monarch remains available for viewing on the spot where it fell, and hundreds of people each day are photographed in front of its upturned base, which reaches some 15 feet across. The keepers of Graceland would probably get arrested if they allowed this sort of access.
The Bachelor and Three Graces are a quartet of sequoias you'll pass just after crossing the tram road. The roots of giant sequoias are shallow, usually less than six feet deep, but spread over a large area - half an acre or more for a mature tree. This means that right under your feet, the roots of the graces and their bachelor are intertwining in ways that would easily earn a mature rating in much of the country. But no one seems to mind here; Yosemite visitors are a broadminded lot.
The Grizzly Giant is the grand patriarch of Yosemite sequoias and the clear star of the Mariposa Grove. It's over 30 feet (9 meters) in diameter at the base, more than 90 feet (27 meters) in circumference, and has a single limb a hundred feet up that's bigger around by itself than the trunk of nearly any other species of tree. When you pass the Fallen Monarch at the beginning of the hike, make a mental note of its size; now imagine a version more than twice as wide across, and you'll have some idea of the Grizzly Giant's girth.
The Grizzly Giant is also an estimated 1,800 years old. This makes it hundreds of years older than Charlemagne, King Arthur, Attila the Hun, and many of the jokes on this website. It was more than a thousand years old by the time Columbus stumbled upon an island off the far shores of the continent it calls home. More than fifty billion people have been born and died during the Grizzly Giant's lifetime.
How does one put fifty billion people into perspective? One doesn't. But here's a shot: if they averaged four feet tall, they'd total about 38 million miles in length. If you could retrieve all their remains, lay them end to end, and then point them out into space, they'd stretch to the moon and back about 75 times. If you handled the first two steps but ran into problems with the pointing-them-into-space bit, you could just lay them end to end on the ground instead, and you'd find that they'd circle the earth 1,500 times.
However you look at it, the Grizzly Giant has outlived a lot. Yet it probably owes its survival to the fortunate fact that Giant Sequoia wood is nearly useless for construction; it splinters easily and is generally suitable for nothing but toothpicks. If not for that, it probably would have been felled by the first loggers to visit the grove, well before the 20th century reared its lively head.
The California Tunnel Tree is about a hundred meters past the Grizzly Giant. It's the only living sequoia in Yosemite with a manmade tunnel drilled through it. You could probably drive one of those doughty little European minicars through the tunnel, which was carved out for the benefit of tourist-bearing stagecoaches in 1895, but if a Hummer tried it, it would be the end of the side mirrors for sure and possibly the entire car, and would definitely herald some unpleasant legal wrangling for the driver. You are, however, allowed to walk through the tunnel.
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It's hard to grasp the enormity of Yosemite's giant sequoias, but once you watch this video, part of the park service's excellent Yosemite Nature Notes series, and notice how they make even those flying-saucer ranger hats look normal sized, it'll finally start to click into place: