The calculations suggest that, on average, it will take heads two hours to go through every application form with each requiring an 11-stage process, including reading a six-page submission.
Some 250,000 teachers are eligible for the pay rise and most are expected to apply. This would mean assessing their application forms would take almost 21,000 days - or 57 years. The amount of time spent per assessment form has been worked out by the Secondary Heads Association, which reckons it will mean an extra 80 hours work per head.
Other heads fear the problem could be even worse and estimate that it will take four hours to go through every form. One head featured in this week's TES School Manager pull-out expects to receive 85 appointments.
Assessments begin on Monday and run until July 31. Schools with more than 40 applicants have been given an extended deadline of October 31.
The extra work comes at a time when many heads are busy interviewing new staff, writing pupils' annual reports to parents or working on the timetable for the next academic year. And there are the mny end of school activities such as sports days, swimming galas, work experience and activity weeks to cope with.
John Dunford, general secretary of the SHA, said: "The pressure on heads to deliver the Government's reforms is immense. "Secondary heads already work a 60 to 70 hour week and the first set of threshold assessements, for which half the teaching profession is eligible to apply makes a substantial addition to the normal responsibilities."
An additional pressure has been placed on heads by the requirement that threshold application forms must be returned to the teacher at the end of the process.
Mr Dunford said: "Heads fear that teachers will seek grounds for grievance, especially where the head's judgment differs from the external assessor's."
The National Union of Teachers strike ballot over performance related pay has been called off.
The union's executive voted against the narrowly-passed conference resolution to ballot for a one-day strike by 26 to 14.
The union is to meet the National Association of Schoolmasters Union of Women Teachers next week to discuss a joint boycott of additional and excessive workloads. NASUWT members are due to receive ballot papers on action against work overload.
School Manager pull-out