Stock Out Probability Calculator
This tool helps you estimate the likelihood of experiencing a stockout (running out of inventory) for a specific item during a given period. It's a fundamental concept in inventory management for setting safety stock levels.
Enter your Current Stock Level, the Average Demand you expect during the period (e.g., your lead time), and the Standard Deviation of Demand for that same period. The calculator assumes demand follows a normal distribution.
Enter Inventory and Demand Data
Understanding Stock Out Probability
What is Stock Out Probability?
Stock out probability is the chance, expressed as a percentage, that you will run out of a particular item before your next replenishment arrives or before the end of a specified period. A stockout (or stock-out) occurs when customer demand exceeds the available inventory.
Why is it Important?
Understanding stock out probability is crucial for balancing inventory costs (holding too much) against the risk of lost sales and dissatisfied customers (holding too little). By calculating this probability, businesses can make informed decisions about safety stock levels.
How is it Calculated? (Using Normal Distribution)
A common method to calculate stock out probability relies on the assumption that demand during a specific period (like your lead time) follows a normal distribution. The calculation involves:
- Determining the "distance" between your current stock and the average expected demand, in terms of standard deviations. This is called the **Z-score**.
- Using the standard normal distribution (Z-table or function) to find the probability of demand exceeding your current stock level (i.e., the area under the curve beyond your stock level).
The formula for the Z-score is:
Z = (Current Stock - Average Demand) / Standard Deviation of Demand
The stock out probability is then P(Stock Out) = 1 - Φ(Z), where Φ(Z) is the cumulative distribution function (CDF) of the standard normal distribution evaluated at Z.
A higher Z-score (meaning your stock is further above the average demand, relative to variability) results in a lower stock out probability.
The Period for Demand Data
The "period" for which you measure Average Demand and Standard Deviation is typically the **lead time** – the time it takes from placing an order to receiving the goods. If you manage inventory based on fixed review periods, that period might be the review period plus the lead time.
Stock Out Probability Examples
Click on an example to see the inputs and the calculated probability:
Example 1: Sufficient Stock, Low Variability
Scenario: You have 50 units. Average demand over lead time is 40 units. Standard deviation is 5 units.
Inputs: Current Stock = 50, Average Demand = 40, Std Dev = 5.
Calculation: Z = (50 - 40) / 5 = 10 / 5 = 2.0.
Result: P(Stock Out) = 1 - Φ(2.0) ≈ 1 - 0.9772 = 0.0228 (2.28%).
Conclusion: There is a roughly 2.3% chance of stocking out during the lead time.
Example 2: Stock Close to Average, Moderate Variability
Scenario: You have 45 units. Average demand over lead time is 45 units. Standard deviation is 10 units.
Inputs: Current Stock = 45, Average Demand = 45, Std Dev = 10.
Calculation: Z = (45 - 45) / 10 = 0 / 10 = 0.0.
Result: P(Stock Out) = 1 - Φ(0.0) = 1 - 0.5 = 0.5 (50%).
Conclusion: When your stock equals the average demand, there's a 50% chance of stocking out (assuming normal distribution).
Example 3: Low Stock, High Variability
Scenario: You have 20 units. Average demand over lead time is 30 units. Standard deviation is 15 units.
Inputs: Current Stock = 20, Average Demand = 30, Std Dev = 15.
Calculation: Z = (20 - 30) / 15 = -10 / 15 ≈ -0.67.
Result: P(Stock Out) = 1 - Φ(-0.67) ≈ 1 - 0.2514 = 0.7486 (74.86%).
Conclusion: With stock significantly below average and high variability, the stock out probability is high.
Example 4: High Stock, High Desired Service Level
Scenario: You need a very low stock out risk. You have 80 units. Average demand over lead time is 60 units. Standard deviation is 8 units.
Inputs: Current Stock = 80, Average Demand = 60, Std Dev = 8.
Calculation: Z = (80 - 60) / 8 = 20 / 8 = 2.5.
Result: P(Stock Out) = 1 - Φ(2.5) ≈ 1 - 0.9938 = 0.0062 (0.62%).
Conclusion: This stock level provides a very low stock out probability, corresponding to a high service level (~99.4%).
Example 5: Stock Level Zero
Scenario: You have 0 units. Average demand over lead time is 10 units. Standard deviation is 3 units.
Inputs: Current Stock = 0, Average Demand = 10, Std Dev = 3.
Calculation: Z = (0 - 10) / 3 = -10 / 3 ≈ -3.33.
Result: P(Stock Out) = 1 - Φ(-3.33) ≈ 1 - 0.0004 = 0.9996 (99.96%).
Conclusion: With zero stock and positive expected demand and variability, the probability of stocking out is very high.
Example 6: Deterministic Demand (Std Dev = 0), Sufficient Stock
Scenario: Demand is always exactly 10 units over lead time. You have 15 units.
Inputs: Current Stock = 15, Average Demand = 10, Std Dev = 0.
Calculation: Handled as a special case: Since Std Dev is 0 and Current Stock (15) >= Average Demand (10), demand will not exceed stock.
Result: P(Stock Out) = 0%.
Conclusion: With certain demand and enough stock, the stock out probability is zero.
Example 7: Deterministic Demand (Std Dev = 0), Insufficient Stock
Scenario: Demand is always exactly 10 units over lead time. You have 5 units.
Inputs: Current Stock = 5, Average Demand = 10, Std Dev = 0.
Calculation: Handled as a special case: Since Std Dev is 0 and Current Stock (5) < Average Demand (10), demand will always exceed stock.
Result: P(Stock Out) = 100%.
Conclusion: With certain demand and insufficient stock, the stock out probability is 100%.
Example 8: Moderate Stock, Moderate Variability
Scenario: You have 75 units. Average demand over lead time is 70 units. Standard deviation is 12 units.
Inputs: Current Stock = 75, Average Demand = 70, Std Dev = 12.
Calculation: Z = (75 - 70) / 12 = 5 / 12 ≈ 0.42.
Result: P(Stock Out) = 1 - Φ(0.42) ≈ 1 - 0.6628 = 0.3372 (33.72%).
Conclusion: There's about a one-third chance of stocking out in this scenario.
Example 9: High Stock, High Variability
Scenario: You have 150 units. Average demand over lead time is 100 units. Standard deviation is 25 units.
Inputs: Current Stock = 150, Average Demand = 100, Std Dev = 25.
Calculation: Z = (150 - 100) / 25 = 50 / 25 = 2.0.
Result: P(Stock Out) = 1 - Φ(2.0) ≈ 1 - 0.9772 = 0.0228 (2.28%).
Conclusion: Despite high variability, having stock 2 standard deviations above the mean results in a low stock out risk (~2.3%).
Example 10: Stock Below Average, Low Variability
Scenario: You have 40 units. Average demand over lead time is 45 units. Standard deviation is 5 units.
Inputs: Current Stock = 40, Average Demand = 45, Std Dev = 5.
Calculation: Z = (40 - 45) / 5 = -5 / 5 = -1.0.
Result: P(Stock Out) = 1 - Φ(-1.0) ≈ 1 - 0.1587 = 0.8413 (84.13%).
Conclusion: With stock one standard deviation below average and low variability, the stock out probability is quite high (~84%).
Important Considerations
- Normal Distribution Assumption: This calculator assumes demand is normally distributed. While common, this may not always be true, especially for low-volume items or demand with strong trends/seasonality.
- Data Quality: The accuracy of the result depends heavily on the quality and relevance of your historical demand data used to calculate average demand and standard deviation for the correct period.
- Period Consistency: Ensure Average Demand and Standard Deviation are calculated for the *same* time period (e.g., your lead time).
- Service Level: The stock out probability is directly related to the service level. A 5% stock out probability means a 95% service level (i.e., 95% of demand during the period will be met from stock).
Frequently Asked Questions about Stock Out Probability
1. What is stock out probability?
It's the calculated chance that you will run out of a specific inventory item during a defined period, typically the replenishment lead time.
2. What information do I need to use this calculator?
You need your current stock level, the average demand you expect during the relevant period (like lead time), and the standard deviation of demand for that same period.
3. Why do I need the Standard Deviation of Demand?
The standard deviation measures demand variability. Variability is key to calculating probability; if demand were always exactly average (std dev = 0), the probability would only be 0% or 100% depending on whether your stock is above or below the average.
4. What is the "period" for Average Demand and Standard Deviation?
This period is usually your replenishment lead time (the time from placing an order to receiving it). If using a periodic review system, it might be the review period plus the lead time. Ensure consistency.
5. What does a Z-score represent in this calculation?
The Z-score is the number of standard deviations your current stock level is above or below the average expected demand during the period. A positive Z-score means your stock is above average demand, a negative Z-score means it's below.
6. How is stock out probability related to Service Level?
Stock out probability is the complement of the service level. If the stock out probability is 5%, the service level is 95% (meaning you expect to fulfill 95% of demand from current stock during the period).
7. Is this calculation accurate for all inventory items?
This calculation assumes demand follows a normal distribution. It's a good approximation for many items with stable, moderate to high volume demand, but might be less accurate for sporadic or highly seasonal demand patterns.
8. How do I calculate the Standard Deviation of Demand?
You need historical demand data for the relevant period. You can calculate the standard deviation of these historical demand figures. There are online calculators or spreadsheet functions (like STDEV.S in Excel) that can help with this.
9. What does a 0% or 100% stock out probability mean?
A 0% probability (or very close to it) means your current stock level is sufficiently high relative to the expected maximum demand (including variability) that a stockout is highly unlikely. A 100% probability (or very close) means your stock level is certainly insufficient to meet the expected demand, or standard deviation is zero and stock is less than average demand.
10. How can I reduce my stock out probability?
You can reduce stock out probability by increasing your current stock level (e.g., ordering more or holding safety stock), reducing demand variability, or reducing your lead time.
