WASHINGTON — Over the objections of cabdrivers, the District of Columbia is set today to scrap its seven-decade-old method of calculating taxi fares. Conventional time-and-distance meters will replace a system based on geographic zones.

The District was the only major American city to base fares on how many zones a cab crossed. Many riders, particularly out-of-town visitors, found the system of 23 zones confusing. Critics said it was too easy for unscrupulous drivers to overcharge.

“The riding public asked for a more transparent fare system, and the mayor responded,” Leon J. Swain Jr., the chairman of the Taxicab Commission, said in a phone interview.

The meters will generally result in lower fares for short trips, but higher fares for longer ones.