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Math.Round Method (Double, MidpointRounding)

.NET Framework 4

Updated: January 2012

Rounds a double-precision floating-point value to the nearest integer. A parameter specifies how to round the value if it is midway between two other numbers.

Namespace: System
Assembly: mscorlib (in mscorlib.dll)

Syntax

C++

Copy

public static double Round(
	double value,
	MidpointRounding mode
)

Parameters

value: Type: System.Double
A double-precision floating-point number to be rounded.

mode: Type: System.MidpointRounding
Specification for how to round value if it is midway between two other numbers.

Return Value

Type: System.Double
The integer nearest value. If value is halfway between two integers, one of which is even and the other odd, then mode determines which of the two is returned.

Exceptions

Exception	Condition
ArgumentException	mode is not a valid value of System.MidpointRounding.

Remarks

The mode parameter controls how value is rounded if the first decimal digit in value is 5 -- that is, if it is halfway between one's digit and a value one greater than the one's digit. mode can have either of two values:

MidpointRounding.ToEven . If the one's digit is odd, it is changed to an even digit. Otherwise, it is left unchanged. This behavior follows IEEE Standard 754, section 4. It is sometimes called rounding to nearest, or banker's rounding. It minimizes rounding errors that result from consistently rounding a midpoint value in a single direction.
MidpointRounding.AwayFromZero . The one's digit is always rounded up to the next digit. This is the most commonly known rounding method. It is known as symmetric arithmetic rounding.

If the value of value is Double.NaN, the method returns Double.NaN. If the value of value is Double.PositiveInfinity or Double.NegativeInfinity, the method returns Double.PositiveInfinity or Double.NegativeInfinity, respectively.

Notes to Callers

Because of the loss of precision that can result from representing decimal values as floating-point numbers or performing arithmetic operations on floating-point values, in some cases the Round(Double, MidpointRounding) method may not appear to round midpoint values to the nearest even integer. In the following example, because the floating-point value .1 has no finite binary representation, the first call to the Round(Double) method with a value of 11.5 returns 11 instead of 12.

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using System;

public class Example
{
   public static void Main()
   {
      double value = 11.1;
      for (int ctr = 0; ctr <= 5; ctr++)    
         value = RoundValueAndAdd(value);

      Console.WriteLine();

      value = 11.5;
      RoundValueAndAdd(value);
   }

   private static double RoundValueAndAdd(double value)
   {
      Console.WriteLine("{0} --> {1}", value, Math.Round(value, 
                        MidpointRounding.AwayFromZero));
      return value + .1;
   }
}
// The example displays the following output:
//       11.1 --> 11
//       11.2 --> 11
//       11.3 --> 11
//       11.4 --> 11
//       11.5 --> 11
//       11.6 --> 12
//       
//       11.5 --> 12

Examples

The following code example demonstrates how to use the Round method with the MidpointRounding enumeration. Although the code example rounds decimal numbers, the Round method rounds double-precision floating-point numbers in a similar way.

C++

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// This example demonstrates the Math.Round() method in conjunction 
// with the MidpointRounding enumeration.
using System;

class Sample 
{
    public static void Main() 
    {
    decimal result = 0.0m;
    decimal posValue =  3.45m;
    decimal negValue = -3.45m;

// By default, round a positive and a negative value to the nearest even number. 
// The precision of the result is 1 decimal place.

    result = Math.Round(posValue, 1);
    Console.WriteLine("{0,4} = Math.Round({1,5}, 1)", result, posValue);
    result = Math.Round(negValue, 1);
    Console.WriteLine("{0,4} = Math.Round({1,5}, 1)", result, negValue);
    Console.WriteLine();

// Round a positive value to the nearest even number, then to the nearest number away from zero. 
// The precision of the result is 1 decimal place.

    result = Math.Round(posValue, 1, MidpointRounding.ToEven);
    Console.WriteLine("{0,4} = Math.Round({1,5}, 1, MidpointRounding.ToEven)", result, posValue);
    result = Math.Round(posValue, 1, MidpointRounding.AwayFromZero);
    Console.WriteLine("{0,4} = Math.Round({1,5}, 1, MidpointRounding.AwayFromZero)", result, posValue);
    Console.WriteLine();

// Round a negative value to the nearest even number, then to the nearest number away from zero. 
// The precision of the result is 1 decimal place.

    result = Math.Round(negValue, 1, MidpointRounding.ToEven);
    Console.WriteLine("{0,4} = Math.Round({1,5}, 1, MidpointRounding.ToEven)", result, negValue);
    result = Math.Round(negValue, 1, MidpointRounding.AwayFromZero);
    Console.WriteLine("{0,4} = Math.Round({1,5}, 1, MidpointRounding.AwayFromZero)", result, negValue);
    Console.WriteLine();
    }
}
/*
This code example produces the following results:

 3.4 = Math.Round( 3.45, 1)
-3.4 = Math.Round(-3.45, 1)

 3.4 = Math.Round( 3.45, 1, MidpointRounding.ToEven)
 3.5 = Math.Round( 3.45, 1, MidpointRounding.AwayFromZero)

-3.4 = Math.Round(-3.45, 1, MidpointRounding.ToEven)
-3.5 = Math.Round(-3.45, 1, MidpointRounding.AwayFromZero)

*/

Version Information

.NET Framework

Supported in: 4, 3.5, 3.0, 2.0

.NET Framework Client Profile

Supported in: 4, 3.5 SP1

Platforms

Windows 7, Windows Vista SP1 or later, Windows XP SP3, Windows XP SP2 x64 Edition, Windows Server 2008 (Server Core not supported), Windows Server 2008 R2 (Server Core supported with SP1 or later), Windows Server 2003 SP2

The .NET Framework does not support all versions of every platform. For a list of the supported versions, see .NET Framework System Requirements.

Reference

Math Class

Round Overload

System Namespace

Change History

Date	History	Reason
January 2012	Noted method behavior with Double.Nan, Double.PositiveInfinity, and Double.NegativeInfinity.	Customer feedback.
May 2010	Added the Notes for Callers section.	Customer feedback.

Date

History

Reason

January 2012

Noted method behavior with Double.Nan, Double.PositiveInfinity, and Double.NegativeInfinity.

Customer feedback.

May 2010

Added the Notes for Callers section.

Customer feedback.

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FAQ

You would think the most common rounding method would be default

The documentation states that symetric arthimetic rounding is the most common rounding method used in the world, but yet the default is bankers rounding. Who the heck decided that bankers rounding should be the default!??!

Why Bankers Rounding?

See my comments on bankers rounding versus symmetric arithmetic rounding at http://msdn.microsoft.com/en-us/library/system.math.round.aspx.

--Ron Petrusha
Common Language Runtime Developer Content
Microsoft Corporation

History

1/31/2011
Matt Olson

2/2/2011
R Petrusha - MSFT

Does not exist in Silverlight (4 or below, afaik)

This needs to be noted, please.

It's becoming a bigger and bigger issue that the help doesn't bother to point out which variants of the framework various items exist in.

If there's some special way that this is noted, please let me know.

Math.Round in Silverlight

Of the eight overloads of Math.Round in the .NET Framework, four are found in Silverlight. The remaining four overloads, all of which include a parameter of type MidpointRounding, do not exist.

More generally, Silverlight documentation is maintained as a a completely separate and independent documentation set from the full .NET Framework documentation. If MDSN is configured to be in Classic mode, though, you can determine whether a particular type or type member is supported by looking for a link to the Silverlight documentation in the version box at the top of the page.

--Ron Petrusha
Developer Division User Education

History

6/21/2010
matteliotspam

6/22/2010
R Petrusha - MSFT