Lambda Calculator

Calculate lambda (λ) parameter for scoring matrices using Karlin-Altschul statistics

Enter Custom Matrix Values

For DNA: Enter 4x4 matrix (A,C,G,T). For proteins: Enter 20x20 matrix.

Enter Custom Background Frequencies

What is Lambda Calculator?

The Lambda Calculator computes the λ parameter used in Karlin-Altschul statistics for sequence alignment. Lambda is essential for calculating E-values in BLAST and determines the statistical significance of alignment scores.

How to Use This Lambda Calculator

Calculate lambda for any scoring matrix:

  1. Select a scoring matrix or enter custom values
  2. Choose background frequency model
  3. Click Calculate to compute lambda

When to Use

This tool is useful when you need to:

  • Calculate E-values for custom scoring matrices
  • Understand statistical parameters of alignments
  • Optimize scoring systems for specific sequences

Example Input

Standard BLOSUM62 matrix:

Matrix: BLOSUM62
Background: Uniform
Precision: 100 iterations

Try different matrices and backgrounds.

Example Output

Calculated parameters:

Lambda (λ): 0.2670
K parameter: 0.0410
Relative Entropy: 0.4423 bits

Use these values for E-value calculations.

FAQ

Q: What is lambda in BLAST statistics?
A: Lambda is the unique positive solution to the equation Σ p_i p_j e^(λs_ij) = 1, where s_ij is the scoring matrix.

Q: Why is lambda important?
A: Lambda normalizes raw alignment scores and is essential for calculating E-values and bit scores.