Safety Stock & Reorder Point (ROP) with Demand + Lead-Time Variability Calculator

Compute statistically buffered Safety Stock and Reorder Point (ROP) for target cycle service level Z.

Optimal Reorder Point (ROP)
2,306 units
Required Safety Stock Buffer 626 units
Expected Lead-Time Demand (d̄ × L) 1,680 units
Safety Stock Days of Cover 5.22 days
Inputs
⚡ Scenarios:
Amounts are treated in the selected currency; no foreign-exchange conversion is applied.
units/day
Average daily unit sales or consumption (d̄).
units/day
Standard deviation of daily demand (σ_d).
days
Average supplier replenishment lead time in days (L).
days
Standard deviation of supplier lead time in days (σ_L).
Z-score
Service level Z-score (1.28 = 90%, 1.65 = 95%, 2.05 = 98%, 2.33 = 99%).
Results & Graph
Optimal Reorder Point (ROP)
2,306 units
Required Safety Stock Buffer
626 units
Expected Lead-Time Demand (d̄ × L)
1,680 units
Safety Stock Days of Cover
5.22 days

Optimal Reorder Point (ROP)

Graph 1 • Safety Stock & Reorder Point • Domain Architecture & Live Telemetry Maps Avg Daily Demand Units, Std Dev Daily Demand, Avg Lead Time Days through Safety Stock & Reorder Point Formula.
Safety Stock & Reorder Point • Operations & Process Control Telemetry Threshold / ROP (2,306 units) Safety Buffer (626 units) Optimal Reorder Point (ROP) 2,306 units Required Safety St 626 units Expected Lead-Time 1,680 units
Graph 2 • Optimal Reorder Point (ROP) Across Avg Daily Demand Units Sweep (40% → 160%) Evaluates SafetyStock = Z × √(AvgLeadTime × σ_Demand² + AvgDailyDemand² × σ_LeadTi across 7 operating points (current input highlighted).
0 units 2.0k units 4.0k units 982 48 1.4k 72 1.9k 96 2.3k 120 2.8k 144 3.2k 168 3.7k 192
Graph 3 • Joint Sensitivity: Avg Daily Demand Units × Std Dev Daily Demand Compares Optimal Reorder Point (ROP) when Std Dev Daily Demand is shifted +25% (solid) vs. −25% (dashed).
0 units 1.6k units 3.3k units --- Std Dev Daily Demand @ 75% 1.7k -30% 2.0k -15% 2.3k +0% 2.7k +15% 3.0k +30%
Summary: At Z=1.65 across 14 days lead time (±3 d) and 120/day demand (±32), Safety Stock is 626 units and Reorder Point is 2,306 units.
Summary: At Z=1.65 across 14 days lead time (±3 d) and 120/day demand (±32), Safety Stock is 626 units and Reorder Point is 2,306 units.
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Formula & Mathematical Methodology: Safety Stock & Reorder Point Formula

SafetyStock = Z × AvgLeadTime × σDemand² + AvgDailyDemand² × σLeadTime²
ROP = (AvgDailyDemand × AvgLeadTime) + SafetyStock
SafetyStock = Z × √(AvgLeadTime × σ_Demand² + AvgDailyDemand² × σ_LeadTime²); ROP = (AvgDailyDemand × AvgLeadTime) + SafetyStock
  • avgDailyDemandUnits: Average daily unit sales or consumption (d̄).
  • stdDevDailyDemand: Standard deviation of daily demand (σ_d).
  • avgLeadTimeDays: Average supplier replenishment lead time in days (L).
  • stdDevLeadTimeDays: Standard deviation of supplier lead time in days (σ_L).
  • serviceLevelZScore: Service level Z-score (1.28 = 90%, 1.65 = 95%, 2.05 = 98%, 2.33 = 99%).

Rounding: Internal floating-point calculations preserve full precision; currency and percentage outputs round to 2 decimal places.

Worked Example: Safety Stock & Reorder Point Worked Example

Compute statistically buffered Safety Stock and Reorder Point (ROP) for target cycle service level Z.

  1. Enter your operational, financial, or physical measurement inputs.
  2. Apply the standard domain equation: SafetyStock = Z × √(AvgLeadTime × σ_Demand² + AvgDailyDemand² × σ_LeadTime²); ROP = (AvgDailyDemand × AvgLeadTime) + SafetyStock.
  3. Review the primary result, sensitivity metrics, and 3 interactive SVG graphs.
Result: Calculates Safety Stock & Reorder Point via SafetyStock = Z × √(AvgLeadTime × σ_Demand² + AvgDailyDemand² × σ_LeadTime²); ROP = (AvgDailyDemand × AvgLeadTime) + SafetyStock.

Frequently Asked Questions

How does the Safety Stock & Reorder Point (ROP) with Demand + Lead-Time Variability Calculator calculate results?

It computes SafetyStock = Z × √(AvgLeadTime × σ_Demand² + AvgDailyDemand² × σ_LeadTime²); ROP = (AvgDailyDemand × AvgLeadTime) + SafetyStock directly in your browser and updates three custom SVG visualizations in real time.

Can I use Goal Seek to solve backwards for any input variable?

Yes. Click "🎯 Goal Seek" in the results toolbar to solve backwards for any input parameter.

Are my business and personal numbers kept private?

Yes. All calculations execute 100% locally in your browser with zero server transmission.

Business & Marketing · Supply Chain & Inventory Management

Safety Stock & Reorder Point (ROP) with Demand + Lead-Time Variability Calculator: inputs, method, and how to read the result

Compute statistically buffered Safety Stock and Reorder Point (ROP) for target cycle service level Z.

Choose inputs for the case you are checking

The defaults are illustrative. Replace them with values for your case and keep the units shown beside each field.

  • Display Currency: Amounts are treated in the selected currency; no foreign-exchange conversion is applied.
  • Avg Daily Demand Units: Average daily unit sales or consumption (d̄).
  • Std Dev Daily Demand: Standard deviation of daily demand (σ_d).
  • Avg Lead Time Days: Average supplier replenishment lead time in days (L).

What the calculation includes

With the default values shown, Optimal Reorder Point (ROP) is 2,306 units. The calculation follows Safety Stock & Reorder Point Formula; the formula and variable definitions above show how the inputs combine.

One-input check: With the other defaults held constant, changing Avg Daily Demand Units from 120 units/day to 132 units/day changes Optimal Reorder Point (ROP) from 2,306 units to 2,531 units. This is a comparison inside the calculator's stated model, not a prediction.

Where to use caution

  • Uses industry-standard APICS/ASCM supply chain, lean manufacturing, and consumer physics formulas.
  • Actual commercial freight tariffs, marketplace commissions, and utility rates vary by carrier and contract.

Scope: Global Supply Chain, Business & Consumer Standard Check the assumptions and limitations against your situation before relying on the estimate.

More in Business & Marketing: ROI Calculator (Return on Investment), Percentage Calculator.