System.Double.Epsilon Field

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

Value: 4.94065645841247E-324

## Syntax

public const double Epsilon

## Remarks

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

code reference: System.Double.Epsilon#5

More precisely, the floating point format consists of a sign, a 52-bit mantissa or significand, and an 11-bit exponent. As the following example shows, zero has an exponent of -1022 and a mantissa of 0. double.Epsilon has an exponent of -1022 and a mantissa of 1. This means that double.Epsilon is the smallest positive double value greater than zero and represents the smallest possible value and the smallest possible increment for a double whose exponent is -1022.

code reference: System.Double.Epsilon#6

However, the double.Epsilon property is not a general measure of precision of the double type; it applies only to double instances that have a value of zero or an exponent of -1022.

Note:

The value of the double.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 4.94065645841247e-324.

Two apparently equivalent floating-point numbers might not compare equal because of differences in their least significant digits. For example, the C# expression, (double)1/3 == (double)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, we do not recommend that you base your algorithm on the value of the double.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 double.Epsilon.) For information about comparing two double-precision floating-point values, see double and double.Equals(double).

## Platform Notes

On ARM systems, the value of the double.Epsilon constant is too small to be detected, so it equates to zero. You can define an alternative epsilon value that equals 2.2250738585072014E-308 instead.

## Requirements

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