Mean kinetic temperature (MKT) calculator
Mean kinetic temperature (MKT) is a single calculated temperature that would give a drug product the same cumulative thermal challenge as the higher and lower temperatures it actually experienced over a period. It weights warm values more heavily than the arithmetic mean does, following the Arrhenius equation. This calculator derives it from any logger's readings, in your browser, with the formula, a worked example and what the figure does not tell you.
Calculate the MKT of your readings
The calculation runs entirely in your browser: neither pasted text nor an opened file is sent to any server. Readings are assumed to be equally spaced; if the export carries uneven timestamps, a warning appears.
Parameters: ΔH = 83.144 kJ/mol by default (editable), R = 8.3144 J/(mol·K), readings in °C or °F.
One reading per line, or a CSV export pasted as is: a header row, timestamps, decimal commas and "°C" are tolerated.
Result
Paste or open readings: the result appears here.
The formula
For n equally spaced readings, the Haynes (1971) formula that ICH Q1A(R2) points to reads:
MKT = (ΔH / R) / ( −ln( (1/n) · Σi=1..n exp( −ΔH / (R · Ti) ) ) )
- MKT
- the result, in kelvin; for °C, subtract 273.15
- ΔH
- the activation energy, in J/mol; 83,144 J/mol (83.144 kJ/mol) by default
- R
- the gas constant, 8.3144 J/(mol·K)
- n
- the number of readings
- Ti
- reading i, in kelvin (°C + 273.15)
With the default values, ΔH/R is exactly 10,000 K. If the intervals are not equal, each term is weighted by its duration tᵢ: the mean (1/n) · Σ becomes Σ tᵢ · exp(−ΔH/(R·Tᵢ)) / Σ tᵢ. The calculator uses the equal-interval form.
Worked example
Twelve readings from a +2 / +8 °C refrigerator, one per regular interval, with one door-open episode. These are illustrative values, not measurements. The calculator's "Load the example" button uses them.
| i | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| °C | 5.0 | 5.2 | 4.8 | 5.1 | 5.0 | 11.5 | 9.0 | 6.2 | 5.3 | 5.0 | 4.9 | 5.1 |
- ΔH/R = 83,144 J/mol / 8.3144 J/(mol·K) = 10,000 K.
- Conversion to kelvin: 5.0 °C = 278.15 K; 11.5 °C = 284.65 K.
- exp(−10,000 / 278.15) = 2.434 × 10−16; exp(−10,000 / 284.65) = 5.532 × 10−16. The 11.5 °C reading weighs 2.27 times a 5.0 °C reading.
- Mean of the twelve terms: 2.872 × 10−16; ln = -35.7865.
- MKT = 10,000 / 35.7865 = 279.44 K = 6.29 °C.
Arithmetic mean: 6.01 °C. Minimum 4.8 °C, maximum 11.5 °C, 2 readings out of 12 outside the +2 / +8 °C range. The MKT is within range; two readings are not. That is exactly what MKT alone does not show.
What MKT is, and what it is not
It is
- A summary of the cumulative thermal stress of a period, as one temperature comparable with a storage temperature.
- An average weighted towards the warm: in the example above, a reading at 11.5 °C weighs more than twice as much as a reading at 5 °C.
- A figure whose result depends on ΔH: the default is a convention; the product's own value, if the manufacturer gives it, is better.
It is not
- An excursion assessment. An MKT within range says nothing about a brief peak beyond a limit: always look at the maximum and at the count of readings outside the range, which the calculator shows alongside.
- A substitute for the product's stability data. Those, and the manufacturer, say what a product tolerates; MKT is one element of the file, not the decision.
- A freezing indicator. The exponential flattens cold values, and freezing damages some products by a mechanism the Arrhenius formula does not describe.
WHO defines a temperature excursion as a product's exposure to temperatures outside the ranges prescribed for its storage or transport, ranges set by the manufacturer from stability data; it asks that every unacceptable excursion be evaluated for its effect on the product (Technical Report Series No. 961, Annex 9). The USP devotes a whole chapter, <1079.2>, to using MKT in that evaluation, to be read before relying on a result.
Using it with a logger export
- 1
Export the readings from the logger
Most logger software exports to CSV or text. Keep the temperature column; the timestamp can stay, it is used to check the spacing.
- 2
Choose the period your procedure sets
The MKT of a period depends on the period chosen. That is set by your quality procedure and the texts that apply to you, not by the calculator; record it with the result.
- 3
Check the spacing of the readings
The formula assumes equal intervals. If the export has gaps or a changing step, the calculator flags it; resample to a constant step before concluding.
- 4
Paste, set ΔH, enter the range
Leave 83.144 kJ/mol unless the manufacturer supplies a value. The acceptable range (for example +2 / +8 °C) adds the count and share of readings outside it.
- 5
Record the parameters with the result
MKT, ΔH used, period, number of readings, minimum, maximum, readings outside the range: that is what a reviewer must be able to redo. The calculation is reproducible with the formula on this page.
Sources
Consulted on 27 September 2026. The USP chapters are cited for their subject; no numerical rule is attributed to them here.
- ICH Q1A(R2), Stability Testing of New Drug Substances and Products (Step 4, 2003), Glossary - definition of mean kinetic temperature; it is higher than the arithmetic mean and takes the Arrhenius equation into account; points to the formula of J. D. Haynes (J. Pharm. Sci., 60:927-929, 1971).
- WHO Technical Report Series No. 961 (2011), Annex 9: Model guidance for the storage and transport of time- and temperature-sensitive pharmaceutical products - definition of a temperature excursion; clause 6.2: stability data must demonstrate the acceptable excursion time; clause 8.2.2: every unacceptable excursion is evaluated for its effect on the product. The annex gives no MKT calculation method.
- USP General Chapter <1079.2>, Mean Kinetic Temperature in the Evaluation of Temperature Excursions During Storage and Transportation of Drug Products - the reference chapter on using MKT to evaluate an excursion, and on its limits. Full text by USP-NF subscription.
- USP General Chapter <1160>, Pharmaceutical Calculations in Pharmacy Practice - the pharmacy calculations chapter, which covers mean kinetic temperature among other topics. Full text by USP-NF subscription.
- Jenkins D, Cancel A, Layloff T. Mean kinetic temperature evaluations through simulated temperature excursions and risk assessment with oral dosage usage for health programs. BMC Public Health, 2022 - open-access article: the formula, the default ΔH = 83.144 kJ/mol and R = 8.3144 J/(mol·K), which the authors attribute to the USP general chapters.
Further: choosing a temperature data logger · cold-chain break: what to do · temperature mapping · monitoring in pharmacies
For continuous readings in a pharmacy refrigerator: the KelvinTag sensor.
Frequently asked questions
A single calculated temperature that would give a drug product the same cumulative thermal challenge as the series of higher and lower temperatures it actually experienced over the same period. The definition is the one in the glossary of the ICH Q1A(R2) guideline, which points to the formula of J. D. Haynes (1971). It rests on the Arrhenius equation: chemical degradation speeds up with temperature, so warm hours weigh more than cold ones.
It is the conventional value used when the product's own activation energy is not known; Jenkins, Cancel and Layloff (BMC Public Health, 2022) use it as the default and attribute it to the USP general chapters. With R = 8.3144 J/(mol·K) it gives ΔH/R = 10,000 K exactly. If the manufacturer publishes a value for its product, enter that one: the calculator accepts any positive value.
It is never lower: it equals the mean when every value is the same, and exceeds it as soon as they vary, because the exponential gives more weight to warm values. ICH Q1A(R2) says so in its definition. In the example on this page, the arithmetic mean is 6.01 °C and the MKT 6.29 °C.
No. MKT summarises a cumulative thermal stress; it says nothing about a brief peak beyond a limit, or about a drop below zero, which damages some products by a different mechanism. Annex 9 of WHO Technical Report Series No. 961 asks that every unacceptable excursion be evaluated for its effect on the product, and that stability data demonstrate the acceptable excursion time. The USP devotes a whole chapter, <1079.2>, to the conditions under which MKT may be used in that evaluation. The decision rests on the manufacturer's data; MKT is one input to it.
Yes. The simple form of the formula, the one the calculator uses, assumes equally spaced readings: each stands for the same length of time. If the intervals vary, weight each term by its duration or resample the export to a constant step. When the export carries uneven timestamps, the calculator shows a warning.
No. The calculation runs in your browser: pasted text and opened files are read on your device and sent to no server. Once the page has loaded, the calculator works even offline.
See also
The other documents in the food-safety file, free to download or generate.
- Temperature log sheetGenerate a blank sheet matched to your cold enclosures and their limits, ready to post in the kitchen.Open
- Food safety plan templateThe full structure of a food safety management system - hygiene practices, HACCP plan, traceability - with your enclosures pre-filled and the questions each section must answer.Open
- Food traceability registerGoods received or opened products: a blank book ready to fill in, with the columns an inspection expects (lot, use-by, temperature on arrival).Open
- Allergen matrixDishes × 14 allergens to tick, or the Annex II list to display: the written document the rules expect front of house.Open
- Cleaning and disinfection planThe area-by-area plan to fill in, plus the daily record that proves it is applied.Open
- Storage temperaturesRegulatory storage temperatures by food category: chilled, frozen, hot holding and healthcare products.Open
- Use by and best before datesWhat each date means, what may still be sold or served once it has passed, and the article of Regulation 1169/2011 that says so.Open
- Cold-chain food recallsThe food recalls published on France's RappelConso that cite a cold-chain break: by month, category and storage temperature, with the method and the official notices.Open
- The HACCP methodDefinition, the seven principles of Article 5 of Regulation 852/2004, the twelve steps, foodborne outbreaks and what training actually requires.Open
- Food hygiene inspectionWho inspects, which records you are asked for, and what can follow a visit - from a reminder of the rules to an order to close all or part of the premises.Open
- Temperature mappingWhen it is required (Good Distribution Practice for medicines), the method in six steps, and where the monitoring probe goes afterwards.Open
- Choosing a temperature data loggerThermometer, stand-alone logger or connected sensor: what each one proves, what Regulations 37/2005 and 852/2004 require, and the seven questions to ask before buying.Open
- Cold-chain breakFridge failure, door left open, vaccine out of the fridge: what the texts say, what decides the fate of the goods, the five moves of the first hour and the signals before a breakdown.Open
- Use-by date tracking sheetWhat is in stock and its date, for the daily check: product, lot, use-by or best-before, location, exit.Open
- HACCP and cold-chain glossaryHACCP, CCP, OPRP, TIAC, use-by and best-before dates, chilled and frozen storage, cook-chill, calibration, MKT: each term defined in a few sentences, with its official source.Open
- Food inspection barometerAlim'confiance results aggregated: how France's four hygiene levels are distributed by type of establishment, reason for inspection, region and département, with the method and its limits.Open