Free · Arithmetic calculators ➗
Floor: Round Down to an Integer
Find the greatest integer less than or equal to a number, including negative decimals.
- Formula & worked example
- Private in your browser
- No signup
Calculator inputs
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How to use this calculator
- Enter the known values in the units shown. Results update as you type.
- Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
- Use the worked example to check the method. Reset restores the starting fields.
Private by default
Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.
Formula and method
The floor of −2.3 is −3. Moving downward on the number line differs from simply deleting the decimal portion, which would give −2.
floor(x) = greatest integer n such that n ≤ x
Worked example
Enter these known values and leave the other values blank.
- Number
- -2.3
- Floor value
- -3
Assumptions and limitations
- Floor rounds toward negative infinity. It is not rounding to the nearest integer.
- An integer is unchanged by the floor operation, including zero and negative integers.
- The result cannot uniquely recover the input: every x in [n, n + 1) has floor n. The output is therefore read-only.
Common questions
Why does −2.3 round down to −3?
−3 is the largest integer that is still less than or equal to −2.3. −2 is greater than −2.3 and cannot be its floor.
What is the floor of an exact integer?
The integer itself. For example, floor(7) = 7 and floor(−7) = −7.
References
The calculation equations, inverse formulas, units, and input rules were imported from this source. Bookify provides the interface and equation solver.
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