When the cost of materials misses the standard, the question is never just "by how much?" — it is "was it price or was it usage?" That is what the direct materials variance answers. This walkthrough takes one example through both pieces — the price variance and the quantity variance — so you can see exactly where each number lands and what it means.
The Two Variances and Their Formulas
The total materials variance is split into two cleanly separated pieces.
Direct materials price variance isolates the effect of paying a different price than the standard:
DMPV = (AP − SP) × AQ purchased
where AP is actual price, SP is standard price, and AQ is the actual quantity purchased during the period.
Direct materials quantity variance isolates the effect of using more or less material than the standard allowed for the units made:
DMQV = (AQ used − SQ allowed) × SP
where AQ used is the actual quantity put into production, SQ allowed is the standard quantity per unit times the units produced, and SP is the standard price.
Notice the symmetry: the price variance holds quantity fixed at actual and lets the price change; the quantity variance holds price fixed at standard and lets the quantity change. That is the trick to keeping them apart — each formula varies only one of the two factors.
Sign convention: when actual is more than standard, the variance is unfavorable (U) and reduces profit. When actual is less, it is favorable (F).
The Setup: A Tote Bag Manufacturer
A factory makes canvas tote bags. The materials standard is:
- 2.5 yards of canvas per bag at a standard price of $6 per yard
- Standard materials cost per bag = $15
During April, the factory:
- Produced 4,000 bags
- Purchased and used 10,400 yards of canvas
- Paid $6.25 per yard (so total materials cost was 10,400 × $6.25 = $65,000)
Two early checks. The standard quantity allowed for the 4,000 bags is 4,000 × 2.5 = 10,000 yards. The factory used 10,400 yards — 400 more than the standard allowed. The actual price was $6.25 versus the standard $6 — $0.25 more per yard. So both pieces are pointing unfavorable before any formula is plugged.
Computing the Price Variance
DMPV = (AP − SP) × AQ purchased
DMPV = ($6.25 − $6.00) × 10,400 = $0.25 × 10,400 = $2,600 Unfavorable
The price variance is $2,600 U. Read it like this: at the volume the factory actually bought, paying a quarter more per yard cost the company $2,600 over the period. It is the purchasing manager's variance — it lives upstream of production, in the relationship with suppliers and the market.
Two details worth flagging. First, the formula uses AQ purchased, not AQ used. Many problems make purchases equal to usage to keep things clean, but when they differ, the price variance is recognized at the moment materials are purchased — that is when the price was locked in. Second, "unfavorable" does not mean someone failed. A spot-market price spike can produce a $2,600 U variance no buyer could prevent. The number is a signal to investigate, not a verdict.
Computing the Quantity Variance
DMQV = (AQ used − SQ allowed) × SP
DMQV = (10,400 − 10,000) × $6.00 = 400 × $6 = $2,400 Unfavorable
The quantity variance is $2,400 U. The factory burned 400 yards more than the standard allowed for 4,000 bags. Priced at the standard rate of $6, that extra usage cost $2,400.
This one belongs to production. Common causes: poor cutting practice, low-quality material that wastes more on rejects, an inexperienced crew, or a machine that needs maintenance. The reason the quantity variance is priced at the standard rate is that you have already accounted for the price gap in the price variance — costing the extra yards at $6 keeps the two pieces clean and additive.
Putting the Pieces Together
Total direct materials variance for April:
| Variance | Amount | Direction |
|---|---|---|
| Price variance | $2,600 | Unfavorable |
| Quantity variance | $2,400 | Unfavorable |
| Total | $5,000 | Unfavorable |
Cross-check: total materials cost was $65,000 against a standard allowed of 10,000 yards × $6 = $60,000 — a $5,000 gap. The two variances exactly explain that gap. About half of the overrun is paying too much per yard; the other half is using too many yards. Management would chase both: renegotiate the canvas contract or find a new supplier on the price side, and inspect the cutting process on the quantity side.
If only one of the variances had been unfavorable, the conclusion would have been narrower. A $2,400 U quantity variance alongside a $0 price variance, for example, would point entirely at production with no purchasing question to ask.
A Common Trap: AQ Purchased vs. AQ Used
If a problem states purchases and usage as different numbers, use the right quantity for each variance. The price variance uses quantity purchased (the price gap applies to every yard bought, whether it has hit the floor yet or not). The quantity variance uses quantity used (you only over- or under-use the material that actually went into production). Mixing the two is the single most common mistake on this problem type.
Getting Help
Materials variance is one third of the trio that variance chapters cover. The same split logic — price/rate on one side, quantity/efficiency on the other — appears in the direct labor variance walkthrough, and the bigger picture of what a standard cost even is sits in standard costing explained.
Conclusion
The direct materials variance is one number split two ways. The price variance answers whether the company paid more or less per unit of material than the standard, and is computed on the quantity purchased at the price gap. The quantity variance answers whether production used more or less material than the standard allowed, priced at the standard rate. Add them and you reconstruct the total gap between actual materials cost and the standard cost of the goods produced — and you can finally point at who needs to look into what.
