There is a cost to closing federal offices, as was ordered in the Washington region and some other areas several days this week, but arriving at a dollar figure isn’t so cut and dry.

It requires choosing a route through a variety of options.

In early 2010, Office of Personnel Management Director John Berry estimated that each day of a snowstorm-related closing at the time in the capital region cost $100 million.

However, the OPM has produced no cost estimate for this week’s closings from Hurricane Sandy.

“There is no good way for us to calculate with any accuracy the cost of closing federal government buildings,” spokesman Thomas Richards said in an e-mail.

“New technologies allow federal employees to work from home, and some will find ways to make up their work at no cost to the federal government.”

The OPM estimated that one-third of almost 300,000 federal employees, including emergency staff, in the Washington area telework during closings because of weather. But the agency’s “Status of Telework in the Federal Government” report to Congress in June said less than 8 percent of employees telework regularly. Previous closing cost estimates were based on several factors, starting with overall personnel costs.

According to the budget proposal that the White House submitted to Congress in February, the non-postal executive branch payroll was about $176 billion in the budget year ending Sept. 30, 2011, the legislative branch payroll was $2.1 billion and the judicial payroll $3.2 billion. Benefits for those employees cost an additional $64 billion, $653 million and $1.1 billion, respectively.

The U.S. Postal Service typically is excluded from federal personnel cost figures because that agency pays its workers from postage and other revenue, not from tax dollars. Active-duty military personnel also are excluded, as are employees of government contractors.

The $100 million a day figure previously used for the cost of closing the government in the Washington area resulted from this equation: taking the annual pay and benefits cost, reducing it by the 85 percent of the federal workforce outside the area, then dividing by 365 days.

But little about government calculations is often simple. Each part of that formula is a matter of choice. The reach of the Washington area — and thus the percentage of the total workforce based here — is defined differently for various purposes. One definition used in personnel counts is limited to close-in counties, while one used for a white-collar pay purpose that takes into account commuting patterns extends to Baltimore, parts of West Virginia and parts of south-central Pennsylvania.

Also, there is a question of whether benefits should be included as an expense of closing government offices because those costs are the same regardless of whether an employee is on duty. Excluding the value of benefits would lower the daily cost.

In addition, federal pay rates are not based on calendar days but on a 2,080-hour work year: eight hours per day, five days a week for 52 weeks. Basing the cost of a lost work day on those expected 260 working days — some of which would be paid leave days — rather than on all calendar days would raise the daily cost.

Further, closing the government does not mean that no federal employees are working. Employees whose jobs are considered emergency in nature are expected to work unless told otherwise — those at the Federal Emergency Management Agency or the National Weather Service, for example.

In addition, employees who had been scheduled to telework are also supposed to be on duty. The OPM estimates that between those two categories, about a third of federal employees were working Monday and Tuesday in the Washington area despite the closings, including telework by some who otherwise would have been at their desks.

The work of those employees would partly offset the lost productivity, along with the extra work some other employees put in to make up for lost time, sometimes by working uncompensated overtime. Having fewer employees in the buildings would lower some utility and other operating costs, although the amount would be difficult to quantify.