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.

Module Example
   Public Sub Main()
      Dim values() As Single = { 0, Single.Epsilon, Single.Epsilon * .5 }

      For ctr As Integer = 0 To values.Length - 2
         For ctr2 As Integer = ctr + 1 To values.Length - 1
            Console.WriteLine("{0:r} = {1:r}: {2}", _
                              values(ctr), values(ctr2), _ 
                              values(ctr).Equals(values(ctr2)))
         Next
         Console.WriteLine()
      Next      
   End Sub
End Module
' The example displays the following output:
'       0 = 1.401298E-45: False
'       0 = 0: True
'       
'       1.401298E-45 = 0: False

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],  
                              values[ctr].Equals(values[ctr2]));
         }
         Console.WriteLine();
      }      
   }
}
// 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.

Note
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.)

.NET Framework

.NET Framework Client Profile

Portable Class Library

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

Reference