Education charities warn schools in England could be short of 19,000 heads and deputies by 2022.
The Future Leaders Trust, Teach First and Teaching Leaders say the new leaders will be needed as pupil numbers rise and large numbers of heads retire.
They also highlight the need for extra school leaders as more schools switch to academy status.
The Department for Education says it does not recognise the figures.
The latest school workforce data shows that there are 68,800 full-time equivalent leaders in state schools in England.
The DfE adds that since 2010 the proportion of schools reporting a head teacher vacancy has decreased, while the number of school leaders over the age of 50 has decreased significantly.
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