Quick Answer

MOD Function

Returns the remainder after division, with the sign of the divisor.

Syntax

MOD

(number, divisor)

Parameters

Parameter	Description	Required
number	The dividend, the number to be divided.	Required
divisor	The number by which to divide. Cannot be 0.	Required

Basic Example

Remainder of 3 divided by 2

=MOD(3, 2)

Result1

3 = 1×2 + 1, so the remainder is 1.

Advanced Examples

Example 1: Negative dividend, positive divisor

Signs differ.

The result takes the divisor's (positive) sign.

=MOD(-3, 2)

Result: 1

MOD(-3,2) = -3 - 2×INT(-3/2) = -3 - 2×(-2) = 1, a positive remainder.

Example 2: Positive dividend, negative divisor

The divisor is negative.

The result takes the divisor's (negative) sign.

=MOD(7, -3)

Result: -2

MOD(7,-3) = 7 - (-3)×INT(7/-3) = 7 - (-3)×(-3) = 7 - 9 = -2.

How MOD Works

MOD computes number - divisor × INT(number / divisor). Because it uses INT, the result always has the same sign as the divisor, unlike a simple remainder that is always non-negative.

1

Select the cell

Click the cell for the result.

2

Enter the formula

Type =MOD(number, divisor).

3

Press Enter

The remainder appears.

Important Notes & Limitations

The divisor cannot be 0; MOD(n, 0) returns #DIV/0!.
The result's sign follows the divisor, which can be counter-intuitive (MOD(-3,2)=1).
Results are floating-point; tiny rounding may appear with non-integer inputs.

Common Errors & Fixes

#DIV/0!The divisor is 0.

Fix: Use a non-zero divisor.

Unexpected signForgetting the result follows the divisor's sign.

Fix: Apply ABS if you need a non-negative remainder, or adjust signs intentionally.

Download Practice File

Practice MOD with Real Data

Download a sample CSV file with pre-populated data and practice exercises for the MOD function. Works in both Excel and Google Sheets.

Works in Google SheetsCompatible with ExcelIncludes exercises

File format: CSV (comma-separated values) - opens in Excel, Google Sheets, and all spreadsheet apps

Related Functions

ABS

ABS converts negative numbers to positive, leaving positive numbers unchanged.

ACOS

Returns the angle (in radians) whose cosine is the supplied number.

ASIN

Returns the angle (in radians) whose sine is the supplied number.

ATAN

Returns the angle (in radians) whose tangent is the supplied number.

ATAN2

Returns the angle in radians to a point given by its x and y coordinates.

CEILING.MATH

Rounds up to a multiple of significance, with a mode for negative numbers.

Frequently Asked Questions

Why is MOD(-3, 2) equal to 1?

MOD returns a result with the same sign as the divisor. Since the divisor 2 is positive, the remainder is positive 1.

Is MOD the same as a programming remainder?

Not always. In many languages '%' gives a sign matching the dividend; Excel's MOD matches the divisor.

How do I get a non-negative remainder?

Wrap with ABS: =ABS(MOD(number, divisor)), or use MOD(MOD(number, d)+d, d) to keep it in [0, d).