Number.EPSILON

## Value

2<sup>-52</sup>, or approximately `2.2204460492503130808472633361816E-16`.

{{js_property_attributes(0, 0, 0)}}

## Description

`Number.EPSILON` is the difference between 1 and the next greater number representable in the Number format, because [double precision floating point format](https://en.wikipedia.org/wiki/Double_precision_floating-point_format) only has 52 bits to represent the [mantissa](/en-US/docs/Web/JavaScript/Reference/Global_Objects/Number#number_encoding), and the lowest bit has a significance of 2<sup>-52</sup>.

Note that the absolute accuracy of floating numbers decreases as the number gets larger, because the exponent grows while the mantissa's accuracy stays the same. {{jsxref("Number.MIN_VALUE")}} is the smallest representable positive number, which is much smaller than `Number.EPSILON`.

Because `EPSILON` is a static property of {{jsxref("Number")}}, you always use it as `Number.EPSILON`, rather than as a property of a number value.

## Examples

### Testing equality

Any number encoding system occupying a finite number of bits, of whatever base you choose (e.g., decimal or binary), will _necessarily_ be unable to represent all numbers exactly, because you are trying to represent an infinite number of points on the number line using a finite amount of memory. For example, a base-10 (decimal) system cannot represent 1/3 exactly, and a base-2 (binary) system cannot represent `0.1` exactly. Thus, for example, `0.1 + 0.2` is not exactly equal to `0.3`:

```js
console.log(0.1 + 0.2); // 0.30000000000000004
console.log(0.1 + 0.2 === 0.3); // false

function equal(x, y) {
  return Math.abs(x - y) < Number.EPSILON;
}

const x = 0.2;
const y = 0.3;
const z = 0.1;
console.log(equal(x + z, y)); // true

function equal(x, y) {
  return Math.abs(x - y) < Number.EPSILON;
}

const x = 1000.1;
const y = 1000.2;
const z = 2000.3;
console.log(x + y); // 2000.3000000000002; error of 10^-13 instead of 10^-16
console.log(equal(x + y, z)); // false

function equal(x, y, tolerance = Number.EPSILON) {
  return Math.abs(x - y) < tolerance;
}

const x = 1000.1;
const y = 1000.2;
const z = 2000.3;
console.log(equal(x + y, z, 2000 * Number.EPSILON)); // true