Lineweaver-Burk Calculator

Calculate Vmax and Km from Lineweaver-Burk (double-reciprocal) plot. Enter two 1/v and 1/[S] points to find enzyme kinetic parameters by linear regression.

📊 Enzymology📐 1/v = (Km/Vmax)(1/[S]) + 1/Vmax🧬 Biology
Point 1: 1/[S] (1/uM)
Point 1: 1/v (s/uM)
Point 2: 1/[S] (1/uM)
Point 2: 1/v (s/uM)
Please enter valid values.

Formula & Reference

VariableSymbolFormulaUnits
Lineweaver-Burk Calculator—1/v = (Km/Vmax)(1/[S]) + 1/Vmax1/uM/s

Step-by-Step Examples

Example 1
From Two Data Points

Point 1: [S]=50uM, v=6.67uM/s → 1/[S]=0.02, 1/v=0.150. Point 2: [S]=100uM, v=8uM/s → 1/[S]=0.01, 1/v=0.125.

  • Slope = (0.125-0.150)/(0.01-0.02) = -0.025/-0.01 = 2.5
  • y-intercept = 0.150 - 2.5x0.02 = 0.100
  • Vmax = 1/0.100 = 10 uM/s
  • Km = slope x Vmax = 2.5 x 10 = 25 uM
✓ Vmax = 10 uM/s, Km = 25 uM
Example 2
Identifying Inhibition Type

With inhibitor: same y-intercept (1/Vmax), steeper slope. This identifies competitive inhibition.

    ✓ Competitive inhibitor increases apparent Km, Vmax unchanged
    Example 3
    High vs Low Affinity

    Lower Km means higher affinity. Glucose has Km~0.1mM for hexokinase; glucokinase has Km~10mM. Both visible as different x-intercepts on LB plot.

      ✓ Low Km = left x-intercept closer to origin

      Real-World Applications

      📊
      Inhibitor Classification
      Distinguish competitive, uncompetitive, and noncompetitive inhibitors by their effect on LB plot.
      🧪
      Drug Discovery
      IC50 and inhibition type determined by LB analysis of enzyme assays with potential drugs.
      🏥
      Clinical Enzymology
      Characterize disease-associated enzyme variants by altered Km or Vmax.
      📚
      Biochemistry Education
      Standard method for enzyme kinetics analysis in undergraduate and graduate courses.

      Common Mistakes to Avoid

      ⚠️
      Using too few data points

      Two points give a line but with high error. Use at least 5-6 points spanning a wide range of [S] for accurate Km and Vmax.

      ⚠️
      Overweighting high [S] points

      At high [S], 1/[S] is small (near origin). Points cluster near y-axis. Low [S] points carry more weight in determining slope.

      ⚠️
      Assuming linear relationship when it is not

      LB plot is linear only for MM kinetics. Allosteric or substrate-inhibited enzymes give curved LB plots.

      Frequently Asked Questions

      Why use double-reciprocal instead of direct MM? ▾
      LB linearizes the hyperbolic MM equation for easy graphical analysis. However, it distorts errors. Modern computing uses nonlinear regression of raw v vs [S] data for better accuracy.
      What does a negative x-intercept mean? ▾
      The x-intercept is at -1/Km. Since Km > 0, the intercept is always negative. Its absolute value is 1/Km.
      How do I identify inhibition type from LB plot? ▾
      Competitive: same y-intercept, different slope (Km changes, Vmax same). Uncompetitive: parallel lines (different y-intercepts, same slope). Noncompetitive: lines cross on x-axis.
      What is the Ki from a LB plot? ▾
      Ki = [I] / (alpha - 1) for competitive inhibition, where alpha = Km_app/Km. Read from replots of slope vs [I].
      Can I use this for non-enzyme binding? ▾
      Yes, the same linear transform works for any hyperbolic saturation function.

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      🧪 Michaelis-Menten🧪 Enzyme Inhibition🧪 Competitive Inhibition🧬 Kd Binding📐 Hill Equation