Floor Function Calculator
Calculate floor(x), ceiling(x), truncation, fractional part, and the floor interval for integers, decimals, fractions, and percentages.
Last Updated: May 2026
floor(x)
7
ceiling(x)
8
trunc(x)
7
fractional part
41/50
Floor Function Input
Enter an integer, decimal, fraction, or percentage. Negative values use the standard floor rule, so floor(-2.4) is -3.
Accepted forms: 7.82, -2.4, 22/7, 62.5%.
Floor Identities
| Measure | Setup | Value |
|---|---|---|
| Input as fraction | 391/50 | Exact parsed value. |
| Input as decimal | 7.82 | Decimal approximation for review. |
| Floor interval | 7 <= x < 8 | The floor is the left endpoint of this interval. |
| Fractional part | 7.82 - 7 | 41/50 |
| Distance to next integer | 8 - 7.82 | 9/50 |
Nearby Integers
| Integer | Relation |
|---|---|
| 5 | less than or equal to x |
| 6 | less than or equal to x |
| 7 | floor result |
| 8 | greater than x |
| 9 | greater than x |
Math Notation Notice
This calculator uses the standard real-number floor function. In programming languages, names such as floor, trunc, integer part, and remainder can follow different conventions, especially for negative values.
Checked by Jitendra Kumar
Floor Function Calculator is checked for formula labels, source links, and result limits.
Jitendra Kumar, Founder & Editorial Standards Lead. Updated May 2026. Scope: math calculators.
How to Use the Floor Function Calculator
Enter a value as an integer, decimal, fraction, or percentage. The calculator parses finite decimals and fractions exactly before evaluating floor(x).
Review the main floor result, then compare it with ceiling, truncation, fractional part, and the interval n <= x < n + 1.
Step 1: Enter x
Type a value such as 7.82, -2.4, 22/7, or 62.5%.
Step 2: Read floor(x)
The primary result shows the largest integer less than or equal to x.
Step 3: Compare related values
Use ceiling, truncation, and fractional part to understand the rounding behavior.
Step 4: Check the interval
Confirm that x lies in the interval from floor(x) up to the next integer.
How This Floor Function Calculator Works
The calculator converts the input to an exact rational number when possible. It then finds the largest integer that is less than or equal to that value.
For positive non-integers, floor(x) looks like dropping the decimal part. For negative non-integers, floor(x) moves to the next more-negative integer, which is why floor(-2.4) is -3.
The fractional part is computed as x - floor(x), so it stays in the interval from 0 up to but not including 1.
Floor Function Guide
Core Floor Function Rules
| Concept | Formula | Use |
|---|---|---|
| Floor definition | floor(x) = greatest integer <= x | Rounds down to the nearest integer at or below x. |
| Ceiling definition | ceiling(x) = smallest integer >= x | Rounds up to the nearest integer at or above x. |
| Floor interval | n <= x < n + 1 | If x is in this interval, floor(x) = n. |
| Fractional part | {x} = x - floor(x) | Always satisfies 0 <= {x} < 1. |
| Integer shift | floor(x + k) = floor(x) + k | Applies when k is an integer. |
Examples
| Input | Result | Why |
|---|---|---|
| floor(7.82) | 7 | Largest integer not greater than 7.82. |
| floor(-2.4) | -3 | Floor moves down on the number line for negatives. |
| floor(22/7) | 3 | 22/7 is about 3.142857. |
| floor(62.5%) | 0 | 62.5% equals 0.625. |
| floor(-5) | -5 | Exact integers are unchanged. |
Floor Function Context
The floor function is a step function. Every real value from an integer n up to, but not including, n + 1 has the same floor value n.
Floor is common in number theory, discrete math, algorithms, indexing, binning, pagination, and formulas that convert continuous quantities into whole-number groups.
Keep the research moving with Integer Calculator, Modulo Calculator, Greater Than Or Less Than Calculator, and Scientific Calculator.
Frequently Asked Questions
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- 1.Wolfram MathWorld - Floor Function(Accessed May 2026)
- 2.Wolfram Documentation - Floor(Accessed May 2026)
- 3.Wolfram MathWorld - Ceiling Function(Accessed May 2026)