# Floor Function Calculator

URL: https://speedycalculator.com/calculators/math/floor-function/
Last updated: 2026-10-30

> The floor function calculator rounds a number down to the nearest integer, ⌊x⌋, and shows the fractional part {x} = x − ⌊x⌋.

## Inputs

- x

## Results

- Floor of x
- Fractional part {x}
- Ceiling of x
- Truncated (towards zero)

## Formula

```
⌊x⌋ = the greatest integer n with n ≤ x
{x} = x − ⌊x⌋
```

## Explanation

The floor function is everywhere in computing and counting: the number of complete boxes you can fill, a person's age in whole years, array indices and integer division all use it.

### How to use the Floor Function Calculator

- **x**

Results update as you type, and everything is calculated in your browser.

### How it works

Positive numbers simply lose their fractional part; negative numbers move away from zero: ⌊−2.3⌋ = −3.

### Tips

- Estimate the answer first so you can spot an impossible result.
- Work with whole numbers where possible and place the decimal point at the end.
- Use the order of operations: brackets, powers, multiplication and division, then addition and subtraction.
- For large integers, the calculator works with exact whole-number arithmetic in your browser.

### Common mistakes to avoid

- Misaligning decimal points when adding or subtracting.
- Forgetting the remainder in whole-number division.
- Rounding too early in a multi-step calculation.

### What each result means

- **Floor of x** = floor([x])
- **Fractional part {x}** = [x] - floor([x])
- **Ceiling of x** = ceil([x])
- **Truncated (towards zero)** = trunc([x])

### Example values

How the main result changes when **x** changes and everything else stays at the example values above:

xFloor of x-1.15-2-1.72-2-2.3-3-2.88-3-3.45-4-4.6-5

## Worked example

Inputs — x: -2.3.

Results — **Floor of x = -3**; Fractional part {x} = 0.7; Ceiling of x = -2; Truncated (towards zero) = -2.

## Key terms

- **Floor function**: ⌊x⌋, the greatest integer ≤ x.

## FAQ

**What is the floor of 3.9?**
3.

**What is the floor of −3.1?**
−4.

**How do floor and truncation differ?**
They agree for positive numbers; for negatives, floor goes down and truncation goes towards zero.

**What is the fractional part of −2.3?**
0.7, because −2.3 − (−3) = 0.7.

**What formula does the Floor Function Calculator use?**
⌊x⌋ = the greatest integer n with n ≤ x.


## Sources

- [OpenStax – Prealgebra 2e](https://openstax.org/details/books/prealgebra-2e)
- [Wolfram MathWorld – Floor function](https://mathworld.wolfram.com/FloorFunction.html)