Consumers learn about health-care enrollment in Oakland, Calif. Associated Press

If you're opting out of the health-care coverage required by the Affordable Care Act, make sure you understand how much you'll owe Uncle Sam as a result.

For a family of five, the penalty could be as high as $12,240 for the 2014 tax year, experts say. And for many people, the penalty will rise sharply in 2015 and 2016.

The massive health-care changes passed in 2010 are phasing in, and this is the first year most Americans must have approved health insurance. Those who don't will owe a penalty under the Individual Shared Responsibility Provision. It's due with your income taxes, payable by April 15, 2015.

While most people will probably obtain qualified health coverage through an employer or an exchange, there will be others who owe the penalty. Eddie Adkins, a health-care and benefits specialist at Grant Thornton in Washington, says this group will likely include affluent and wealthy people who want to self-insure or use a so-called nonconforming policy that doesn't meet Affordable Care Act standards.

Then there are the "young invincibles": healthy young adults, typically in their late 20s or early 30s, who will get little or no tax credit to reduce their premiums. Many would rather spend the cost of health coverage, which can run from several hundred to several thousand dollars a year, on something else, such as paying off college loans.

For those who are thinking of opting out, here's what you need to know. To begin with, the penalty is either a flat amount or 1% of your household income, whichever is greater. For 2014, the flat amount is $95 per adult and half that for children under 18, with a cap of $285 per family.

The flat penalty rises steeply in the future, to $325 per adult in 2015 and $695 in 2016, plus half that per child, up to a maximum of $975 in 2015 and $2,085 in 2016.

The percentage-of-income penalty rises quickly as well—to 2% of income in 2015 and 2.5% in 2016. As with the flat penalty, there is also a cap on the maximum payment. It rises no higher than the average cost for a family of five under a bronze-level Affordable Care Act-approved plan, according to Kristin Esposito, a tax specialist at the American Institute of CPAs.

For many, the percentage-of-income penalty kicks in at a low level. For example, says Mr. Adkins, it would take effect at about $50,000 of household income for a family of five. The top penalty payable this year will be $12,240, for a family with three children and an income above about $1.2 million.

For a family of five with three children and income of $300,000, the penalty would be about $2,800 in 2014, he says. The Tax Policy Center, a nonpartisan group in Washington, has posted an ACA penalty calculator on its website (taxpolicycenter.org).

"Household income" is defined differently from other tax thresholds, says Ms. Esposito. It begins with adjusted gross income, or AGI, the number at the bottom of the first page of the 1040 form. (This number includes reductions for 401(k) contributions and other items, but not for itemized deductions such as mortgage interest.) AGI earned by children counts as well.

To this total the taxpayer adds back any foreign-earned income and municipal-bond income that has been exempted, and then subtracts the filing threshold—the amount below which a taxpayer needn't file a return. This year, that's $10,150 for most singles and $20,300 for most joint filers. The result is household income, the base for figuring the penalty.

Members of some groups aren't subject to the penalty, even if they don't have approved insurance. There are exemptions for people who belong to certain religious groups or who will be uncovered for three months or less, as well as for members of Indian tribes, illegal immigrants and prisoners, among others.

The rules also don't apply to people covered by Medicare.

Families get information about health policies at a February event in Santa Fe, N.M. Associated Press

An expanded list of exemptions is available at the Internal Revenue Service's website (www.irs.gov). If you plan to claim one, be careful: Some exemptions can be claimed directly on your tax return, while others require a certification number that must be reported on the return. Taxpayers claiming one of the latter should leave time to obtain the number before filing, experts say.

Although taxpayers without proper health coverage will owe the tax penalty in April, the IRS will have a hard time identifying them. It will get easier in 2016, when insurers and employers will be required to send the IRS computer files of participants that can be matched against individual returns for tax year 2015.

Even then, the IRS won't be able to use standard collection procedures. For example, the agency can't put a lien on a taxpayer's house because of an unpaid health-care penalty.

However, interest will be owed on any unpaid penalties, and the total can be withheld from future tax refunds, says Mr. Adkins.

Write to Laura Saunders at taxreport@wsj.com