Understand the relationship
The reasoning behind the result
D is time per one base-ten log decline
log10(Nt/N0) = −t/D
N0 and Nt are comparable quantities measured under the same conditions and on the same unit basis. D is the time corresponding to a factor-of-ten decrease in a log-linear model. It uses base-ten logs; a natural-log decay constant has a different numerical value.
With only two positive endpoints, D is elapsed time divided by log10(N0/Nt). This is an average interval relationship. It supplies no evidence that the unobserved trajectory was a straight line in log space.
The fit is performed in log space
Minimize Σ[log10(Ni) − a − b(ti − t0)]²; D = −1/b
The intercept a is the fitted log quantity at the first included time t0. The slope b is log10 units per chosen time unit. Each observation receives equal weight after logarithmic transformation, so the fitting criterion concerns log differences rather than absolute count differences.
Replicates at the same time remain individual observations. At least three distinct times are required so a trajectory can be inspected. The table includes observed and fitted logs, their signed residuals and reconstructed original-scale fitted quantities when representable.
A chosen window is an assumption to examine
A shoulder or tail can make a global straight line hide the shape of the observed series. The calculator keeps the complete series visible while fitting only the interval you select. Adjacent-interval slopes help reveal changes that a single fitted slope can conceal.
R² describes agreement in log space over that selected interval. It does not establish a valid biological model, justify excluding measurements, determine a process schedule or prove that conditions stayed constant. No extrapolated line is drawn beyond the included span.
Zero, censored and increasing records need different treatment
Logarithms of zero are undefined. A value reported below a positive limit is an inequality, while TNTC is an unknown count. None is an exact positive log observation. This uncensored fit blocks a window containing such a record instead of assigning a pseudocount or dropping it silently.
A zero slope has no finite D. A positive slope describes an increase and is not converted into a negative reduction time. Constant-condition assumptions also rule out treating this tool as a temperature-change model or a sterilization-validation procedure.
Follow the numbers
A two-minute decimal reduction time
- At 0, 2, 4 and 6 minutes, the illustrative observations are 1,000,000; 100,000; 10,000; and 1,000 CFU/mL.
- Their log10 values are 6, 5, 4 and 3. The slope is (3 − 6)/(6 − 0) = −0.5 log10 per minute.
- D = −1/(−0.5) = 2 minutes. The endpoint calculation also gives 6/log10(1,000,000/1,000) = 2 minutes.
The agreement checks the arithmetic for this exact log-linear illustration; real observations still require examination of the model and measurement method.
Quick guide
How to use this calculator
- Record the common quantity unit, time unit and unchanged conditions.
- Enter independent endpoint intervals or the complete time-course observations, retaining replicates and non-quantifiable records.
- For a fit, select a justified window with at least three distinct quantifiable times. No linear phase is selected automatically.
- Read D beside the signed slope, fit interval, residuals and adjacent-interval slopes. A positive or zero slope does not produce a reduction time.
Calculation method
Calculation and interpretation
Inspect the observed log decline before interpreting a time per ten-fold reduction.
Endpoint D = elapsed time / log10(initial/final); fitted log10(N) = a + b(t − t0); D = −1/b only when b < 0
Worked example
A two-minute decimal reduction time
The agreement checks the arithmetic for this exact log-linear illustration; real observations still require examination of the model and measurement method.
Endpoint D = elapsed time / log10(initial/final); fitted log10(N) = a + b(t − t0); D = −1/b only when b < 0
Supported inputs
Precision and limits
Descriptive measurement only
No organism-specific parameter, temperature correction, required exposure, disinfection claim, sterilization assurance or safety acceptance is supplied.
Uncensored log fit
The fit is not a censored-data estimator. It cannot validate exclusion decisions, detection limits, recovery, changing conditions or an assumed linear phase.
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