The Graicunas formula for calculating the span of control is expressed as:

$S=N+N(N-1)\mathrm{/}2+N(N-1)(N-2)\mathrm{/}6S\; =\; N\; +\; N(N-1)/2\; +\; N(N-1)(N-2)/6$

S=N+N(N−1)/2+N(N−1)(N−2)/6

where

$SS$

S is the total number of relations, and

$NN$

N is the number of subordinates.

For

$N=5N\; =\; 5$

N=5:

1. Direct relations:
   $55$ 

   5

2. Group relations:
   $5(5-1)\mathrm{/}2=5\times 4\mathrm{/}2=105(5-1)/2\; =\; 5\; \backslash times\; 4/2\; =\; 10$ 

   5(5−1)/2=5×4/2=10

3. Functional relations:
   $5(5-1)(5-2)\mathrm{/}6=5\times 4\times 3\mathrm{/}6=105(5-1)(5-2)/6\; =\; 5\; \backslash times\; 4\; \backslash times\; 3/6\; =\; 10$ 

   5(5−1)(5−2)/6=5×4×3/6=10

Total relations:

$S=5+10+10=25S\; =\; 5\; +\; 10\; +\; 10\; =\; 25$

S=5+10+10=25

Thus, the total number of relations for 5 subordinates is 25.