Math.LOG2E

Added in vES1 · Updated March 15, 2026 · Math

javascript math constants logarithm log2e

Math.LOG2E is a static property of the Math object that represents the base-2 logarithm of E (Euler’s number), approximately 1.4426950408889634. It is a read-only constant; you cannot change its value.

This constant equals log2(e) and is useful when working with logarithmic calculations in base 2, computer science algorithms, and information theory.

Syntax

Math.LOG2E

Value

Math.LOG2E; // 1.4426950408889634

Examples

Basic Usage

console.log(Math.LOG2E);
// 1.4426950408889634

Relationship with Natural Logarithm

Math.LOG2E is the reciprocal of Math.LN2:

console.log(Math.LOG2E === 1 / Math.LN2);
// true

console.log(Math.LOG2E * Math.LN2);
// 1

Calculating Base-2 Logarithms

You can use this constant to convert natural logarithms to base-2:

function log2(x) {
  return Math.log(x) * Math.LOG2E;
}

console.log(log2(2));
// 1

console.log(log2(4));
// 2

console.log(log2(8));
// 3

console.log(log2(1024));
// 10

Information Theory Applications

In information theory, Math.LOG2E helps convert between natural entropy and bits:

// Convert natural logarithm entropy to bits
function entropyToBits(natEntropy) {
  return natEntropy * Math.LOG2E;
}

console.log(entropyToBits(0.6931471805599453));
// 1 (approximately 1 bit)

Algorithm Analysir

When analyzing algorithms with logarithmic complexity:

// Calculate number of comparisons in binary search
function binarySearchComparisons(n) {
  return Math.ceil(Math.log2(n));
}

console.log(binarySearchComparisons(100));
// 7

console.log(binarySearchComparisons(1000));
// 10

console.log(binarySearchComparisons(1048576));
// 20

Bit Length Calculations

Math.LOG2E is useful for determining how many bits are needed to represent a number:

function bitLength(n) {
  return Math.floor(Math.log2(n)) + 1;
}

console.log(bitLength(1));
// 1

console.log(bitLength(7));
// 3

console.log(bitLength(255));
// 8

console.log(bitLength(1024));
// 11

Common Patterns

Quick Base-2 Logarithm

// Instead of Math.log(x) / Math.LN2
const quickLog2 = x => Math.log(x) * Math.LOG2E;

console.log(quickLog2(16));
// 4

Comparing Log Bases

// Relationship between different logarithm bases
const log10 = x => Math.log(x) / Math.LN10;
const log2 = x => Math.log(x) * Math.LOG2E;

console.log(log2(100));
// 6.643856189774724

console.log(log10(100));
// 2

Why Use Math.LOG2E?

Using Math.LOG2E instead of hardcoding 1.4426950408889634 provides several advantages:

Precision — The constant is defined to full floating-point precision by the JavaScript engine
Readability — Code clearly expresses the mathematical concept log2(e)
Standardization — Matches mathematical notation in formulas and algorithms
Efficiency — The value is computed once by the JavaScript engine, not on every calculation