# Remainder (%)

The remainder (`%`) operator returns the remainder left over when one operand is divided by a second operand. It always takes the sign of the dividend.

## Syntax

js

``````x % y
``````

## Description

The `%` operator is overloaded for two types of operands: number and BigInt. It first coerces both operands to numeric values and tests the types of them. It performs BigInt remainder if both operands become BigInts; otherwise, it performs number remainder. A `TypeError` is thrown if one operand becomes a BigInt but the other becomes a number.

For the operation `n % d`, `n` is called the dividend and `d` is called the divisor. The operation returns `NaN` if one of the operands is `NaN`, `n` is ±Infinity, or if `d` is ±0. Otherwise, if `d` is ±Infinity or if `n` is ±0, the dividend `n` is returned.

When both operands are non-zero and finite, the remainder `r` is calculated as `r := n - d * q` where `q` is the integer such that `r` has the same sign as the dividend `n` while being as close to 0 as possible.

Note that while in most languages, '%' is a remainder operator, in some (e.g. Python, Perl) it is a modulo operator. Modulo is defined as `k := n - d * q` where `q` is the integer such that `k` has the same sign as the divisor `d` while being as close to 0 as possible. For two values of the same sign, the two are equivalent, but when the operands are of different signs, the modulo result always has the same sign as the divisor, while the remainder has the same sign as the dividend, which can make them differ by one unit of `d`. To obtain a modulo in JavaScript, in place of `n % d`, use `((n % d) + d) % d`. In JavaScript, the modulo operation (which doesn't have a dedicated operator) is used to normalize the second operand of bitwise shift operators (`<<`, `>>`, etc.), making the offset always a positive value.

For BigInt division, a `RangeError` is thrown if the divisor `y` is `0n`. This is because number remainder by zero returns `NaN`, but BigInt has no concept of `NaN`.

## Examples

### Remainder with positive dividend

js

``````13 % 5; // 3
1 % -2; // 1
1 % 2; // 1
2 % 3; // 2
5.5 % 2; // 1.5

3n % 2n; // 1n
``````

### Remainder with negative dividend

js

``````-13 % 5; // -3
-1 % 2; // -1
-4 % 2; // -0

-3n % 2n; // -1n
``````

### Remainder with NaN

js

``````NaN % 2; // NaN
``````

### Remainder with Infinity

js

``````Infinity % 2; // NaN
Infinity % 0; // NaN
Infinity % Infinity; // NaN
2 % Infinity; // 2
0 % Infinity; // 0
``````

## Browser compatibility

BCD tables only load in the browser