round : Java Glossary

DecimalFormat automatically rounds output to the displayed number of decimal places, so there is nothing to do if you are rounding simply to make output look pretty.

• Integer Division

  If you want to use pure integer arithmetic likely you can use one of these three forms of division.

  // integer division
  // What percentage is "after" of "before" expressed as number 0..100 percent
  int percent = ( after * 100 ) / before;  // truncated down
  int percent = ( after * 100 + before - 1) / before;  // rounded up
  int percent = ( after * 100 + before/2) / before;  // rounded

• Round

  Numbers less that x.5 are rounded down toward zero, and those x.5 and above are rounded up to the next integer. Unfortunately rint does not give you an easy way to round to a given number of decimal places. You have to do it by multiplying and dividing.
  rint does not round 0.5 up, it rounds it up or down, whichever of the lower or higher integer is even!

  long Math.round( double );
  int Math.round( float );
  double Math.rint( double );
  
  // rounding to two decimal places
  double roundedValue = Math.rint( value * 100.0d ) / 100.0d;

  value	round
  -1.6	-2
  -1.5	-2
  -1.4	-1
  +1.4	+1
  +1.5	+2
  +1.6	+2

• Ceiling

  Numbers

  double Math.ceil( double );

  See the description of covered quotient division.

  value	ceil
  -1.6	-1
  -1.5	-1
  -1.4	-1
  +1.4	+2
  +1.5	+2
  +1.6	+2

• Floor

  Numbers

  double Math.floor( double );

  See floored division.

  value	floor
  -1.6	-2
  -1.5	-2
  -1.4	-2
  +1.4	+1
  +1.5	+1
  +1.6	+1

• Truncate

  Numbers

  int i = (int)d;

  value	truncate
  -1.6	-1
  -1.5	-1
  -1.4	-1
  +1.4	+1
  +1.5	+1
  +1.6	+1

• Cover

  Numbers are always rounded up away from zero. There is no simple function to do this.

  d < 0 ? Math.floor( d ) : Math.ceil( d );

  value	cover
  -1.6	-2
  -1.5	-2
  -1.4	-2
  +1.4	+2
  +1.5	+2
  +1.6	+2

Rounding Gotcha

Rounding to a Multiple

// rounding m up to next highest multiple of n
int ceil = ( m + n - 1 ) / n * n;

// rounding m down to multiple of n
int floor = m / n * n;

// rounding m to nearest multiple of n
int near = ( m + n/2 ) / n * n;

Rounding Currency

Rounding To The Nickel

On 2013-02-04 Canada discontinued the penny. Transactions are still computed to the penny, but are rounded to the nickel. The government has suggested (but not mandated) the following rounding rules.

• Final amounts ending in .01 or .02 will be rounded down to nearest .00
• Final amounts ending in .03 or .04 will be rounded up to nearest .05
• Final amounts ending in .06 or .07 will be rounded down to nearest .05
• Final amounts ending in .08 or .09 will be rounded up to nearest .10

The formula to compute the rounded amount could be described in words as.

1. Start with the cost in pennies.
2. add 2
3. divide by 5, discarding the fraction.
4. multiply by 5

You can calculate the rounded amount in a spreadsheet with =ROUNDDOWN((A1+2)/5)*5

The Canadian Sales Tax Calculator will compute the final sale amount including sales tax both penny and nickel-rounded.

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