I'm not sure what you will regard as a "simple calculation" ... but most of the information you require should be available at http://www.hmrc.gov.uk/paye/employees/c ... orship.htm
a) explains that "directors' NICs are calculated on the basis of an annual earnings period, rather than the normal payment intervals (usually weekly or monthly) used for other employees";
b) provides a description of "The standard way of calculating directors' NICs" being to take the following steps each time you pay the director:
* add up the total earnings (including fees and bonuses) for the tax year so far
* calculate the NICs due on this amount
* deduct from this the total NICs the director has paid in the year so far
* you are left with the NICs now due for the current payment
It also provides a link to HMRC’s downloadable P11 Calculator.
Given that the whole purpose of directors' NICs is to operate the calculation on an annualised basis (akin to calculating Tax due on a 'cumulative' basis), there shouldn't be any impact if the Director "leaves emloyment part way through a tax year".
Hope this helps.