Floor and Ceiling Calculator

About this calculator

The floor and ceiling calculator returns four related values for any number: the floor ⌊x⌋ (the greatest integer less than or equal to x), the ceiling ⌈x⌉ (the smallest integer greater than or equal to x), the conventionally rounded value, and the truncated value (the integer part with the decimal simply dropped). For a positive number like 4.7 these differ only for the fractional part, but for negatives like −4.7 floor and ceiling diverge sharply — floor(−4.7) = −5 while truncation gives −4.

The distinction matters constantly in programming and quantitative work: pagination logic uses ceiling to make sure a partial page still gets its own page, batch-sizing and inventory calculations use floor or ceiling depending on whether you're allowed to round up, and languages like Python, JavaScript, and SQL don't all implement integer division consistently. Developers, students learning discrete math, and anyone auditing a spreadsheet formula use this tool to check exactly what a given rounding function will output before relying on it in code.