How to get the square root of a number in JavaScript
Łukasz Holeczek
Follow Łukasz Holeczek on GitHub
Connect with Łukasz Holeczek on LinkedIn
Follow Łukasz Holeczek on X (Twitter)
Calculating square roots is important for geometric calculations, distance formulas, statistical analysis, and data visualization in JavaScript applications. With over 25 years of experience in software development and as the creator of CoreUI, I’ve used square root calculations in geometric utilities, chart scaling, and physics-based animations. For rounding results before display, see how to round a number in JavaScript.
Use Math.sqrt() to calculate the square root of a number.
Math.sqrt(16) // 4
Math.sqrt(2.25) // 1.5
Math.sqrt(2) // 1.4142135623730951
Math.sqrt(0) // 0
Math.sqrt(-1) // NaN — negative numbers have no real square root
1. Basic Usage and Edge Cases
Math.sqrt(9) // 3
Math.sqrt(0.25) // 0.5
Math.sqrt(1) // 1
Math.sqrt(0) // 0
Math.sqrt(-4) // NaN
Math.sqrt(Infinity) // Infinity
Math.sqrt(NaN) // NaN
Math.sqrt(null) // 0 — null coerces to 0
Math.sqrt(undefined) // NaN
Math.sqrt('9') // 3 — numeric strings are coerced
Math.sqrt('hello') // NaN
Validate inputs with Number.isNaN() when the source is user input or an API.
2. Exponentiation Operator Alternative
The ** 0.5 exponentiation operator (ES2016) is a concise alternative to Math.sqrt() and generalises to any root.
16 ** 0.5 // 4 — square root
27 ** (1/3) // 3 — cube root
16 ** 0.25 // 2 — fourth root
// Math.sqrt is equivalent for square roots:
Math.sqrt(16) === 16 ** 0.5 // true
Math.sqrt() is typically preferred for square roots due to clarity; use ** (1/n) when you need nth roots.
3. Euclidean Distance with Math.hypot()
For distance calculations involving two or more dimensions, Math.hypot() is more readable and numerically stable than manually squaring, summing, and square-rooting.
// Distance between two points — manual approach
const dist = (x1, y1, x2, y2) => Math.sqrt((x2 - x1) ** 2 + (y2 - y1) ** 2)
dist(0, 0, 3, 4) // 5
// Same with Math.hypot — cleaner and avoids overflow on large values
const distHypot = (x1, y1, x2, y2) => Math.hypot(x2 - x1, y2 - y1)
distHypot(0, 0, 3, 4) // 5
// 3D distance
Math.hypot(1, 2, 2) // 3 — √(1² + 2² + 2²) = √9 = 3
Math.hypot() avoids intermediate overflow when components are very large — prefer it over the manual formula in production code.
4. Pythagorean Theorem
function hypotenuse(a, b) {
return Math.sqrt(a ** 2 + b ** 2)
}
hypotenuse(3, 4) // 5
hypotenuse(5, 12) // 13
hypotenuse(1, 1) // 1.4142135623730951 (√2)
5. Standard Deviation
Square root appears in the standard deviation formula — the final step after computing variance.
function standardDeviation(values) {
const mean = values.reduce((s, v) => s + v, 0) / values.length
const variance = values.reduce((s, v) => s + (v - mean) ** 2, 0) / values.length
return Math.sqrt(variance)
}
standardDeviation([2, 4, 4, 4, 5, 5, 7, 9]) // 2
6. BigInt Limitation
Math.sqrt() does not accept BigInt — it throws a TypeError. Convert to Number first (with precision loss for very large integers).
Math.sqrt(16n) // TypeError: Cannot convert a BigInt value to a number
Math.sqrt(Number(16n)) // 4 — safe for values within Number.MAX_SAFE_INTEGER
For cryptographic or arbitrary-precision square roots, use a dedicated BigInt math library.
Best Practice Note:
Use Math.hypot() instead of the manual Math.sqrt(dx**2 + dy**2) pattern for distance calculations — it is cleaner and avoids overflow.
Always guard against negative inputs when computing square roots; Math.sqrt(-x) silently returns NaN.
For absolute value of the difference before squaring, pair Math.abs() and Math.sqrt() together in magnitude calculations.
