MOD

Return the remainder after dividing one number by another. The result has the sign of the divisor, as in Excel.

Syntax

MOD(number, divisor)

Argument	Required	Description
`number`	Required	The number to divide.
`divisor`	Required	The number to divide by. Zero returns #DIV/0!.

Examples

Every example below was executed against VisiGrid engine 0.54.0 — not transcribed from another vendor's documentation. Reproduce any of them with vgrid calc.

Formula	Result	Notes
`=MOD(10,3)`	`1`
`=MOD(A2,2)=0`	`FALSE`	The standard even-number test. 7 is odd.
`=MOD(-1,12)`	`11`	The result takes the divisor's sign, so a negative offset wraps round a cycle.
`=MOD(10,-3)`	`-2`
`=MOD(5.5,2)`	`1.50`	Works on fractions too.
`=MOD(10,0)`	`#DIV/0!`

Even, odd, every Nth

MOD with a divisor of 2 is 0 for even numbers and 1 for odd ones. With ROW() it picks out every other row, or every Nth, for banding or sampling:

=MOD(ROW(),2)=0

Wrapping round a cycle

Because the remainder takes the sign of the divisor, MOD keeps a value inside a cycle even when it goes negative. Going back one month from January:

=MOD(1-1-1,12)+1  → 12

— December, not month 0 or -1. The same pattern wraps hours round a clock, angles round a circle and days round a week.

Some programming languages keep the sign of the dividend instead, so -1 % 12 is -1. Formulas moved between the two need checking wherever the first argument can be negative.

Splitting whole units from the rest

INT(n/d) gives how many whole times d fits in n, and MOD(n,d) gives what is left over — 130 minutes is INT(130/60) hours and MOD(130,60) minutes.

Excel compatibility

Matches Excel, including the sign of the result following the divisor.