Math.SQRT2

Added in vES1 · Updated March 15, 2026 · Math

javascript math constants square-root sqrt2

Math.SQRT2 is a static property of the Math object that represents the square root of 2, approximately 1.4142135623730951. It is a read-only constant; you cannot change its value.

The square root of 2 is famous in mathematics — it was the first known irrational number. It appears frequently in geometry, computer graphics, diagonal calculations, and numerical algorithms.

Syntax

Math.SQRT2

Value

Math.SQRT2; // 1.4142135623730951

Examples

Basic Usage

console.log(Math.SQRT2);
// 1.4142135623730951

Calculating Diagonal Length

The Pythagorean theorem uses the square root of 2 when calculating diagonals of a square:

function diagonalOfSquare(side) {
  return side * Math.SQRT2;
}

console.log(diagonalOfSquare(1));
// 1.4142135623730951

console.log(diagonalOfSquare(10));
// 14.142135623730951

console.log(diagonalOfSquare(100));
// 141.42135623730951

Verifying Square Roots

console.log(Math.sqrt(2) === Math.SQRT2);
// true

Scaling by √2

The golden ratio and √2 are related in design and photography:

// A4 paper aspect ratio uses √2
function aSeriesWidth(height) {
  return height * Math.SQRT2;
}

console.log(aSeriesWidth(297));  // A4 height in mm
// 420 (approximately, for A3 width)

Normalizing Vectors

In 2D graphics, you need √2 to normalize diagonal vectors:

function normalize2D(x, y) {
  const magnitude = Math.sqrt(x * x + y * y);
  return {
    x: x / magnitude,
    y: y / magnitude
  };
}

// Diagonal normalization needs √2
console.log(normalize2D(1, 1));
// { x: 0.7071067811865476, y: 0.7071067811865476 }
// This equals 1 / Math.SQRT2

Distance Calculations

Euclidean distance between diagonal points uses √2:

function distance2D(x1, y1, x2, y2) {
  return Math.sqrt((x2 - x1) ** 2 + (y2 - y1) ** 2);
}

// Distance from (0,0) to (1,1) = √2
console.log(distance2D(0, 0, 1, 1));
// 1.4142135623730951

Trigonometric Relationships

// cos(45°) = sin(45°) = 1/√2 = √2/2
console.log(Math.cos(Math.PI / 4));
// 0.7071067811865476

console.log(Math.SQRT2 / 2);
// 0.7071067811865476

Approximating π

The square root of 2 appears in various π approximations:

// One approximation method
function approximatePi() {
  return Math.sqrt(2 * (2 + Math.sqrt2));
}

console.log(approximatePi());
// 3.1449074048195

Common Patterns

Avoiding Repeated Calculations

// Instead of computing sqrt(2) each time
function calculateHypotenuse(a, b) {
  return Math.sqrt(a * a + b * b);
}

// For unit square diagonal, use the constant
const unitDiagonal = Math.SQRT2;

Scale Factor Calculations

// Doubling the area of a square
function sideForDoubleArea(originalSide) {
  return originalSide * Math.SQRT2;
}

console.log(sideForDoubleArea(5));
// 7.071067811865476

Why Use Math.SQRT2?

Using Math.SQRT2 instead of hardcoding 1.4142135623730951 provides several advantages:

Precision — The constant is defined to full floating-point precision
Readability — Code clearly expresses the mathematical concept
Standardization — Matches mathematical notation in formulas
Performance — The value is pre-computed by the JavaScript engine
Intent — Using Math.SQRT2 signals to other developers that √2 is intentionally used