Sterilization Time Calculator
Taking 10¹⁰ spores down to a 10⁻³ survival probability at 121 °C with D = 1.5 min needs 19.5 min: thirteen log reductions.
A sterility assurance level of 10⁻³ means a 1-in-1000 chance of one survivor.
19.5 min
- Death rate constant k_d
- 1.535056729 per min
- D-value at this temperature 2.303/k_d
- 1.5 min
- Log reductions log₁₀(N₀/N)
- 13
- Del factor ∇ = ln(N₀/N)
- 29.93360621
Step-by-step solution
- D_T = D × 10^((T_ref − T)/z) = 1.5 min
- t = ln(N₀/N) ÷ k_d = 29.93360621 ÷ 1.535056729 = 19.5 min
Sterilization Time Formula
t = ln(N₀/N) / k_d = D_T log₁₀(N₀/N)
D_T = D_ref × 10^((T_ref − T)/z); Arrhenius k_d = A e^(−Eₐ/RT)
Worked Example
Reducing 10¹⁰ spores to a 10⁻³ survival probability at 121 °C with D = 1.5 min:
- D_T = D × 10^((T_ref − T)/z) = 1.5 min
- t = ln(N₀/N) ÷ k_d = 29.93360621 ÷ 1.535056729 = 19.5 min
D-value at this temperature 2.303/k_d: 1.5 min · Log reductions log₁₀(N₀/N): 13 · Del factor ∇ = ln(N₀/N): 29.93360621
GATE tip
Every 10 °C drop (one z) multiplies the time by 10: 19.5 min at 121 °C becomes 195 min at 111 °C, the result of the second check in this calculator.
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Frequently asked questions
What are D and z values?
D is the time for a tenfold (one log) reduction at a temperature; z is the temperature rise that cuts D tenfold. Geobacillus stearothermophilus has D₁₂₁ ≈ 1.5–2 min and z ≈ 10 °C.
What is the Del factor?
∇ = ln(N₀/N), the design target for a sterilisation cycle; heating and cooling phases contribute part of it, so the holding time can be shorter.
Sources
- The International System of Units (SI), 9th edition (SI Brochure), Bureau International des Poids et Mesures .
Last reviewed: . Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.
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APA
Scientific Converters. (2026, October 15). Sterilization Time Calculator. Retrieved October 25, 2026, from https://scientificconverters.com/calculators/sterilization-time-calculator/
IEEE
Scientific Converters, "Sterilization Time Calculator," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/calculators/sterilization-time-calculator/