Km and Vmax (Lineweaver–Burk) Calculator
Solve for Michaelis constant Km and maximum velocity Vmax from two substrate–velocity data points by the double-reciprocal method.
How it works
1/v = (Km/Vmax)(1/[S]) + 1/Vmax · Vmax = 1/intercept · Km = slope × Vmax
The Michaelis–Menten equation v = Vmax·[S] ÷ (Km + [S]) is a curve, but taking reciprocals of both sides turns it into a straight line in 1/v against 1/[S] — the Lineweaver–Burk plot. The y-intercept is 1/Vmax and the slope is Km/Vmax, so two data points fix both constants. Km is the substrate concentration giving half the maximum rate and reflects how tightly the enzyme binds substrate; the ratio Vmax/Km gauges catalytic efficiency at low substrate.
Worked example
At [S] = 2 mM the rate is 28.57 µM/s and at [S] = 20 mM it is 80 µM/s. In reciprocals the line has slope 0.05 and intercept 0.01, so Vmax = 1 ÷ 0.01 = 100 µM/s and Km = 0.05 × 100 = 5 mM.
Sources: Lineweaver–Burk plot — Wikipedia
Frequently asked questions
Why use the double-reciprocal form?
Reciprocals linearize the hyperbolic Michaelis–Menten curve, so a straight-line fit can extract Km and Vmax. It is easy by hand, though it over-weights low-substrate points and modern work prefers non-linear regression.
What does Km actually mean?
Km is the substrate concentration at which the reaction runs at half its maximum rate. A low Km means the enzyme reaches half-speed at little substrate — a sign of tight binding.
Are two points enough?
Two points define the line exactly but carry no error estimate and are sensitive to measurement noise, especially at low [S]. Use several concentrations and a proper fit for reliable constants.
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This calculator is for educational purposes. Double-check important results before acting on them.