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Single.Epsilon Field

Updated: January 2010

Represents the smallest positive Single value greater than zero. This field is constant.

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

public const float Epsilon

The value of the Epsilon property reflects the smallest positive Single value that is significant in numeric operations or comparisons when the value of the Single instance is zero. For example, the following code shows that zero and Epsilon are considered to be unequal values, whereas zero and half the value of Epsilon are considered to be equal.

using System;

public class Example
   public static void Main()
      float[] values = { 0f, Single.Epsilon, Single.Epsilon * .5f };

      for (int ctr = 0; ctr <= values.Length - 2; ctr++)
         for (int ctr2 = ctr + 1; ctr2 <= values.Length - 1; ctr2++)
            Console.WriteLine("{0:r} = {1:r}: {2}", 
                              values[ctr], values[ctr2],  
// The example displays the following output: 
//       0 = 1.401298E-45: False 
//       0 = 0: True 
//       1.401298E-45 = 0: False

However, the Epsilon property is not a general measure of precision of the Single type; it applies only to Single instances that have a value of zero.


The value of the Epsilon property is not equivalent to machine epsilon, which represents the upper bound of the relative error due to rounding in floating-point arithmetic.

The value of this constant is 1.4e-45.

Two apparently equivalent floating-point numbers might not compare equal because of differences in their least significant digits. For example, the C# expression, (float)1/3 == (float)0.33333, does not compare equal because the division operation on the left side has maximum precision while the constant on the right side is precise only to the specified digits. If you create a custom algorithm that determines whether two floating-point numbers can be considered equal, you must use a value that is greater than the Epsilon constant to establish the acceptable absolute margin of difference for the two values to be considered equal. (Typically, that margin of difference is many times greater than Epsilon.)

Windows 7, Windows Vista, Windows XP SP2, Windows XP Media Center Edition, Windows XP Professional x64 Edition, Windows XP Starter Edition, Windows Server 2008 R2, Windows Server 2008, Windows Server 2003, Windows Server 2000 SP4, Windows Millennium Edition, Windows 98, Windows CE, Windows Mobile for Smartphone, Windows Mobile for Pocket PC, Xbox 360, Zune

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

.NET Framework

Supported in: 3.5, 3.0, 2.0, 1.1, 1.0

.NET Compact Framework

Supported in: 3.5, 2.0, 1.0

XNA Framework

Supported in: 3.0, 2.0, 1.0




January 2010

Removed the example.

Customer feedback.

December 2009

Expanded the Remarks section.

Customer feedback.

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