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

code reference: System.Single.Epsilon#5

More precisely, the single-precision floating-point format consists of a sign, a 23-bit mantissa or significand, and an 8-bit exponent. As the following example shows, zero has an exponent of -126 and a mantissa of 0. float.Epsilon has an exponent of -126 and a mantissa of 1. This means that float.Epsilon is the smallest positive float value that is greater than zero and represents the smallest possible value and the smallest possible increment for a float whose exponent is -126.

code reference: System.Single.Epsilon#6

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

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 float.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 float.Epsilon.)

Platform Notes

On ARM systems, the value of the float.Epsilon constant is too small to be detected, so it equates to zero. You can define an alternative epsilon value that equals 1.175494351E-38 instead.

Namespace: System
Assembly: mscorlib (in mscorlib.dll)
Assembly Versions: 1.0.5000.0, 2.0.0.0, 4.0.0.0