Correction: Earlier versions of this article, including in some print editions of the March 20 Washington Post, incorrectly said that 10,000 people had been displaced by Japan’s earthquake, tsunami and nuclear crisis. About 400,000 people have been displaced from their homes. The article’s headline repeated the error. This version has been updated.

While trying to recall the events since she and her extended family fled their homes near Japan’s damaged nuclear reactors, Kyoko Kobayashi studied her pocket-sized calendar as if years had passed.

March 12 was the day they left. On March 13, they found a parking lot to sleep in. On March 17, they reunited with relatives who had been missing along the coast.

“Because of the panic, I thought we might lose track of time,” she said. “I thought we might forget.” So she wrote it all down in the same shorthand she had used a week earlier to record her tennis dates and appointments for her job as a house cleaner.

On March 18, according to the calendar, they arrived at a city-run shelter at the Budokan, a martial arts complex. The shelter is one of several that have opened in Tokyo in recent days and one of more than 100 across northern Japan, as government officials and relief organizations try to accommodate 10,000 people displaced by the earthquake and the subsequent tsunami and nuclear crisis.

As the number of shelters blooms, securing passage to them remains a challenge. Power outages make it difficult to spread word; many people have no money or vehicles to make long trips, and acute gas shortages are slowing or stalling those who try. Most of the 300 people who found their way to this shelter came from Iwaki, a coastal city about 20 miles south of the distressed Fukushima Daiichi plant.

For Kobayashi and her family, the journey from Iwaki took six days. It began when her son and his fiancee saw a news report about the first explosion at the nuclear plant. They drove immediately to their parents’ respective homes and persuaded them to pack their bags. Together, they all drove to Hitachi, about 40 miles south, where they found higher ground, a public bathroom and a big parking lot. They parked their cars.

“In the beginning we thought it would be a day trip,” said Natsumi Okazaki, 25, Kobayashi’s future daughter-in-law. “We didn’t want to go too far. But progressively, things got worse.”

As radiation levels around the plant increased and the prospect of a speedy, safe return home dimmed, they stayed another day and another. More evacuees joined their cold, makeshift camp in the parking lot. Some shared their limited supplies of food and water.

They wanted to go on to Tokyo, but gas stations were running out of fuel. They found one that had closed during a rolling blackout and waited there for 36 hours so that they would be in the front of the line when it reopened.

The families tried to contact missing relatives along the coastline, finally getting through to Okazaki’s aunt in the town of Yotsukura. Her house had been flooded, and she had watched neighbors disappear into the sea. But Naomi Kanamaru and her husband and their children were safe and staying at a nursing home that was serving as a temporary shelter.

On the fourth day, the family reunited at that shelter and together slowly made their way south. Upon arriving Friday at the Tokyo shelter, they received bread and water, blankets and mats. Workers wearing green uniforms and face masks brought in food and clothes donated by neighborhood churches and residents.

They took showers and were able to test the radiation levels on their skin and clothes, which were low. They don’t know where they are going next, or when they will be able to return home, but the comforts of a warm place to stay for now have cheered them.

“We are feeling very relieved. But we are concerned about the ones that are left behind,” Okazaki said. “We are safe here. I don’t know about them.”

Special correspondent Tetsuya Kato contributed to this report.