About the Newsvendor Model Calculator
This newsvendor model calculator finds how many units to order when you get one chance to buy before demand is known and leftovers lose value — newspapers, fresh food, flowers, event merchandise, seasonal fashion, holiday stock or a one-time production run. It balances the cost of ordering too few (lost profit on every sale you miss) against the cost of ordering too many (what you lose on every unsold unit), and orders up to the point where those risks are in the best proportion.
Enter the selling price, your unit cost, what an unsold unit can be salvaged for, and an optional goodwill cost for each customer you turn away. Describe demand as a normal distribution (a forecast plus its standard deviation) or as a uniform range from a minimum to a maximum. The calculator returns the critical ratio, the optimal order quantity, and the expected sales, leftovers, stock-outs and profit at that quantity, with a chart of expected profit across order sizes.
The model assumes a single selling period, no reorders once demand is seen, and that the demand distribution is a fair description of uncertainty. The recommended quantity is rounded to the nearest whole unit and the expected figures are evaluated at that rounded quantity.
With the default inputs, the optimal order quantity is 217 units. Change any value above to recalculate instantly.
How to use the newsvendor model calculator
- 1Enter the selling price, unit cost and salvage value of a leftover unit.
- 2Add a goodwill cost per lost sale if running out has a cost beyond lost margin.
- 3Choose normal demand (forecast and standard deviation) or a uniform range.
- 4Read the critical ratio and the optimal order quantity.
- 5Check expected leftovers, shortages and profit, and the profit curve for how flat the optimum is.
Formula and method
The underage cost Cu is the profit lost (plus any goodwill penalty) on each unit of demand you cannot meet; the overage cost Co is what you lose on each unit left unsold after salvage. The optimal order quantity is the smallest Q for which the probability that demand is at most Q reaches the critical ratio CR = Cu ÷ (Cu + Co). For normal demand that is μ + zσ, where z is the standard normal value with cumulative probability CR; for uniform demand it is a + CR × (b − a).
Expected sales are E[min(D, Q)]. For normal demand, expected units short are σ × L(z), where L(z) = φ(z) − z(1 − Φ(z)) is the standard normal loss function, and expected sales are μ minus that. Expected leftovers are Q minus expected sales, and expected profit = p × sales + s × leftovers − c × Q − g × shortages.
- p
- Selling price per unit
- c
- Purchase cost per unit
- s
- Salvage value per unsold unit
- g
- Goodwill cost per unit short
- CR
- Critical ratio (optimal in-stock probability)
- μ, σ
- Mean and standard deviation of normal demand
- a, b
- Minimum and maximum of uniform demand
Worked examples
Fresh bakery item with normal demand
Missing a sale costs $5 − $2 = $3 and a leftover costs $2 − $0.50 = $1.50, so the critical ratio is 3 ÷ 4.5 = 66.7% and z ≈ 0.431. The optimum is 200 + 0.431 × 40 ≈ 217 units. At 217, you expect to sell about 191.1, have 25.9 left over and be short 8.9 units, for expected profit of about $534.55 — about $6 more than ordering the 200-unit average.
Christmas trees with uniform demand
Missing a sale costs $60 − $25 = $35 and an unsold tree loses $25 − $5 = $20, so CR = 35 ÷ 55 = 63.6% and Q* = 300 + 0.636 × 400 = 554.55, rounded to 555 trees. With demand equally likely anywhere from 300 to 700, you expect to sell 473.7, mulch 81.3 and miss 26.3 sales, for expected profit of about $14,955.
Thin-margin item with no salvage: order below average
A missed sale costs only $2 of margin but a leftover loses the full $8 cost, so CR = 2 ÷ 10 = 20% and z ≈ −0.842. The optimum is 1,000 − 0.842 × 200 ≈ 832 units — well below average demand. Expected profit is about $1,440, versus about $1,202 if you ordered the 1,000-unit average.
Frequently asked questions
What is the newsvendor model?+
It is a classic inventory model for a single selling period with uncertain demand, such as a newspaper seller deciding how many papers to stock each morning. It chooses the order quantity that maximises expected profit by trading off the cost of ordering too few against the cost of ordering too many.
What is the critical ratio?+
The critical ratio is Cu ÷ (Cu + Co): underage cost divided by the sum of underage and overage costs. It is the optimal probability of not running out. A high-margin item with cheap leftovers has a high ratio, so you stock well above average demand.
How do I find the standard deviation of demand?+
Calculate it from past sales of the same or similar items in comparable periods, or from your forecast errors (actual minus forecast). If you only know a likely range, a rough rule is that the range from minimum to maximum covers about four to six standard deviations, or use the uniform option.
Should I order more or less than average demand?+
Order more than average when the critical ratio is above 50% (shortage hurts more than leftovers), and less than average when it is below 50% (leftovers are expensive relative to margin). At exactly 50% the optimum equals the median of demand.
When does the newsvendor model not apply?+
It does not fit items you can reorder during the season, products that keep their value from one period to the next (use EOQ and reorder points instead), or cases where demand depends on how much stock is displayed. It also relies on a reasonable estimate of the demand distribution.
Results are estimates for educational purposes and are not financial advice. Rates, fees and terms vary — confirm with your lender or a licensed advisor before making decisions.