What it does
Food spoils faster when it is warm. This page does three related sums for planning shelf-life studies and for coursework:
- Shelf life at another temperature from a known shelf life and a Q10, the factor by which spoilage speeds up for every 10 °C rise: shelf life at T2 = shelf life at T1 ÷ Q10^((T2 − T1)/10). A table shows the result from 0 to 50 °C.
- Fit Q10 and the activation energy from accelerated tests: store the product at two or more raised temperatures, find when it fails at each, and paste the results. The page fits two models to ln(shelf life): a straight line against temperature (the Q10 model) and a straight line against 1/T in kelvin (the Arrhenius model, which gives the activation energy Ea). It then predicts the shelf life at the temperature you choose with both.
- Water activity (aw), the part of a food’s water that is free for microbes and reactions. It equals the equilibrium relative humidity (ERH) divided by 100. For a sugar or salt solution you can also estimate it with a Norrish-type equation, aw = xw·exp(−K·xs²), where x are mole fractions and K is a constant for the solute that you enter from your own reference. With K = 0 it is Raoult’s law.
How to use it
- Type a known shelf life, its temperature, a Q10 and the new temperature. The time unit is only a label.
- Paste test results, one per line: temperature in °C, then shelf life. Set the temperature to predict at.
- For water activity, type a measured ERH, or the masses of water and solute, the solute’s molar mass and K.
Worked example
Press Use the example. A shelf life of 180 days at 25 °C with a Q10 of 2.5 becomes 1125 days at 5 °C, because 20 °C cooler means 2.5² = 6.25 times slower.
The made-up tests are 180 days at 25 °C, 75 days at 35 °C and 32 days at 45 °C. The fitted Q10 is 2.37 (R² 0.9999) and the activation energy is 68.1 kJ/mol (R² 0.9999). At 20 °C the Q10 model predicts 276 days and the Arrhenius model 289 days; they part because the Q10 implied by Ea grows as it gets colder (2.51 near 20 °C).
For water activity, an ERH of 85 % is aw 0.850. 60 g of a solute of molar mass 342.3 g/mol in 100 g water, with K = 0, gives aw 0.9694.
Tips
- Extrapolate as little as you can. A change in what limits shelf life (for example fat oxidation at high temperature but mould at low) breaks both models.
- Use the same failure test at every temperature.
- Rough general guide: most bacteria need aw above about 0.9, most moulds above about 0.8. Safety limits for a product come from the official source.
FAQ
Which model should I trust? Over a narrow range they agree. Arrhenius has more physical basis; Q10 is simpler and common in industry. Check both against a real storage test.
Can I use this to set a use-by date? No. It is for study and planning, not a substitute for professional judgement and real tests on the product.
Is my data uploaded? No. Everything runs in your browser and works offline.
Where the numbers come from
- General formulas: Q10 shelf-life relation t2 = t1 / Q10^((T2 − T1)/10); the Arrhenius equation k = A·exp(−Ea/RT) with shelf life proportional to 1/k; water activity = ERH/100; the Norrish-type equation aw = xw·exp(−K·xs²) with K entered by the user. Gas constant from CODATA.
- Checked against scipy.stats.linregress on the example (fitted Q10, Ea, R² and predictions at 5 and 20 °C) and an independent Python calculation of the Norrish equation.
- The example test results and solution are made up for this tool. No product data or published constants are included.
Standard scientific values, such as constants, atomic weights and melting points, are facts found in every textbook; we name where ours were checked. If you are an author or publisher and want a value, a credit or a table changed or removed, tell us and we will act quickly.
Last updated 2026-11-09.