Example 1
- x = 3.7
3
What is ⌊3.7⌋? 3. The fraction drops down, not up to four.
Floor calculator
Type an x. Floor is the greatest integer that does not exceed x. ⌊3.7⌋ = 3. ⌊−1.2⌋ = −2. ⌊5⌋ = 5. A minus does not clip to −1.
The calculator takes the integer part toward −∞. Negatives go toward −∞: −1.2 gives −2, not −1. A whole x stays itself.
Results
Enter data and click Calculate.
How it works
Floor (integer part) is the greatest integer that is not larger than x. School writes ⌊3.7⌋ = 3, because 3 sits under 3.7 and 4 does not. The calculator takes the integer part toward −∞ and shows 3, a plain integer string, with no six zeros.
A negative x does not clip toward zero. Floor walks toward −∞. ⌊−1.2⌋ = −2, because −2 is smaller than −1.2 and −1 is already larger. This is not “round down away from the axis from zero”. Minus 1.2 does not leave −1.
The field is x. A comma and a dot are the same decimal. 3.7 and 3,7 both give 3. Whole 5 stays 5. The header units switch does not multiply anything here.
Ceiling goes the other way: ⌈−1.2⌉ = −1. Rounding to n places keeps a fraction and only shortens it to k digits. Here the result is always an integer.
The fractional part is x minus its integer part. Absolute value drops the sign and does not clip the fraction. Here you stay with floor alone.
⌊3.7⌋ = 3. ⌊−1.2⌋ = −2. ⌊5⌋ = 5. 0.9 gives 0. −0.1 gives −1.
Formula
⌊x⌋ = Math.floor(x)
How to use
- Type x, for example 3.7.
- Click Calculate. Floor gives 3.
- −1.2 gives −2, not −1. Floor goes toward −∞.
- 5 stays 5. A whole number does not change.
- Ceiling of the same x lives on the neighbouring card.
⌊3.7⌋ = 3
Floor is the greatest integer ≤ x. ⌊3.7⌋ = 3. ⌊−1.2⌋ = −2. ⌊5⌋ = 5. Negatives go toward −∞.
- floor
- Integer part toward −∞ on the page. 3.7 gives 3. −1.2 gives −2. 5 stays 5.
- integer
- The result has no fraction. 3.7 drops to 3. 5 stays 5.
- negative
- Walks toward −∞, not toward zero. −1.2 gives −2, not −1.
Examples
Example 2
- x = -1.2
-2
What is ⌊−1.2⌋? −2, not −1. Floor goes toward minus infinity.
Example 3
- x = 5
5
What is ⌊5⌋? 5. A whole number stays itself.
Related calculators
Common questions
What is ⌊3.7⌋?
3. The greatest integer that does not exceed 3.7.
What does floor (integer part) mean?
The greatest integer ≤ x. The calculator takes the integer part toward −∞ and shows a plain integer string.
What is ⌊−1.2⌋?
−2, not −1. Floor goes toward −∞. −1 is already larger than −1.2.
What is ⌊5⌋?
5. When x is already an integer, the result is that same x.
Does a negative x work?
Yes. A minus is not an error. −0.1 gives −1. −3 gives −3.
How is floor different from ceil?
Floor steps toward −∞. Ceil steps toward +∞. For −1.2, floor is −2 and ceil is −1.
Does a comma in 3.7 work?
Yes. 3.7 and 3,7 both give 3.
Where does the fraction go?
On the fractional-part page: x minus its integer part. Here you get the integer alone.
Does 0.9 give 0?
Yes. 0 is the greatest integer under 0.9.
Do header units change floor?
No. 3.7 stays 3 under every label.
Knowledge sources
The calculator computes the same formula as the definition below.
Page updated in 2026.