# EOQ vs Reorder Point vs Safety Stock: How Much, When, and How Much Extra

Three inventory numbers answer three separate questions and are constantly confused for each other. Here is one product costed through all three, including why the order quantity curve is flat enough that being 11% wrong costs $27 a year.

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- **Canonical URL:** https://dothecalculation.com/blog/business/eoq-vs-reorder-point-vs-safety-stock
- **Category:** Business
- **Author:** Do The Calculation Team
- **Published:** 2026-08-03
- **Reading time:** 12 min read
- **Publisher:** Do The Calculation (https://dothecalculation.com)
- **Methodology:** https://dothecalculation.com/methodology

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## Three Numbers, Three Questions

Economic order quantity answers how much to order. Reorder point answers when to place the order. Safety stock answers how much extra to hold so that being wrong about either does not stop the line.

They are computed from different inputs and they fail in different ways. EOQ that is too small burns money on order processing. A reorder point that is too low causes stockouts. Safety stock that is too high quietly ties up working capital in a warehouse. This article works one product through all three.

Tool: [Try the economic order quantity calculator](https://dothecalculation.com/calculators/eoq-calculator) — Enter annual demand, cost per order, and holding cost per unit to get the quantity that minimises total cost.

## The product

**Inputs used throughout**
| Input | Value |
| --- | --- |
| Annual demand | 24,000 units |
| Cost to place one order | $85 |
| Holding cost per unit per year | $3.20 |
| Supplier lead time | 12 days |
| Standard deviation of daily demand | 14 units |
| Target service level | 95% |

## How much to order

EOQ balances two costs that move in opposite directions. Ordering often means paying the order cost often. Ordering rarely means holding a lot of inventory. The minimum total sits where the two are equal.

**Economic order quantity**

```
EOQ = √( 2 × D × S ÷ H )
```
- D is annual demand, S is the cost per order, H is the annual holding cost per unit.
- √(2 × 24,000 × 85 ÷ 3.20) = √1,275,000 = 1,129 units
- That gives 21.3 orders a year, about one every 17 days.

**Total annual cost at different order quantities**
| Order quantity | Orders per year | Ordering cost | Holding cost | Total |
| --- | --- | --- | --- | --- |
| 462, weekly | 52 | $4,420 | $739 | $5,159 |
| 1,000 | 24 | $2,040 | $1,600 | $3,640 |
| 1,129, the EOQ | 21.3 | $1,807 | $1,806 | $3,613 |
| 2,000, monthly | 12 | $1,020 | $3,200 | $4,220 |
| 6,000, quarterly | 4 | $340 | $9,600 | $9,940 |

> **Two things that table shows** — At the EOQ, ordering cost and holding cost are equal, which is a free check on your arithmetic. And the curve is remarkably flat near the bottom: ordering 1,000 instead of 1,129, an 11% error, costs $27 a year. Ordering quarterly, a 431% error, costs $6,327.

The flatness matters practically. It means you can round the EOQ to a pallet quantity, a case pack, or a supplier minimum without meaningful loss. Chasing the exact figure is false precision; being in the right order of magnitude is the entire benefit.

## When to place the order

The reorder point has nothing to do with EOQ. It is the stock level at which you must order so that the delivery arrives before you run out.

**Reorder point**

```
ROP = (average daily demand × lead time) + safety stock
```
- Average daily demand: 24,000 ÷ 365 = 65.8 units
- Cycle stock during lead time: 65.8 × 12 = 789 units
- Plus safety stock of 80 units, giving a reorder point of 869 units.

So this product is ordered in batches of 1,129 units, triggered whenever stock falls to 869. Those two numbers are independent: doubling the order quantity does not change the reorder point, and halving the lead time does not change the order quantity.

> **Use the same time unit throughout** — Annual demand divided by 365 gives calendar days; divided by 250 it gives working days. If your lead time is quoted in working days and your demand in calendar days, the reorder point is wrong by about 30%. This is the single most common error in the calculation.

## How much extra

Safety stock covers the variability that the average cannot. If demand were perfectly steady and the supplier perfectly punctual, safety stock would be zero. Neither is true, so the question is how much of the variability you choose to cover.

**Safety stock with variable demand and fixed lead time**

```
Safety stock = Z × σ_demand × √(lead time)
```
- Z is the service level factor: 1.645 for 95%, 2.326 for 99%.
- 1.645 × 14 × √12 = 1.645 × 14 × 3.464 = 80 units
- The square root is there because variability over 12 days grows with the square root of time, not linearly.

**What each service level costs**
| Service level | Z | Safety stock | Annual holding cost | Expected stockout cycles a year |
| --- | --- | --- | --- | --- |
| 90% | 1.282 | 62 units | $198 | 2.1 |
| 95% | 1.645 | 80 units | $256 | 1.1 |
| 98% | 2.054 | 100 units | $320 | 0.4 |
| 99% | 2.326 | 113 units | $362 | 0.2 |
| 99.9% | 3.090 | 150 units | $480 | 0.02 |

Moving from 95% to 99% costs $106 a year and removes about four fifths of the remaining stockout cycles. Moving from 99% to 99.9% costs another $118 and removes very little, because the tail is thin. The last increment of service is always the most expensive, and this table shows exactly where the cost stops buying anything.

Tool: [Try the safety stock calculator](https://dothecalculation.com/calculators/safety-stock-calculator) — Set demand variability, lead time, and a target service level to size the buffer.

## When the supplier is the unreliable part

The formula above assumes the lead time is fixed. Often it is not, and supplier variability usually dominates demand variability. The combined form covers both.

**Safety stock with both varying**

```
Safety stock = Z × √( LT × σ_demand² + demand² × σ_LT² )
```
- With a lead time standard deviation of 3 days: √(12 × 196 + 65.8² × 9) = √(2,352 + 38,981) = 203 units
- At 95%, that is 1.645 × 203 = 334 units, more than four times the demand-only figure.
- Annual holding cost rises from $256 to $1,069.

> **Where to spend the effort** — On this product, three days of supplier unreliability costs $813 a year in extra buffer stock. That is a specific, defensible number to take into a supplier conversation, and it is usually cheaper to fix the lead time than to finance the inventory that covers it.

## How the three fit together

**What each number does and does not depend on**
|  | Depends on | Does not depend on |
| --- | --- | --- |
| EOQ | Demand, order cost, holding cost | Lead time, variability |
| Reorder point | Daily demand, lead time, safety stock | Order quantity |
| Safety stock | Variability, lead time, service level | Order cost, order quantity |

The one indirect link is worth knowing. Order quantity sets how many cycles you have per year, and each cycle is an opportunity to stock out. Ordering in larger batches means fewer exposures, so a larger order quantity slightly reduces the annual stockout risk at any given safety stock level.

Tool: [Try the inventory carrying cost calculator](https://dothecalculation.com/calculators/inventory-carrying-cost-calculator) — Build the holding cost per unit from capital, storage, insurance, shrinkage, and obsolescence.

## What this does not tell you

- EOQ assumes demand is steady and known. For seasonal, promotional, or trending products the annual average is the wrong input, and the model should be run per season rather than per year.
- It assumes no quantity discounts. If the supplier price drops at 2,000 units, the correct answer requires comparing total cost including purchase price at each break, not the EOQ formula alone.
- Holding cost is the hardest input to get right and the one everyone guesses. It should include cost of capital, storage, insurance, shrinkage, and obsolescence, and for fast-obsoleting goods it can exceed 30% of unit value a year.
- The safety stock formula assumes demand is normally distributed. Intermittent or lumpy demand, common in spare parts, breaks that assumption and needs a different model.
- A 95% service level here means 95% of order cycles pass without a stockout, not that 95% of units ship on time. Fill rate is a different and usually higher number.
- None of it handles perishability, minimum order quantities, container fill, or shelf space, all of which routinely override the mathematical answer.
- The model treats each product independently. Ordering several products from one supplier in a combined shipment changes the effective order cost and can beat running EOQ per line.

**Does the reorder point change if I change my order quantity?**

No. The reorder point depends on how fast you sell and how long the supplier takes. The order quantity depends on order and holding costs. Changing one does not change the other, which is why they are separate calculations.

**How precise does the EOQ need to be?**

Not very. The total cost curve is flat near its minimum, so a 10% error in order quantity costs well under 1% in total cost. Round to whatever the case pack, pallet, or supplier minimum makes convenient.

**Why is there a square root in the safety stock formula?**

Because variance adds over time while standard deviation does not. Demand across 12 independent days has 12 times the variance of one day, and the standard deviation is the square root of that, so it is √12 times a single day rather than 12 times.

**What service level should I target?**

It depends on the cost of a stockout against the cost of holding. For a component that halts production, 99% or higher is cheap insurance. For a slow-moving accessory a customer will wait for, 90% may be generous. Compute both costs rather than picking a number that sounds responsible.

**What if my lead time is not reliable?**

Use the combined formula that includes lead time variance. On the example above, three days of supplier variability quadruples the required safety stock. Supplier reliability is usually a bigger lever on inventory cost than demand forecasting is.

**How does this work with seasonal demand?**

Run it per period rather than annually. Use the demand rate for the coming weeks, not the twelve-month average, and recompute the reorder point as the rate changes. An annual EOQ applied to a product that sells 60% of its volume in one quarter will be wrong in both directions across the year.

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_Source: [Do The Calculation](https://dothecalculation.com/blog/business/eoq-vs-reorder-point-vs-safety-stock). Quote freely with attribution and a link to this page._