ceil always rounds up.

Math.round is underspecified, and I believe its behavior has actually changed in the past -- see http://bugs.java.com/view_bug.do?bug_id=6430675 -- but generally speaking it behaves like RoundingMode.HALF_UP, which has an extensive table of its differences from RoundingMode.CEILING or RoundingMode.FLOOR.

This is apples vs. oranges. In most languages/APIs, min/max take two (or more) inputs, and return the smallest/biggest. floor/ceil take one argument, and round it down or up to the nearest integer.

In MATLAB, round, fix, floor, and ceil are all functions used for rounding numbers, but they differ in their behavior: round: rounds to the nearest integer. If the fractional part is exactly 0.5, it rounds to the nearest even integer. For example: round(3.5) % Output: 4 round(2.3) % Output: 2 fix: simply truncates the decimal part of the number, essentially removing it and keeping only the integer part. For example: fix(3.5) % Output: 3 fix(-3.5) % Output: -3 floor: always rounds down towards the nearest integer. For example: floor(3.5) % Output: 3 floor(2.1) % Output: 2 floor(-2.1) % Output: -3 ceil: always rounds up towards the nearest integer. For example: ceil(3.5) % Output: 4 ceil(2.1) % Output: 3 ceil(-2.1) % Output: -2 for negative values, the results appear a bit different for floor and ceil as floor (-2.1) will result in -3 instead of -2 (because -3 is smaller than -2), and ceil(-2.1) will result in -2 instead of -3 (because -2 is greater than -3). In simple words, one gives you the upper conversion of the number, and the other gives you the lower conversion of the number. Hopefully that will clear your confusion...

The answer is here

Round does a standard rounding. If value is .5 or over then you get back 1. If it’s less than .5 you get back 0

Ceiling returns the integer equal to or higher than the value passed in.

SELECT ROUND(235.400,0); 

Answer= 235.000 

SELECT  CAST(ROUND(235.400,0) as int) 

Answer= 235

John wrote:

I am looking for a single function that will do EITHER a ROUNDUP or ROUNDOWN based on the value.  (i.e. on a scale from 1-10, if the value is 1-4, I want to round the value down; if value is 5-10, I want to round the value up). Is there such a function that will do this in a single calculation?

That's the very definition of ROUND.  But your example is ambiguous insofar as it is unclear what digit you are talking about rounding.

If you want 1.4 in A1 to round to 1 and 1.5 to round to 2, use ROUND(A1,0).

If you want 14 to round to 10 and 15 to round to 20, use ROUND(A1,-1).

See the ROUND help page for more details.

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PS:  For future reference, when you have a question, start a new discussion instead of piggybacking an old discussion, much less a discusion marked "answer".

First, usually no two questions are every identical in all details.  So your specifics might require a completely different direction.

Second, some helpful people might never see your new "response" because they do not look at discussions marked "answer".

Finally, since you are not the original poster, you have no way to mark responses to your question as "answer".