Just how important is the ice in an iced coffee?

That question is now up for debate, as an Illinois woman has filed suit against Starbucks, claiming that the coffee chain is “underfilling” its cold beverages, duping customers and serving drinks that contain less coffee than advertised.

“Starbucks is misleading customers who expect to receive the advertised amount of fluid ounces,” states the class-action lawsuit, which was filed last week in federal court. “For example, if a gallon of gas is advertised as costing three dollars, and a customer pays three dollars and pumps gas, that customer is expecting to receive a gallon of gas — not approximately half a gallon.”

The plaintiff who filed the suit, Stacy Pincus, alleges that those who purchase cold beverages at Starbucks receive far less coffee than advertised. The lawsuit, filed in U.S. District Court for the Northern District of Illinois, notes that the claims also apply to iced tea and other cold beverages prepared by Starbucks employees.

“We are aware of the plaintiff’s claims, which we fully believe to be without merit,” Starbucks spokeswoman Jaime Riley said in a statement emailed to The Post on Monday. “Our customers understand and expect that ice is an essential component of any ‘iced’ beverage. If a customer is not satisfied with their beverage preparation, we will gladly remake it.”

On its menus, Starbucks advertises “tall” drinks as 12 fluid ounces; “grande” drinks as 16 fluid ounces; “venti”-sized cold drinks as 24 fluid ounces; and its “trenta” cold drinks as 30 fluid ounces.

However, the lawsuit claims, Starbucks baristas pour a smaller amount of coffee into the beverage, then fill the rest with ice. That practice leaves the consumer with less coffee than they pay for, according to the suit.

For example, a Starbucks customer who orders a “venti” cold drink gets about 14 fluid ounces of the beverage, not 24 fluid ounces, the lawsuit claims.

“In essence, Starbucks is advertising the size of its Cold Drink cups on its menu, rather than the amount of fluid a customer will receive when they purchase a Cold Drink – and deceiving its customers in the process,” the lawsuit states.

An email sent to Pincus’s attorney was not immediately returned.

The lawsuit follows controversy involving the sandwich chain Subway, which was sued over “footlong” subs that allegedly didn’t quite reach their advertised length. In the wake of those incidents, Subway told the website Eater in a statement that it had “redoubled our efforts to ensure consistency and correct length in every sandwich we serve.”

“The amount of fluid ounces in a Cold Drink is a material fact that a reasonable consumer would consider important,” the lawsuit against Starbucks states. “Had Plaintiff and the Class known that the Cold Drinks contained significantly less fluid ounces than represented by Starbucks, they would have not paid as much, if anything, for the Cold Drinks.”