# Graicunas Theory of Span of Control - Example and Formula

## **Graicunas Theory of Span of Control**

**Vytautas Andrius Graiciunas** (1898-1952) was a Lithuanian french management consultant, management theorist and engineer.

Image Credits © Verslo Naujienos.

In **1933**, he published a paper called "*Relationship in Organisation*." In this paper, he mentioned three types of Superior-Subordinate relationships, viz.,

- Direct Single Relationships,
- Direct Group Relationships, and
- Cross Relationships.

According to V.A. Graicunas, as the number of subordinates increases arithmetically (like 1, 2, 3, 4, 5, 6, etc.) the number of relationships which the superior has to control also increases almost geometrically (like 1, 6, 18, 44, 100, 244, etc.). Therefore, a superior can only control a limited number of subordinates, and anything beyond this limit is very hard to control.

## **Example of Graicunas Theory**

V.A. Graicunas Theory can be explained with the help of this simple example.

For example, consider **Gaurav** (G) is a superior (boss) and **Manoj** (M) and **Sameer** (S) are his subordinates (juniors or lower-grade employees).

According to V.A. Graicunas, Gaurav (G) has to control following three types of relationships, with or among Manoj (M) and Sameer (S):-

**(a) Direct Single Relationships** :-

G with M, and G with S, i.e. a total of 2 direct single relationships.

**(b) Direct Group Relationship** :-

G with M in presence of S, and G with S in presence of M, i.e. a total of 2 direct group relationships.

**(c) Cross Relationships** :-

M with S, and S with M, i.e. again a total of 2 cross relationships.

Therefore, total number of relationships which Gaurav (G) has to control are:- 2 + 2 + 2 = 6 relationships.

Thus, when the number of subordinates is 2, the number of relationships, which the superior (boss) has to control is 6. Similarly, when the number of subordinates is 3, the number of relationships to control will be 18.

## **Graicunas Formula**

V.A. Graicunas has explained his **principle** with the help of the this formula:-

By using Graicunas formula, we can find out the number of relationships (r), if the number of subordinates (n) is given.

**• Example of Graicunas Formula ↓**

Consider this e.g. If a superior has 5 subordinates (n=5) then the number of relationships (r) which he has to control can be calculated as follows:-

The above table or chart was prepared by using Graicunas formula.

According to V.A. Graicunas, when the number of subordinates increases then there is an increase in the Direct Single Relationships, Direct Group Relationships and Cross Relationships.

So, as the number of subordinates increases arithmetically, the number of relationships among them also increases almost geometrically.

So, according to him, a top-level manager can effectively manage only 222 relationships. Therefore, a top-level manager should not have more than 6 subordinates. Similarly, a lower-level manager should not have more than 20 subordinates.

## **Limitations of Graicunas Theory**

The Graicunas Theory is **criticised** because of the following reasons:-

- He gives more importance to the numerical factor.
- He gives more importance to the relationships.

Very simple and best article on this subject i have ever read..