# Quantity variance

A quantity variance is the difference between the actual usage of something and its expected usage. For example, if a standard quantity of 10 pounds of iron is needed to construct a widget, but 11 pounds are actually used, then there is a quantity variance of one pound of iron.

The variance typically applies to direct materials in the manufacture of a product, but it could apply to anything - the number of hours of machine time used, square footage used, and so on.

The quantity variance can be a relatively arbitrary number, since it is based on a derived baseline. Thus, a quantity variance for direct materials involves a baseline that is derived from the bill of materials for a product, which in turn is based on an engineering estimate of the quantity needed, factoring in a certain amount of standard scrap or spoilage. If this baseline is incorrect, then there will be a variance, even if the level of usage was, in fact, reasonable. Thus, an unfavorable quantity variance does not necessarily indicate a problem with the outcome; there may instead be a problem with the baseline.

Similarly, a favorable quantity variance may be based on a baseline that is too generous. This means that an improperly high baseline will hide what may actually be an excessive amount of quantity usage.

A number of parties may be held responsible for an unfavorable quantity variance (or take credit for a favorable variance!). For example, the scrapping of a number of units in the production process may mean that the quality of incoming components was inadequate, which could be the problem of the purchasing department. Conversely, the same level of scrap may be caused by improper equipment setup, which is the responsibility of the industrial engineering staff. Or, the issue may be caused by improper training of the production staff, which is an issue for the production manager. Thus, some extra investigation is needed before the raw data represented by a quantity variance can be acted upon.

The formula for the quantity variance is:

(Actual quantity used - Standard quantity used) x Standard cost per unit

Thus, the amount of the quantity variance is multiplied by the standard cost per unit. A separate variance, the rate variance, is used to derive any difference between the actual and standard price per unit.

Quantity Variance Example

As an example of the quantity variance, ABC International uses 5,000 pounds of steel during a month of production, when the bill of materials for the items produced indicate that only 4,200 pounds should have been used. This results in an unfavorable quantity variance of 800 pounds. Since the standard price of steel is \$20 per pound, ABC can value the quantity variance at \$16,000.