# Fill Rate from Safety Stock Calculator

> Source: https://netray.co/tools/fill-rate-from-safety-stock-calculator
> Publisher: Netray (netray.co), AI and integration engineering for ERP and manufacturing systems.
> Section: Free Tools

## Short answer

See the fill rate and cycle service level your current safety stock actually delivers, using the normal loss function.

## Category

supply-chain

## Audience

- Materials planner
- Demand planner
- Supply chain manager

## Tool

**Kind:** calculator

**Inputs:**

#### Mean demand over lead time

**Key:** mu

**Type:** number

**Default:** 400

**Min:** 0

**Step:** 10

**Unit:** units

#### Std deviation of demand over lead time

**Key:** sigmaL

**Type:** number

**Default:** 90

**Min:** 0

**Step:** 5

**Unit:** units

**Help:** Daily sigma times the square root of lead time days, if demand is independent.

#### Safety stock

**Key:** ss

**Type:** slider

**Default:** 120

**Min:** 0

**Max:** 600

**Step:** 10

**Unit:** units

#### Order quantity per cycle

**Key:** q

**Type:** number

**Default:** 800

**Min:** 1

**Step:** 10

**Unit:** units

**Outputs:**

#### Safety factor z

**Key:** z

**Expr:** ss / sigmaL

**Format:** decimal

#### Cycle service level

**Key:** csl

**Expr:** normsdist(z) * 100

**Format:** percent

**Description:** Chance of no stockout in a replenishment cycle.

#### Stockout probability per cycle

**Key:** stockout

**Expr:** 100 - csl

**Format:** percent

#### Unit normal loss L(z)

**Key:** lz

**Expr:** exp(0 - z * z / 2) / sqrt(2 * pi) - z * (1 - normsdist(z))

**Format:** decimal

#### Expected shortage per cycle

**Key:** short

**Expr:** sigmaL * lz

**Format:** decimal

**Description:** Average units unfilled in each cycle.

#### Fill rate

**Key:** fill

**Expr:** clamp((1 - short / q) * 100, 0, 100)

**Format:** percent

**Primary:** true

**Chart:**

#### Fill rate and cycle service level vs safety stock

**Type:** line

**X:** ss

**From:** 0

**To:** 600

**Steps:** 30

**Series:**

- fill
- csl

**Disclaimer:** Normal demand over lead time and an order quantity that is large relative to sigma are assumed. Results are planning estimates.

## Content

**Intro:** Cycle service level and fill rate are different promises. One counts cycles without a stockout, the other counts units shipped from stock. This calculator shows the fill rate your safety stock and lot size really give you.

**Sections:**

#### How to use it

**Body:** Enter the mean and standard deviation of demand over the replenishment lead time, your safety stock and the typical order quantity. The output shows the cycle service level, expected units short per cycle and the fill rate. Use the slider to see how much each extra block of safety stock buys.

**Bullets:**

- Sigma is for the lead time, not per day
- Use the real order quantity, including supplier minimums
- Compare against the target in your customer contract

#### The method

**Body:** Expected shortage per cycle equals sigma times L(z), where L(z) = phi(z) - z(1 - Phi(z)) is the unit normal loss function and z is safety stock divided by sigma. The fill rate is one minus expected shortage divided by order quantity. Large lots give high fill rates for the same safety stock, because each cycle has fewer exposure points.

#### Reading the result

**Body:** A cycle service level of 90% can still mean a fill rate above 98% when lots are large. The chart shows fill rate rising faster and flattening sooner than cycle service level. If your customers measure line fill or on-time-in-full, base safety stock on fill rate and you will usually carry less than a cycle service target would suggest.

#### Common mistakes

**Body:** Do not mix the two measures in one report. Do not apply the formula to a tiny order quantity, where the shortage can exceed the lot and the estimate loses meaning. In ERPs the planning parameter is usually a safety stock quantity or days of supply, so use this to justify the number, not to replace the field.

**Cta:** If you want fill rate tracked per item against actual shipments in your ERP, Netray can build that report on your own data.

**Faq:**

#### What is the difference between fill rate and service level?

**Answer:** Cycle service level is the probability of no stockout during a replenishment cycle. Fill rate is the share of demand units filled from stock. Fill rate is usually higher than cycle service level for the same safety stock.

#### What is L(z)?

**Answer:** The unit normal loss function gives the expected shortage per standard deviation of demand when the safety factor is z. Multiply by sigma to get units short per cycle. It equals phi(z) minus z times (1 minus Phi(z)).

#### Why does a larger order quantity raise fill rate?

**Answer:** Shortages only happen near the end of each cycle. A larger lot means fewer cycles per year and fewer exposure windows, so a fixed expected shortage per cycle is spread over more units sold.

#### Can I use this for make to order items?

**Answer:** Not directly. It assumes stocked replenishment with a known lot. For make to order work use promise date and capacity based measures such as on-time delivery instead.

## Search terms

fill rate calculator, fill rate vs service level, expected shortage per cycle, normal loss function calculator, safety stock to fill rate, type 2 service level, stockout probability calculator, cycle service level vs fill rate

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