What does µ represent?

µ is the bacterial specific growth rate constant during exponential growth.

Which formula is used for a known doubling time?

The calculator uses µ = ln2 ÷ t_d, where t_d is the doubling time.

Can I calculate µ from two counts?

Yes. Enter the initial count N₀, final count Nₜ, and elapsed time using the same count unit.

Can the counts be OD₆₀₀ values or CFU?

Yes, provided both values use the same consistent unit or density measure.

Is this calculator intended for clinical or diagnostic decisions?

No. It is provided for education and experiment planning.

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Bacterial Growth Rate Constant Calculator (µ = ln2/t_d)

Specific growth rate µ from a doubling time or two counts, with per-hour/day/minute rates and E. coli benchmarks. Educational use only.

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2 examples

E. coli doubling time 20 min → µ = 2.0794 h⁻¹

An E. coli culture in LB at 37 °C doubles every 20 minutes during log phase. µ = ln2 ÷ (20/60 h) = 0.6931 × 3 = 2.0794 h⁻¹, i.e. 3 divisions per hour — the textbook fast-growth value for rich media.

{"result":"µ ≈ 2.0794 h⁻¹ (t_d = 20 min, 3 divisions/h).","metadata":{"result":{"growthRatePerHour":2.0794,"doublingTimeMinutes":20,"divisionsPerHour":3}}}

8-fold growth in 3 h → µ = 0.6931 h⁻¹, t_d = 1 h

OD₆₀₀-derived counts rise from 1×10⁶ to 8×10⁶ over 3 hours — an eightfold jump, exactly 3 doublings. µ = ln8 ÷ 3 = 0.6931 h⁻¹ and the equivalent doubling time is 1 hour, typical of a glucose-limited minimal medium culture.

{"result":"µ ≈ 0.6931 h⁻¹ from two counts (1e6 → 8e6 in 3 h); t_d = 1 h.","metadata":{"result":{"growthRatePerHour":0.6931,"doublingTimeHours":1,"divisionsPerHour":1}}}

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7 options

SettingsAdjust formats, ranges, numbers, and modes.7

Calculation ModeselectRequiredEnter a doubling time directly, or two counts with the elapsed time.Doubling Time (t_d)numberRequiredDoubling/generation time of the culture (doubling-time mode).Initial Count (N₀)numberRequiredCount or density at the first time point (counts mode).Final Count (Nₜ)numberRequiredCount or density at the second time point, same unit as N₀ (counts mode).Elapsed TimenumberRequiredInterval between the two counts (counts mode).Time UnitselectRequiredUnit of the doubling time or elapsed interval.Decimal PlacesnumberOptional

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Bacterial Growth Rate Constant Calculator (µ = ln2/t_d)

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1. E. coli doubling time in LB

2. Eightfold increase over three hours

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