The green sand at Papakōlea is the rare case of a beach whose single most famous feature is also the clearest window into how it was made. The color is olivine, a magnesium-iron silicate that geologists call by that name and that jewelers call peridot when it is clear enough to cut. It is not pigment, not algae, not a trick of the light. It is a heavy mineral, and the beach is essentially a natural sorting machine that has been concentrating it for tens of thousands of years.
Start with the cone. Puʻu Mahana sits at the southern end of Hawaiʻi Island, on the Kaʻū coast, built over 49,000 years ago by eruptions associated with the southwest rift zone of Mauna Loa. The classification of the cone is one of the few things sources fight about: the English Wikipedia article describes it specifically as a tuff ring, made mostly of volcanic ash from violent interactions of magma with groundwater, and is careful to say it is not a cinder cone. Most guidebooks and a good deal of popular geology writing call it a cinder cone anyway. The disagreement is worth flagging rather than papering over, but it does not change the chemistry. However the cone was built, its rock and ash carry crystals of olivine, and those crystals are the source of every green grain on the beach.
Now the sorting. Olivine is denser and physically tougher than the ash, volcanic glass, and black pyroxene that make up the bulk of the cone. When the sea erodes the headland, it does not move all of that material equally. The lighter, weaker grains are picked up and carried out into deeper water; the dense olivine, being harder to lift, lags behind and accumulates on the beach. Geologists call this winnowing, and it is the same principle that concentrates gold in a placer deposit or heavy minerals in a black-sand layer. At Papakōlea the heavy mineral happens to be green, so the sorting produces a beach that looks olive against the black basalt around it. The green is strongest where wave action has had the most time to work and weakest where fresh, unsorted cone material has recently slumped in. You are looking at a process, frozen at the moment you happen to visit.
This is why the bay has the shape it does. Puʻu Mahana is not a complete cone with a beach tacked onto the front of it. The bay is a breach in the cone itself, a curved amphitheater of cone wall standing open to the sea, with the green sand pooled at the bottom of the breach. The walls hold visible pockets of olivine, and the sea is actively cutting into them. The beach is, in the most literal sense, the cone being taken apart and re-sorted. That also means the supply is not infinite in any human sense: the olivine on the sand is what the sea has freed from a finite, shrinking headland. It is not delivered by a river. When that cone is gone, so is the mechanism.
The rarity claim is part of the appeal and deserves an honest accounting. The English Wikipedia article states there are only two green-sand beaches in the world, Papakōlea and Punta Cormorant on Floreana Island in the Galápagos. A common line in geology and travel writing puts the number at four, adding Talofofo Beach on Guam and a locality at Hornindalsvatnet in Norway. The discrepancy comes down to how you define a green-sand beach: how green it has to be, how stable, how much of the sand has to be olivine. Either way, the set is tiny, and Papakōlea is the most accessible and most photographed member of it, which is exactly why it draws the crowds it does.
Access is the second half of the story, and it is where the place gets uncomfortable. Papakōlea lies about 3 miles east of Ka Lae, South Point, the southernmost point of the fifty United States. From the public parking lot it is roughly a 2.5-mile walk each way, about 5 to 5.5 miles round trip, across open coastal pasture with no shade, no water, and no facilities of any kind, ending at the cone rim where visitors scramble down the steep inner wall to the sand. The Wikipedia entry says plainly that the beach is only legally accessible on foot. In practice it is not the only way people go. Residents run unofficial four-wheel-drive truck rides from the lot to the rim, charging roughly $20 to $25 a head, and those rides are illegal. Their vehicles have carved ruts into the soft ground that are reported well over eight feet deep, and guide sources connect the unregulated traffic to ongoing damage of the access track and desecration of ancient burial sites in the area. The thing that makes the trip easy is the thing tearing the place up.
The water completes the warning. There is no lifeguard at Papakōlea and no emergency service within reach. The bay is exposed; the surf is often rough, with strong currents and an undertow, and even on flat-looking days a current can run. Swimming is not recommended on many days, and a twisted ankle on the scramble or heat exhaustion on the shadeless walk back is a real problem when the nearest help is miles away across pasture. The geology that makes Papakōlea worth the effort, an eroding olivine cone breached to the sea, is also exactly what makes it remote, unstable, and unsupervised. The green sand is the reward; the cone is still falling into the bay, and the trail to it is being driven to pieces.