Enter a dividend and a divisor to compute the floor division result — the largest integer less than or equal to the exact quotient. The calculator returns the floor quotient, the remainder, and the regular decimal result side by side, so you can see exactly how floor division differs from standard division.
Floor Quotient ⌊Dividend ÷ Divisor⌋
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Remainder
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Exact Decimal Result
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Expression
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Floor division is a type of division where the result is rounded down to the nearest integer (whole number), regardless of whether the remainder is positive or negative. For example, 13 ÷ 4 = 3.25 in regular division, but the floor division result is 3. It is sometimes called 'integer division' or 'division with remainder'.
Regular division returns a decimal (floating-point) result — for example, 7 ÷ 2 = 3.5. Floor division always returns the largest integer that is less than or equal to the exact result, so 7 ÷ 2 gives 3. The key difference becomes obvious when the division is not exact.
They give the same answer whenever the dividend is perfectly divisible by the divisor — meaning there is no remainder. For example, 8 ÷ 4 = 2 exactly, so both regular and floor division return 2.
The name comes from the mathematical 'floor function' ⌊x⌋, which maps any real number to the largest integer less than or equal to it. Imagine a number line where the 'floor' beneath a decimal value is the integer directly below it.
With negative numbers, floor division still rounds toward negative infinity — not toward zero. For example, ⌊−7 ÷ 2⌋ = ⌊−3.5⌋ = −4, not −3. This differs from truncation (which rounds toward zero), so be careful when working with negatives.
9 ÷ 2 = 4.5 in regular division. Applying the floor function gives ⌊4.5⌋ = 4, so the floor division result is 4 with a remainder of 1.
In Python, the floor division operator is `//` (e.g., `9 // 2` returns `4`). In other languages like Java, C, and C++, integer division of two integers also truncates toward zero, but for negative numbers you may need `Math.floor()` explicitly to match true floor behavior.
Floor division is used in many practical scenarios: splitting items evenly among groups (e.g., how many full boxes of 12 can you pack from 50 items?), calculating how many complete weeks fit in a number of days, time conversions (minutes to hours), and pagination in software (how many full pages does a list require).