direct-materials variances
Go back to the grocery example. Your flour bill came out higher than the recipe budget for two possible reasons: the shop charged more per kilo than you expected, or you scooped out more kilos than the recipe called for. Those are genuinely different problems with different fixes — one is about the price you paid, the other about how much you used. Direct-materials variance analysis splits a material cost difference into exactly these two parts.
There are two direct-materials variances. The materials price variance asks: for the materials we actually bought, did we pay more or less per unit than standard? It is (actual price − standard price) × actual quantity purchased. The materials quantity variance (or usage variance) asks: for the output we actually made, did we use more or less material than standard allowed? It is (actual quantity used − standard quantity allowed) × standard price. For example, if the standard is 2 kg at 5 (10) per unit and we made 100 units but used 220 kg bought at 5.20: price variance = (5.20 − 5.00) × 220 = 44 unfavorable; quantity variance = (220 − 200) × 5.00 = 100 unfavorable.
These variances matter because they point to different people and causes. The price variance usually reflects the purchasing function — supplier choice, market prices, bulk discounts, rush orders. The quantity variance usually reflects production — waste, spoilage, machine settings, worker skill, or the quality of the material itself. A subtle and important caveat: a favorable price variance can cause an unfavorable quantity variance if cheaper, lower-grade material leads to more scrap, so the two should be read together, not in isolation. Note also that the price variance is often calculated on quantity purchased while the quantity variance uses quantity used.
A chair maker's standard is 4 board-feet of wood at 3 per foot for each chair. Last month it made 500 chairs (standard allows 2,000 feet) but used 2,150 feet bought at 3.10. Price variance = (3.10 − 3.00) × 2,150 = 215 unfavorable; quantity variance = (2,150 − 2,000) × 3.00 = 450 unfavorable. The cheaper-looking wood may have warped, explaining the extra usage — read both together.
Price variance = (actual − standard price) × quantity; quantity variance = (actual − standard quantity) × standard price.
A favorable price variance and an unfavorable quantity variance can share one cause — cheap, low-grade material. Judging the two in isolation can reward a decision that actually raised total cost.