Modulo Calculator (Remainder and Mod)

The remainder follows the dividend's sign, the way the % operator behaves in most languages, so -7 % 3 is -1. The floored modulo follows the divisor's sign, so the same inputs give 2. The two agree whenever the dividend and divisor share a sign and only split when their signs differ.

The remainder is computed as dividend % divisor, which truncates toward zero and keeps the dividend's sign. The modulo is ((dividend % divisor) + divisor) % divisor, which shifts the result into the divisor's sign. So 7 and -3 give a remainder of 1 but a modulo of -2.

Only when the divisor is positive. A positive divisor forces a non-negative modulo, while a negative divisor produces a non-positive modulo. That is why the sign of the divisor, not the dividend, determines the sign of this result.

The quotient uses truncated division, Math.trunc(dividend / divisor), which rounds toward zero rather than down. So -7 divided by 3 gives a quotient of -2, not -3. Multiplying the quotient by the divisor and adding the remainder always returns the original dividend.

Division and the modulo operation are undefined when the divisor is zero, so the calculator rejects it with an error rather than returning a meaningless value or infinity.

No. The calculator accepts decimals, and the underlying % operator extends to them, so 5.5 divided by 2 gives a remainder and modulo of 1.5. Floating point rounding can appear with numbers that cannot be represented exactly in binary.

It varies. C, Java, Go and JavaScript use the truncated remainder shown here, so their % can be negative. Python and Ruby use the floored modulo instead, matching the Modulo card. Knowing which one your language uses avoids subtle bugs with negatives.

Apply the same trick the Modulo card uses: ((a % n) + n) % n. Adding n before the final modulo lifts a negative remainder back into the 0 to n minus 1 range whenever n is positive.

Yes. Everything runs locally in your browser, so the numbers you enter are never uploaded to a server.