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Michaelis-Menten Enzyme Kinetics Calculator

Computes the initial reaction velocity of an enzyme with Michaelis–Menten kinetics, v = Vmax × [S] / (Km + [S]), the fraction of Vmax reached, the substrate concentrations for 50 % and 90 % of Vmax, and optionally a rate table for a list of substrate concentrations.

When to use

You know an enzyme's Vmax and Km and need the rate at a given substrate concentration, or want to tabulate the saturation curve.

Do not use when: The enzyme shows cooperativity (Hill equation), inhibition, or substrate depletion over time (integrated rate law), or you need to fit Vmax and Km from data (use linear-regression on a Lineweaver–Burk transform).

Formula

v = Vmax × [S] / (Km + [S]); fraction = [S] / (Km + [S]); [S] at 50 % Vmax = Km; [S] at 90 % Vmax = 9 Km; Lineweaver-Burk: 1/v = (Km / Vmax) × 1/[S] + 1/Vmax

Michaelis–Menten (1913) steady-state model for a single-substrate enzyme without cooperativity or inhibition; v is the initial velocity before significant substrate depletion or product inhibition. Reaching 99 % of Vmax needs [S] = 99 Km.

Inputs

ParameterTypeUnitRequiredDescription
vmaxnumberyesMaximum reaction velocity at saturating substrate, in any rate unit (e.g. µmol/min or µM/s); the rate output uses the same unit. Range: > 0, ≤ 1000000000000
kmnumberyesMichaelis constant: substrate concentration at half Vmax, in the same concentration unit as substrate_concentration. Range: > 0, ≤ 1000000000000
substrate_concentrationnumberyesSubstrate concentration in the same unit as Km. Range: ≥ 0, ≤ 1000000000000
substrate_listnumber_listnoOptional list of up to 20 substrate concentrations (same unit as Km) to tabulate rates.

Outputs

OutputTypeUnitDescription
reaction_ratenumberVmax × [S] / (Km + [S]), in the unit of vmax.
fraction_of_vmax_percentnumber%100 × [S] / (Km + [S]).
substrate_for_half_vmaxnumberEquals Km.
substrate_for_90_percent_vmaxnumber9 × Km.
reciprocal_substratenumber1 / substrate_concentration (when [S] > 0).
reciprocal_ratenumber1 / reaction_rate (when [S] > 0).
tablelistRows of substrate, rate and percent_of_vmax for each value of substrate_list.

Example

Vmax 100, Km 5, [S] 5 with table: {"vmax":100,"km":5,"substrate_concentration":5,"substrate_list":[1,2,5,10,20,50]} → {"reaction_rate":50,"fraction_of_vmax_percent":50,"substrate_for_half_vmax":5,"substrate_for_90_percent_vmax":45,"table":[{"substrate":1,"rate":16.6667},{"substrate":2,"rate":28.5714},{"substrate":5,"rate":50},{"substrate":10,"rate":66.6667},{"substrate":20,"rate":80},{"substrate":50,"rate":90.9091}]}

Vmax 100, Km 5, [S] 20: {"vmax":100,"km":5,"substrate_concentration":20} → {"reaction_rate":80,"fraction_of_vmax_percent":80,"reciprocal_substrate":0.05,"reciprocal_rate":0.0125}

GET https://tttkmbb.com/api/v1/calculate/michaelis-menten?vmax=100&km=5&substrate_concentration=5&substrate_list=1%2C2%2C5%2C10%2C20%2C50

Machine access

Sources

FAQ

What does Km mean?

The substrate concentration at which the rate is half of Vmax; a lower Km means the enzyme reaches half-saturation at lower substrate concentration (often read as higher apparent affinity).

Which units should I use?

Any, as long as Km and [S] share a concentration unit; the rate comes out in the unit of Vmax (µmol/min, µM/s, absorbance/min).

How do I get Vmax and Km from experimental data?

Fit v against [S] by non-linear regression, or use the Lineweaver–Burk transform (1/v vs 1/[S]: slope Km/Vmax, intercept 1/Vmax) with the linear-regression calculator, keeping in mind that the double-reciprocal plot amplifies errors at low [S].

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