➗ Remainder Calculator: Quotient and Remainder of Division

What is the Remainder Calculator?

When you divide two whole numbers that do not divide evenly, you are left with a leftover amount called the remainder. A remainder calculator does this for you: it finds how many whole times the divisor fits into the dividend (the quotient) and how much is left over (the remainder). For 17 divided by 5, the divisor 5 fits into 17 three whole times, using up 15, and the leftover 2 is the remainder. Every division with remainder obeys the same identity: dividend = quotient x divisor + remainder, so 17 = 3 x 5 + 2.

The quotient here is the truncated (integer) quotient, meaning it drops any fractional part rather than rounding. That is different from the exact decimal quotient, which for 17 divided by 5 is 3.4. This remainder calculator shows both so you never confuse the two: the whole-number quotient 3 with remainder 2 is what you use for long division and clock arithmetic, while 3.4 is the true value of the fraction. A handy check is that the fractional part of the exact quotient, 0.4, is exactly the remainder over the divisor, 2 divided by 5.

The remainder is closely related to the modulo operation, often written a mod b or a % b in programming. For positive numbers they are the same thing, but the sign of the result depends on the convention. This remainder calculator truncates the quotient toward zero, so the remainder always carries the sign of the dividend, exactly like the JavaScript, C and Java % operator. That means -17 divided by 5 gives a quotient of -3 and a remainder of -2. Some mathematicians and languages such as Python instead use a floored modulo that keeps the remainder the same sign as the divisor, giving -4 remainder 3 for the same inputs.

Because the two conventions disagree only when the dividend is negative, this remainder calculator shows both a truncated remainder and an always-positive floored remainder whenever you enter a negative dividend. That way you can match whichever definition your textbook, spreadsheet, or programming language uses. For everyday positive division the answer is unambiguous, and the remainder calculator simply gives you the quotient and remainder you would get from long division, only faster and without arithmetic slips.

When to use it

• Checking a long division answer by confirming the quotient and remainder are correct.
• Working out how many full groups fit and how many items are left over, such as seating 100 guests at tables of 7.
• Understanding how the modulo operator behaves for negative numbers before writing code.
• Finding the day of the week or a clock time using remainder (modular) arithmetic.
• Teaching or learning the relationship dividend = quotient x divisor + remainder.
• Splitting a total into equal shares and seeing the leftover that cannot be shared evenly.

How to use the Remainder Calculator

1. Enter the dividend, the number you want to divide, in the first box.
2. Enter the divisor, the number you are dividing by, in the second box (it cannot be 0).
3. Read the headline result in the form "dividend divided by divisor = quotient remainder r".
4. Check the quotient, remainder, exact decimal quotient, and modulo in the four result panels.
5. If the dividend is negative, compare the truncated and always-positive remainder in the extra panel, then copy the result if you need it.

Formula & method

Worked examples

Quotient and remainder for common divisions

Truncated vs floored remainder for a negative dividend (-17 / 5)

Common mistakes to avoid

• Confusing the remainder with the decimal part of the quotient. For 17 divided by 5 the remainder is 2, not 0.4. The decimal 0.4 is the remainder divided by the divisor (2 / 5). The remainder is a whole number left over, while 0.4 is the fractional part of the exact quotient.
• Rounding the quotient instead of truncating it. The integer quotient drops the fractional part toward zero, it does not round. 17 / 5 = 3.4 gives a quotient of 3, and even 19 / 5 = 3.8 still gives a quotient of 3 with remainder 4, not a rounded 4.
• Expecting a positive remainder for a negative dividend. With the truncated convention used here, -17 divided by 5 gives a remainder of -2 because the remainder shares the sign of the dividend. If you need an always-positive remainder, use the floored value of 3 shown in the negative-dividend panel.
• Trying to divide by zero. The divisor can never be 0, because dividing by zero is undefined and has no quotient or remainder. This remainder calculator shows a friendly error and asks for a non-zero divisor.

Glossary

Dividend

The number being divided, the total you are splitting up. In 17 / 5, the dividend is 17.

Divisor

The number you divide by, the size of each group. In 17 / 5, the divisor is 5.

Quotient

How many whole times the divisor fits into the dividend. In 17 / 5, the quotient is 3.

Remainder

The amount left over after taking out all the whole groups. In 17 / 5, the remainder is 2.

Modulo

The remainder operation, written a mod b or a % b in code. For positive numbers it equals the remainder.

Truncation

Dropping the fractional part of a number toward zero, so 3.4 and -3.4 become 3 and -3.

Frequently asked questions

Sources

• Euclidean division , Wikipedia
• Modulo operation , Wikipedia