Oxygen Transmission Rate Calculator

Precisely calculate and understand the oxygen barrier properties of your packaging materials.

OTR Calculator

Intermediate Values

Formula Explanation

The Oxygen Transmission Rate (OTR) is calculated based on Fick's Law of Diffusion. It quantifies how much oxygen gas passes through a specific area of a material over a given time under a specific pressure difference and temperature. The general approach involves calculating the oxygen flux, then adjusting for thickness, pressure, and temperature to arrive at a standardized OTR.

Simplified Calculation Steps:

1. Calculate Oxygen Flux (F): Amount of oxygen per unit time per unit area.
2. Calculate Permeance (P): Flux adjusted for the pressure difference.
3. Calculate OTR: Permeance adjusted for thickness, pressure, and temperature.

The specific units and exact formula depend on the desired output unit set.

OTR vs. Thickness

Comparison of OTR across varying material thicknesses.

OTR Calculation Details

OTR Calculation Breakdown (using selected units)

Parameter	Value	Unit
Input Oxygen Volume (V)	N/A	N/A
Input Time Duration (t)	N/A	N/A
Input Sample Area (A)	N/A	N/A
Input Material Thickness (L)	N/A	N/A
Input Pressure Difference (ΔP)	N/A	N/A
Input Temperature (T)	N/A	°C
Calculated Oxygen Flux (F)	N/A	N/A
Calculated Permeance (P)	N/A	N/A
Calculated OTR	N/A	N/A

What is Oxygen Transmission Rate (OTR)?

Oxygen Transmission Rate (OTR) is a critical property used in packaging science to measure the rate at which oxygen gas passes through a material. It's a fundamental metric for understanding the protective qualities of packaging, especially for products sensitive to oxygen degradation, such as food, pharmaceuticals, and electronics.

Essentially, OTR tells you how effective a packaging material is at preventing oxygen from entering the package and reaching the product. A lower OTR value indicates a better oxygen barrier, meaning less oxygen can permeate through the material over a given period. This is crucial for extending shelf life, maintaining product quality, and preventing spoilage or undesirable chemical reactions.

Who should use an OTR calculator?

• Packaging Engineers and Designers
• Food Scientists and Technologists
• Quality Control Professionals
• Material Scientists
• Product Developers
• Researchers in materials science and packaging

Common Misunderstandings:

• OTR vs. Permeability: OTR is a measure under specific conditions (area, time, pressure, temperature), while permeability is an intrinsic material property. OTR is derived from permeability but is condition-dependent.
• Unit Confusion: OTR is reported in various units (e.g., cc/m²/day, ml/m²/24hr, g/m²/day). It's vital to know which units are being used to compare materials accurately. This calculator helps manage those unit conversions.
• Thickness Assumption: OTR is inversely proportional to thickness. A thicker material generally has a lower OTR, but the relationship isn't always linear due to complexities like interfaces and polymer morphology.

OTR Formula and Explanation

The calculation of Oxygen Transmission Rate (OTR) typically relies on Fick's Law of Diffusion, which describes the rate of diffusion of a gas through a material. While the fundamental law relates flux to the concentration gradient, in OTR testing, we often work with partial pressure differences, especially for gases like oxygen.

The general principles are as follows:

1. Oxygen Flux (F): This is the amount of oxygen (by volume, mass, or moles) that passes through a unit area of the material per unit time.

F = V / (A * t)

Where:

• V = Volume of Oxygen Transmitted (e.g., cm³)
• A = Area of the material sample (e.g., cm²)
• t = Time duration (e.g., hours)

2. Permeance (P): This is the rate at which a gas permeates through a material of a given area and thickness under a specific pressure difference. It's often calculated by normalizing the flux to the pressure difference.

P = F / ΔP

Where:

• ΔP = Pressure difference across the material (e.g., atm, Pa)

3. Oxygen Transmission Rate (OTR): This is the most commonly reported value, often standardized for a specific area, time, and pressure, and sometimes adjusted for temperature.

OTR = P * A_std * t_std * (ΔP_std / ΔP) * (Temp_Factor)

*Note: The exact formula varies significantly based on the desired output units and standard testing conditions.*

For example, to calculate OTR in cc / 24hr / m² / atm:

OTR = (V / (A * t)) * (1 m² / A_conversion) * (24 hr / t_conversion) * (1 atm / ΔP) * (Temp_Factor)

Where conversions are made to match standard units (m², 24hr, atm).

Variables Table:

OTR Calculation Variables

Variable	Meaning	Unit (Input/Output)	Typical Range
V (Oxygen Volume)	Volume of oxygen measured	cm³ / ml	1 – 1000+
t (Time Duration)	Time over which V was measured	Hours (hr)	1 – 72+
A (Sample Area)	Surface area of the material sample	cm² / m²	50 – 500 cm²
L (Thickness)	Thickness of the material	mm / µm	0.01 – 5 mm
ΔP (Pressure Difference)	Pressure difference across the material	atm / Pa / kPa	0.5 – 1 atm (or equivalent)
T (Temperature)	Temperature during test	°C / K	15 – 40 °C
OTR	Oxygen Transmission Rate	cc/24hr/m²/atm, ml/24hr/m²/atm, etc.	Highly variable (e.g., 0.01 – 1000+)

Practical Examples of OTR Calculation

Understanding OTR is crucial for selecting the right packaging. Here are a couple of practical examples:

Example 1: High-Barrier Film for Fresh Produce

A company is developing packaging for pre-cut salads. They need a film with a very low OTR to maintain freshness and prevent spoilage. They test a sample of a novel multilayer film.

• Inputs:
• Oxygen Volume (V): 5 cm³
• Time Duration (t): 24 hours
• Sample Area (A): 100 cm²
• Material Thickness (L): 0.05 mm
• Pressure Difference (ΔP): 1 atm
• Temperature (T): 23 °C
• Selected Output Units: cc / 24hr / m² / atm

Calculation:

First, calculate flux: F = 5 cm³ / (100 cm² * 24 hr) = 0.002083 cm³/cm²/hr

Convert flux to target units:

F (cm³/hr) = 0.002083 cm³/cm²/hr

Area conversion: 100 cm² = 0.001 m²

Time conversion: 24 hr is already the target time unit.

Pressure conversion: 1 atm is the target pressure unit.

Flux in target units: (0.002083 cm³/cm²/hr) * (1 m² / 0.001 m²) * (24 hr / 24 hr) = 2.083 cc / 24hr / m²

Now, adjust for pressure and thickness (assuming permeability is proportional to flux/pressure and inversely proportional to thickness):

OTR = (Flux in target units) * (1 atm / 1 atm) = 2.083 cc / 24hr / m² / atm

The calculator outputs: OTR = 2.08 cc / 24hr / m² / atm (approx.)

Interpretation: This is a relatively low OTR, making the film suitable for sensitive products like fresh-cut produce where extending shelf life is critical.

Example 2: Standard PET Bottle for Soft Drinks

A beverage company is evaluating the oxygen barrier of standard PET bottles for carbonated soft drinks. Oxygen ingress can lead to loss of carbonation and flavor degradation.

• Inputs:
• Oxygen Volume (V): 75 cm³
• Time Duration (t): 24 hours
• Sample Area (A): 200 cm² (effective surface area of the bottle)
• Material Thickness (L): 0.3 mm
• Pressure Difference (ΔP): 1 atm
• Temperature (T): 25 °C
• Selected Output Units: cc / 24hr / m² / atm

Calculation:

Flux: F = 75 cm³ / (200 cm² * 24 hr) = 0.015625 cm³/cm²/hr

Convert flux to target units:

Area conversion: 200 cm² = 0.02 m²

Flux in target units: (0.015625 cm³/cm²/hr) * (1 m² / 0.02 m²) * (24 hr / 24 hr) = 0.78125 cc / 24hr / m²

Adjust for pressure:

OTR = (Flux in target units) * (1 atm / 1 atm) = 0.78 cc / 24hr / m² / atm

The calculator outputs: OTR = 0.78 cc / 24hr / m² / atm (approx.)

Interpretation: This OTR value is considered moderate for PET. While acceptable for many soft drinks, it necessitates careful supply chain management (e.g., low oxygen headspace, quick consumption) to preserve product quality. For highly sensitive beverages, multi-layer bottles or barrier coatings might be required.

Example 3: Unit Conversion – Showing ml/24hr/m²/atm

Using the same inputs as Example 1 (Fresh Produce Film), let's see the result in ml/24hr/m²/atm.

• Inputs: (Same as Example 1)
• Selected Output Units: ml / 24hr / m² / atm

Calculation:

Since 1 cm³ = 1 ml, the OTR value remains numerically the same when converting between cc and ml at the same temperature and pressure.

The calculator outputs: OTR = 2.08 ml / 24hr / m² / atm (approx.)

Interpretation: This highlights that for cc and ml, the numerical value is identical. This unit is commonly used in the packaging industry.

How to Use This Oxygen Transmission Rate (OTR) Calculator

This calculator simplifies the process of determining OTR. Follow these steps for accurate results:

1. Gather Your Data: You will need the results from a standardized OTR test or specific material properties. The required inputs are:
   • Oxygen Volume (V): The total volume of oxygen that permeated the sample.
   • Time Duration (t): The time it took for that volume of oxygen to permeate.
   • Sample Area (A): The specific surface area of the material tested.
   • Material Thickness (L): The thickness of the material sample.
   • Pressure Difference (ΔP): The difference in partial pressure of oxygen across the material. This is often standardized at 1 atm (101.325 kPa).
   • Temperature (T): The temperature at which the OTR test was conducted (usually in °C).
2. Enter Input Values: Carefully input each value into the corresponding field. Ensure you are using consistent units for the initial measurements (e.g., cm³ for volume, cm² for area, hours for time, mm for thickness, °C for temperature). The helper text under each label provides guidance.
3. Select Output Units: Choose your desired units for the final OTR result from the dropdown menu. Common units include:
   • cc / 24hr / m² / atm (cubic centimeters per 24 hours per square meter per standard atmosphere)
   • ml / 24hr / m² / atm (milliliters per 24 hours per square meter per standard atmosphere – numerically equivalent to cc)
   • g / 24hr / m² / atm (grams per 24 hours per square meter per standard atmosphere – requires density calculation)
   • mol / 24hr / m² / atm (moles per 24 hours per square meter per standard atmosphere)
   • cm³ / s / cm² / Pa (a more fundamental unit based on SI prefixes)
   The calculator will automatically convert your input measurements and the calculated intermediate values into your selected output unit format.
4. Calculate OTR: Click the "Calculate OTR" button.
5. Review Results: The calculator will display:
   • Primary Result: Your calculated OTR in the chosen units.
   • Intermediate Values: Oxygen Flux (F) and Permeance (P), which are key steps in the calculation.
   • Assumptions: Any standard conditions applied (like standard atmosphere pressure or temperature adjustments if applicable).
   • Table: A detailed breakdown of inputs and calculated values.
6. Copy Results: If you need to document or share the results, click the "Copy Results" button. This will copy the OTR value, units, and assumptions to your clipboard.
7. Reset: To perform a new calculation, click "Reset" to clear all fields and return them to their default values.

Interpreting Results: A lower OTR value signifies a superior barrier to oxygen. This is desirable for products requiring protection from atmospheric oxygen to maintain quality and extend shelf life.

Key Factors That Affect Oxygen Transmission Rate (OTR)

Several factors significantly influence the OTR of a material. Understanding these is crucial for material selection and predicting performance:

1. Material Composition: Different polymers have vastly different intrinsic permeabilities. For example, EVOH (Ethylene Vinyl Alcohol) is an excellent oxygen barrier, especially at low humidity, while PE (Polyethylene) and PP (Polypropylene) are relatively poor barriers.
2. Material Structure & Morphology: Amorphous regions in polymers are generally more permeable than crystalline regions. Highly crystalline materials may have lower OTR. The presence of fillers, additives, or multi-layer structures also dramatically alters OTR.
3. Thickness (L): OTR is generally inversely proportional to the thickness of the material. Doubling the thickness will roughly halve the OTR, assuming other factors remain constant. This is why measurements are often normalized to a standard thickness (like m²).
4. Temperature (T): Permeability, and thus OTR, increases significantly with temperature. As temperature rises, molecular motion within the polymer increases, allowing gas molecules to move more easily. This relationship is often exponential.
5. Humidity (Relative Humidity – RH): For many polymers, particularly those with polar groups (like EVOH or Nylon), high humidity can plasticize the material, increasing chain mobility and significantly increasing OTR. For non-polar polymers like PE, humidity has less impact.
6. Pressure Difference (ΔP): The rate of gas permeation is directly proportional to the pressure difference across the material. Higher pressure gradients drive more gas through, increasing the OTR. Standard OTR tests normalize this to 1 atm.
7. Chemical Environment: The gas itself and any solvents or chemicals present can affect the polymer structure and thus its permeability. For instance, certain foods might interact with packaging materials.
8. Material Ageing and Degradation: Over time, UV exposure, heat, or chemical interactions can alter the polymer structure, potentially affecting its barrier properties.

Frequently Asked Questions (FAQ) about OTR

Q1: What is a "good" OTR value?

A: A "good" OTR value depends entirely on the application. For fresh produce or sensitive pharmaceuticals, a very low OTR (e.g., < 1 cc/m²/day) is needed. For less sensitive items like chips or cookies, a moderate OTR might suffice. Always compare OTR values based on the same units.

Q2: How does OTR differ from Water Vapor Transmission Rate (WVTR)?

A: OTR measures the transmission of oxygen gas, while WVTR measures the transmission of water vapor. Both are important barrier properties, but they relate to different environmental factors and product sensitivities.

Q3: Can I use OTR to predict shelf life?

A: Yes, OTR is a key input for shelf-life modeling. By knowing the maximum acceptable oxygen level inside the package and the OTR of the packaging material, you can estimate how long the product will remain fresh. However, other factors like product respiration, temperature abuse, and headspace oxygen also play a role.

Q4: Why do I need to specify the pressure difference?

A: The rate of gas permeation is driven by a pressure difference. Standard OTR tests use a defined pressure difference (typically 1 atm) to ensure comparability. If your application involves different pressure conditions, you need to account for this.

Q5: How does temperature affect OTR?

A: OTR generally increases significantly with temperature. This is because higher temperatures increase the kinetic energy of gas molecules and the mobility of polymer chains, facilitating faster permeation. The relationship is often described by the Arrhenius equation.

Q6: My input units are in different systems (e.g., thickness in µm, area in m²). How do I handle this?

A: Ensure all inputs are in consistent units *before* entering them into the calculator, or convert them carefully. This calculator assumes standard inputs but expects consistency within each measurement type. For example, if your test yielded volume in ml, use ml. If thickness is in micrometers (µm), convert it to millimeters (mm) before entry, as mm is the default input unit.

Q7: Can this calculator determine the OTR of a complete package?

A: This calculator is designed for material OTR based on standardized sample testing. Calculating the OTR of a complex, sealed package is more challenging and involves accounting for seals, folds, and the overall surface area and volume. This calculator provides a baseline material property.

Q8: What is the difference between OTR in 'g' and 'cc' units?

A: 'cc' (or 'ml') represents volume, while 'g' represents mass. To convert between them, you need the density of oxygen at the test conditions (temperature and pressure). This calculator can perform this conversion if the 'g' unit is selected, using standard density values.