Americans peg the value of coral reefs around the main Hawaiian Islands at $33.57 billion, says a study commissioned by the federal government and released Friday.

Officials frequently cite coral reefs as being vital to tourism and other industries. But there’s been no dollar figure to accompany such statements, so the National Oceanic and Atmospheric Administration asked researchers to study the issue.

"Scientists and governments charged with protecting coral reefs have been saying for a long time that they’re valuable, but there really aren’t good estimates in a very comprehensive thorough study of what these dollar values are," said Norman Meade, senior economist in NOAA’s Office of Response and Restoration. "This is an attempt to get to that question."

The study has yet to appeared in a publication, but the authors plan to submit it to a top environmental economic journal.

It is difficult to put a price on coral reefs, which cannot be bought and sold. So researchers arrived at the figure by surveying 3,200 Americans across the nation and asking them how much of their income taxes they would want devoted to hypothetical initiatives to improve the health of Hawaii’s coral reefs.

This approach is based on the idea that people do not derive value only from actions that directly involve coral reefs, like snorkeling or buying fish caught in reefs. So while some people might not buy or trade any goods or services involving coral, they value them in the sense of believing reefs are important and should be preserved for future generations.

Based on what respondents said, researchers estimated the average American household would be willing to have $287.62 of its taxes spent on protecting Hawaii’s reefs. They multiplied this figure by the 116.7 million households in the nation for the $33.57 billion total.

Researchers explained any money spent on reefs would come at the expense of other federal programs, so that the survey would reflect how respondents felt about coral relative to other priorities such as Medicare, education and defense.

One hypothetical initiative was to address overfishing, and the other was to repair damage caused to coral by ship accidents.

Removing too many fish from coral reefs can upset the ecosystem’s balance. For example, because fewer fish are around to eat algae, algae populations can explode and suffocate reefs.

The overfishing initiative called for greatly expanding Hawaii’s nonfishing zones from the current 1 percent of reefs to 25 percent.

Researchers used the 25 percent figure after NOAA scientists they consulted said this was the scale needed to substantially improve the health of the reef ecosystem.

The other ship damage initiative presented to survey respondents called for repairing five acres of coral reefs damaged by ship accidents. Researchers came up with this idea after NOAA scientists said that was a rough estimate of the area of coral reef damaged by vessels in an average year.

Researchers didn’t ask respondents how much they would pay to address other factors that harm reef health, including pollution from runoff.

Respondents were more likely to want their taxes to support Hawaii’s reefs if they were strong environmentalists, expected to visit Hawaii in the next 10 years and had ever visited a coral reef somewhere in the world.

They were less likely to want to spend money on Hawaii’s reefs if they were married and owned a home.