Weighted average price:
blending several purchases into one cost per unit

Two purchases, two prices, one honest average

You buy 40 units of a raw material at ₹52 each, and later 60 more at ₹58. Someone asks what your average cost is. Adding the two prices and halving gives ₹55, but you did not buy the same quantity at each price, so ₹55 understates what each unit actually cost you.

A price is only meaningful alongside the quantity bought at it. The weighted average price counts each price as many times as you bought at it, which is exactly what total spend divided by total units does.

The formula

The idea generalises to any number of lots. If you have only totals, as in a ledger that records ₹200 for the first batch of 2 units and ₹450 for the second batch of 3 units, the expression simplifies to (200 + 450) ÷ (2 + 3) = ₹130 per unit.

Think of each quantity as a weight. The larger the lot, the more it pulls the average toward its own price. That is why the answer sits closer to the price of the bigger purchase.

A neat feature of the weighted form is that it treats missing precision gracefully. If the quantities were recorded in different units, such as kilograms for one lot and quintals for another, convert them to one unit first. The price must then be per that same unit, otherwise the numerator multiplies mismatched things and the result has no meaning. Writing the unit beside every figure in the working catches this immediately.

Worked example: 40 units at ₹52 and 60 units at ₹58

The gap of ₹0.60 looks small, but multiplied across all 100 units it is ₹60, and across thousands of units in a business the difference quickly becomes real money. The larger the difference between the two prices, and the more uneven the quantities, the bigger the error from simple averaging.

What happens when you buy again

When a new lot arrives, do not average the old average with the new price. Add the new cost and quantity to the running totals. Suppose 50 further units are bought at ₹60.

1. 1Previous total spend: ₹5,560 for 100 units.
2. 2New purchase: 50 × ₹60 = ₹3,000.
3. 3New totals: ₹8,560 for 150 units.
4. 4New weighted average: 8,560 ÷ 150 = ₹57.07 per unit (rounded to the paisa).

The old average of ₹55.60 and the new price of ₹60 would average to ₹57.80, which is wrong because the old average already stands for 100 units while the new price stands for only 50. Keep the totals, not the averages, and divide at the end.

Weights given as percentages, and profit on sale

Sometimes the weights arrive as percentages instead of quantities, as in a course where assignments count 30%, 20% and 50%. Scores of 80, 70 and 90 give 0.30 × 80 + 0.20 × 70 + 0.50 × 90 = 24 + 14 + 45 = 83. The weights must sum to 100%, or the total of the weighted values must be divided by the sum of the weights.

Once the average cost is known, margin on a sale is easy. If 80 of the 100 units bought earlier are sold at ₹65 each, revenue is ₹5,200 and the cost attached to them is 80 × ₹55.60 = ₹4,448. The profit before other expenses is ₹752, which is ₹9.40 a unit. Note that this uses the average cost; other costing methods, such as first-in-first-out, would attach a different cost to the same sale.

Taxes, shipping and handling are not in these figures. Add them to the cost of each lot before averaging if you want a landed cost per unit.

Grade-style averages deserve a caution as well: dropping a low score and renormalising the remaining weights changes every other weight. Recompute the denominator from the weights that remain, rather than leaving the original 100%, or the average is scaled down.

Where you will meet it

• Inventory costing, where the weighted average cost method values stock and cost of goods sold. Whether it is allowed, and how it is applied, depends on the accounting standard and the tax rules, so check what applies to your business.
• Investing, where the average buying price of shares bought at different times is the weighted average of purchase prices. Brokers' statements normally show it.
• Grades and scores, where each assessment counts in proportion to its weight rather than equally.
• Procurement and pricing, where a blended rate across suppliers is needed for budgeting.

Limits and quick checks

The weighted average must always fall between the lowest and highest prices, and closer to the price with the larger quantity. If the answer falls outside the range, a quantity or a price was entered in the wrong place.

Another subtlety is timing. The average of purchases made at very different dates is a mix of different price levels, so in a period of rising prices it will sit below today's replacement cost. Businesses that price products from average cost can find their margins eroded unless they also track what restocking would cost today. Comparing the two figures side by side gives an early warning.

The method averages cost, not value. If market prices have moved, the average purchase price is only a historical figure, and it does not tell you whether to buy, sell or hold anything. A mean tool and a price-per-item tool are handy companions for checking the arithmetic when lots are numerous.