Floor Function Calculator

Name: Floor Function Calculator
Author: Jitendra Kumar

Calculate floor(x), ceiling(x), truncation, fractional part, and the floor interval for integers, decimals, fractions, and percentages.

Last Updated: May 2026

floor(x)

ceiling(x)

trunc(x)

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.

Value of x

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.

Reviewed For Methodology, Labels, And Sources

Every CalculatorWallah calculator is published with visible update labeling, linked source references, and founder-led review of formula clarity on trust-sensitive topics. Use results as planning support, then verify institution-, policy-, or jurisdiction-specific rules where they apply.

Reviewed By

Jitendra Kumar, Founder & Editorial Standards Lead, oversees methodology standards and trust-sensitive publishing decisions.

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Topic Ownership

Sales tax and tax-sensitive estimate tools, Education and GPA planning calculators, Health, protein, and screening-formula pages, Platform-wide publishing standards and methodology

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Methodology & Updates

Page updated May 2026. Trust-critical pages are reviewed when official rates or rules change. Evergreen calculator guides are checked on a recurring quarterly or annual cycle depending on topic volatility.

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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.