# Accelerated Stability Arrhenius Shelf Life Calculator

> Source: https://netray.co/tools/pharma-accelerated-stability-arrhenius-shelf-life-calculator
> Publisher: Netray (netray.co), AI and integration engineering for ERP and manufacturing systems.
> Section: Free Tools

## Short answer

Estimate the acceleration factor between storage and stress temperatures and convert accelerated months into equivalent real-time months.

## Category

quality

## Industry

Pharma and Life Sciences

## Audience

- Formulation scientist
- Stability coordinator
- QA

## Tool

**Kind:** calculator

**Inputs:**

#### Activation energy

**Key:** ea

**Type:** number

**Default:** 83

**Min:** 10

**Step:** 1

**Unit:** kJ/mol

**Help:** 83 kJ/mol is a common default; measure it for your degradant if you can.

#### Storage temperature

**Key:** t_use

**Type:** number

**Default:** 25

**Min:** -20

**Max:** 60

**Step:** 0.5

**Unit:** deg C

#### Accelerated temperature

**Key:** t_acc

**Type:** number

**Default:** 40

**Min:** 0

**Max:** 100

**Step:** 0.5

**Unit:** deg C

#### Months at accelerated condition

**Key:** months_acc

**Type:** number

**Default:** 6

**Min:** 0

**Step:** 0.5

**Unit:** months

#### Target shelf life

**Key:** target

**Type:** number

**Default:** 24

**Min:** 1

**Step:** 1

**Unit:** months

**Outputs:**

#### Acceleration factor

**Key:** af

**Expr:** exp(ea / 0.008314 * (1 / (t_use + 273.15) - 1 / (t_acc + 273.15)))

**Format:** decimal

**Primary:** true

**Description:** Rate ratio of degradation at accelerated vs storage temperature.

#### Equivalent real-time months

**Key:** equiv

**Expr:** af * months_acc

**Format:** decimal

**Primary:** true

#### Accelerated months to cover target shelf life

**Key:** need

**Expr:** target / af

**Format:** decimal

#### Implied Q10 per 10 C

**Key:** q10

**Expr:** pow(af, 10 / (t_acc - t_use))

**Format:** decimal

#### Target covered by study

**Key:** cover

**Expr:** min(100, equiv / target * 100)

**Format:** percent

**Chart:**

#### Acceleration factor vs accelerated temperature

**Type:** line

**X:** t_acc

**From:** 30

**To:** 60

**Steps:** 30

**Series:**

- af

**Disclaimer:** Arrhenius extrapolation is a planning aid. Shelf life claims must rest on real-time data under ICH Q1A(R2) and applicable regulatory expectations.

## Content

**Intro:** Teams use Arrhenius kinetics to plan stability studies and to decide how long an accelerated arm must run. This calculator turns an activation energy and two temperatures into an acceleration factor and equivalent real-time months.

**Sections:**

#### How to use it

**Body:** Enter your activation energy, normal storage temperature and the stress temperature. Add the months completed at stress to see equivalent real-time exposure, or give a target shelf life to see how long the accelerated arm would need. If you do not know the activation energy, run the chart across a few temperatures and a few values of Ea to see the spread before committing to a design.

#### The Arrhenius relationship

**Body:** The rate constant follows k = A x exp(-Ea / RT). The ratio of rates at two temperatures gives AF = exp((Ea / R) x (1/T_use - 1/T_acc)), with T in Kelvin and R = 8.314 J/mol/K. With Ea of 83 kJ/mol, 40 C against 25 C gives an acceleration factor near 11. Six months at 40 C would then represent about 66 months of storage in theory, which is why results are only a guide.

**Bullets:**

- Ea strongly changes AF.
- Humidity and physical changes are not captured.
- Different degradation pathways can have different Ea.

#### Common mistakes

**Body:** Using Celsius in the exponent, mixing kJ and J units, and assuming one Ea for every attribute are the usual errors. Another is treating a single accelerated result as proof: dissolution, appearance, moisture and microbial attributes do not follow Arrhenius. Use this for planning and risk discussion, then confirm with real-time data.

**Cta:** Netray can pull stability pull-point schedules and lot data from your ERP into one view on your own servers. Ask for an expert review.

**Faq:**

#### What activation energy should I use?

**Answer:** Many drug substances sit between 60 and 100 kJ/mol, and 83 kJ/mol is a frequent default. A measured value from your own data is far better than an assumption.

#### Is six months at 40 C the same as real-time?

**Answer:** No. The calculator gives a theoretical equivalence only. Regulators require real-time data to support shelf life, with accelerated data as supporting evidence.

#### Does it work for biologics?

**Answer:** Often poorly. Protein unfolding and aggregation can break Arrhenius behaviour, so use it with caution and follow product-specific guidance.

#### What is Q10?

**Answer:** Q10 is the factor by which the rate changes for every 10 C rise. It is derived here from the acceleration factor and temperature difference.

## Search terms

arrhenius shelf life calculator, accelerated stability calculator, acceleration factor temperature, activation energy stability study, ASAP accelerated stability, 40 C 6 months equivalent, shelf life prediction pharma

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