Floor and Ceiling Calculator

This floor and ceiling calculator rounds a number down and up to whole numbers. The floor is the greatest integer that is less than or equal to the number, and the ceiling is the smallest integer that is greater than or equal to it. Enter a value and the calculator returns the floor, the ceiling, the nearest integer by ordinary rounding, and the fractional part. These functions are everywhere in programming, in working out how many containers or pages you need, and in mathematics. For negative numbers the floor moves away from zero and the ceiling towards it, which sometimes surprises people. The definitions, a worked example and the assumptions are set out below.

Number

Nearest integer (round)

Fractional part

The formula

The floor of x, written with the down brackets, is the largest integer not greater than x. The ceiling of x, the up brackets, is the smallest integer not less than x. The fractional part is x minus the floor of x.

Worked example

For 3.7 the floor is 3 and the ceiling is 4, the nearest integer is 4, and the fractional part is 0.7. For minus 3.7 the floor is minus 4 and the ceiling is minus 3. Enter 3.7 to confirm.

Frequently asked questions

What is the floor of a number?

The greatest integer that is less than or equal to it. The floor of 3.7 is 3, and the floor of minus 3.7 is minus 4.

What is the ceiling?

The smallest integer greater than or equal to the number. The ceiling of 3.2 is 4.

How do they behave for negatives?

For minus 2.5 the floor is minus 3 (further from zero) and the ceiling is minus 2 (towards zero).

Who this calculator is for

This calculator is for students and anyone needing a quick, reliable result.

What this calculator assumes

You enter valid numbers.
The standard formula is applied.
Results are rounded for display.

Formula and sources

Related calculators

Scientific Calculator: general scientific maths.
Percentage Calculator: percentages and changes.
Ratio Calculator: simplify and scale ratios.

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