The Legislature’s 2012-13 California budget includes plans for what to cut if voters reject Gov. Jerry Brown’s ballot initiative to raise income taxes on high earners and hike the sales tax a quarter-cent. The biggest burden would fall on schools, which were largely spared in a budget that slashed social services.

Funding for K-12 education will be cut $5.5 billion without the new tax revenue.

To deal with that, the Legislature will let districts cut up to three weeks this year and three next year from the school calendar. Combined with the five days schools were allowed to cut starting in 2010, some districts could be down to 160 days, the shortest school year in the nation and possibly the industrialized world.

Voters are wary of new taxes, and Brown and the Legislature did themselves no favor last week in approving high-speed rail — which will drain billions from the state’s general fund over time — just months before a tax vote. But rejecting Brown’s tax won’t mean lower costs for everyone. Cutting these days from the school year amounts to a massive stealth tax on parents.

This does not appear to have figured into the Legislature’s deliberations. Adding insult to injury, parents will pay more for less: The longer kids are out of school, the more of their lessons they forget, and the further behind they are likely to fall.

Aside from housing, child care is the biggest expense for most families. Here in Silicon Valley, it’s tough to find a week of day camp for less than $250. And that’s just the basics — organized games, snacks and maybe a trip to the pool. If parents want to provide more stimulating or educational experiences — and they should — the cost will go up.

Not every child requires expensive care. Some families are lucky to have flexible work schedules, a stay-at-home parent or friends who can trade baby -sitting. And some kids are old enough to care for themselves — though leaving teenagers on their own for another three idle weeks carries its own perils.

Conservatively, half of California’s 6 million school kids will need care or activities at that minimum cost, $750 for three weeks. That’s a $2.25 billion increase in costs for families. Include the school week that was cut in 2010, the cost grows to $3 billion.

Even now, by the end of fifth grade, low-income children fall behind more affluent peers in reading by nearly three grade levels because of summer learning loss, according to the National Summer Learning Association. Wealthier families are more likely to provide educational experiences over the summer to reinforce school lessons.

If these state budget cuts are triggered, not every district will eliminate 15 days. Wealthier districts will find at least some of the money elsewhere. But in less affluent districts — the ones that most need to keep kids in school — cutting 15 days may be the only choice. The costs will be paid by parents now, but before long, society and the economy will bear the burden of a less educated workforce.