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title description ms.date dev_langs
System.Single struct
Learn about the System.Single struct.
12/31/2023
CSharp
FSharp
VB

System.Single struct

[!INCLUDE context]

The xref:System.Single value type represents a single-precision 32-bit number with values ranging from negative 3.402823e38 to positive 3.402823e38, as well as positive or negative zero, xref:System.Single.PositiveInfinity, xref:System.Single.NegativeInfinity, and not a number (xref:System.Single.NaN). It is intended to represent values that are extremely large (such as distances between planets or galaxies) or extremely small (such as the molecular mass of a substance in kilograms) and that often are imprecise (such as the distance from earth to another solar system). The xref:System.Single type complies with the IEC 60559:1989 (IEEE 754) standard for binary floating-point arithmetic.

xref:System.Single?displayProperty=nameWithType provides methods to compare instances of this type, to convert the value of an instance to its string representation, and to convert the string representation of a number to an instance of this type. For information about how format specification codes control the string representation of value types, see Formatting Types, Standard Numeric Format Strings, and Custom Numeric Format Strings.

Floating-point representation and precision

The xref:System.Single data type stores single-precision floating-point values in a 32-bit binary format, as shown in the following table:

Part Bits
Significand or mantissa 0-22
Exponent 23-30
Sign (0 = positive, 1 = negative) 31

Just as decimal fractions are unable to precisely represent some fractional values (such as 1/3 or xref:System.Math.PI?displayProperty=nameWithType), binary fractions are unable to represent some fractional values. For example, 2/10, which is represented precisely by .2 as a decimal fraction, is represented by .0011111001001100 as a binary fraction, with the pattern "1100" repeating to infinity. In this case, the floating-point value provides an imprecise representation of the number that it represents. Performing additional mathematical operations on the original floating-point value often increases its lack of precision. For example, if you compare the results of multiplying .3 by 10 and adding .3 to .3 nine times, you will see that addition produces the less precise result, because it involves eight more operations than multiplication. Note that this disparity is apparent only if you display the two xref:System.Single values by using the "R" standard numeric format string, which, if necessary, displays all 9 digits of precision supported by the xref:System.Single type.

:::code language="csharp" source="./snippets/System/Single/Overview/csharp/representation1.cs" interactive="try-dotnet" id="Snippet3"::: :::code language="fsharp" source="./snippets/System/Single/Overview/fsharp/representation1.fs" id="Snippet3"::: :::code language="vb" source="./snippets/System/Single/Overview/vb/representation1.vb" id="Snippet3":::

Because some numbers cannot be represented exactly as fractional binary values, floating-point numbers can only approximate real numbers.

All floating-point numbers have a limited number of significant digits, which also determines how accurately a floating-point value approximates a real number. A xref:System.Single value has up to 7 decimal digits of precision, although a maximum of 9 digits is maintained internally. This means that some floating-point operations may lack the precision to change a floating-point value. The following example defines a large single-precision floating-point value, and then adds the product of xref:System.Single.Epsilon?displayProperty=nameWithType and one quadrillion to it. However, the product is too small to modify the original floating-point value. Its least significant digit is thousandths, whereas the most significant digit in the product is 10-30.

:::code language="csharp" source="./snippets/System/Single/Overview/csharp/representation2.cs" interactive="try-dotnet" id="Snippet4"::: :::code language="fsharp" source="./snippets/System/Single/Overview/fsharp/representation2.fs" id="Snippet4"::: :::code language="vb" source="./snippets/System/Single/Overview/vb/representation2.vb" id="Snippet4":::

The limited precision of a floating-point number has several consequences:

  • Two floating-point numbers that appear equal for a particular precision might not compare equal because their least significant digits are different. In the following example, a series of numbers are added together, and their total is compared with their expected total. Although the two values appear to be the same, a call to the Equals method indicates that they are not.

    :::code language="csharp" source="./snippets/System/Single/Overview/csharp/precisionlist3.cs" interactive="try-dotnet" id="Snippet6"::: :::code language="fsharp" source="./snippets/System/Single/Overview/fsharp/precisionlist3.fs" id="Snippet6"::: :::code language="vb" source="./snippets/System/Single/Overview/vb/precisionlist3.vb" id="Snippet6":::

    If you change the format items in the xref:System.Console.WriteLine%28System.String%2CSystem.Object%2CSystem.Object%29?displayProperty=nameWithType statement from {0} and {1} to {0:R} and {1:R} to display all significant digits of the two xref:System.Single values, it is clear that the two values are unequal because of a loss of precision during the addition operations. In this case, the issue can be resolved by calling the xref:System.Math.Round%28System.Double%2CSystem.Int32%29?displayProperty=nameWithType method to round the xref:System.Single values to the desired precision before performing the comparison.

  • A mathematical or comparison operation that uses a floating-point number might not yield the same result if a decimal number is used, because the binary floating-point number might not equal the decimal number. A previous example illustrated this by displaying the result of multiplying .3 by 10 and adding .3 to .3 nine times.

    When accuracy in numeric operations with fractional values is important, use the xref:System.Decimal type instead of the xref:System.Single type. When accuracy in numeric operations with integral values beyond the range of the xref:System.Int64 or xref:System.UInt64 types is important, use the xref:System.Numerics.BigInteger type.

  • A value might not round-trip if a floating-point number is involved. A value is said to round-trip if an operation converts an original floating-point number to another form, an inverse operation transforms the converted form back to a floating-point number, and the final floating-point number is equal to the original floating-point number. The round trip might fail because one or more least significant digits are lost or changed in a conversion. In the following example, three xref:System.Single values are converted to strings and saved in a file. As the output shows, although the values appear to be identical, the restored values are not equal to the original values.

    :::code language="csharp" source="./snippets/System/Single/Overview/csharp/precisionlist4a.cs" id="Snippet17"::: :::code language="fsharp" source="./snippets/System/Single/Overview/fsharp/precisionlist4a.fs" id="Snippet17"::: :::code language="vb" source="./snippets/System/Single/Overview/vb/PrecisionList4a.vb" id="Snippet17":::

    In this case, the values can be successfully round-tripped by using the "G9" standard numeric format string to preserve the full precision of xref:System.Single values, as the following example shows.

    :::code language="csharp" source="./snippets/System/Single/Overview/csharp/PrecisionList5a.cs" id="Snippet18"::: :::code language="fsharp" source="./snippets/System/Single/Overview/fsharp/PrecisionList5a.fs" id="Snippet18"::: :::code language="vb" source="./snippets/System/Single/Overview/vb/PrecisionList5a.vb" id="Snippet18":::

  • xref:System.Single values have less precision than xref:System.Double values. A xref:System.Single value that is converted to a seemingly equivalent xref:System.Double often does not equal the xref:System.Double value because of differences in precision. In the following example, the result of identical division operations is assigned to a xref:System.Double value and a xref:System.Single value. After the xref:System.Single value is cast to a xref:System.Double, a comparison of the two values shows that they are unequal.

    :::code language="csharp" source="./snippets/System/Double/Overview/csharp/precisionlist1.cs" interactive="try-dotnet" id="Snippet5"::: :::code language="fsharp" source="./snippets/System/Double/Overview/fsharp/precisionlist1.fs" id="Snippet5"::: :::code language="vb" source="./snippets/System/Double/Overview/vb/precisionlist1.vb" id="Snippet5":::

    To avoid this problem, either use the xref:System.Double data type in place of the xref:System.Single data type, or use the xref:System.Math.Round%2A method so that both values have the same precision.

Test for equality

To be considered equal, two xref:System.Single values must represent identical values. However, because of differences in precision between values, or because of a loss of precision by one or both values, floating-point values that are expected to be identical often turn out to be unequal due to differences in their least significant digits. As a result, calls to the xref:System.Single.Equals%2A method to determine whether two values are equal, or calls to the xref:System.Single.CompareTo%2A method to determine the relationship between two xref:System.Single values, often yield unexpected results. This is evident in the following example, where two apparently equal xref:System.Single values turn out to be unequal, because the first value has 7 digits of precision, whereas the second value has 9.

:::code language="csharp" source="./snippets/System/Single/Overview/csharp/comparison1.cs" interactive="try-dotnet" id="Snippet9"::: :::code language="fsharp" source="./snippets/System/Single/Overview/fsharp/comparison1.fs" id="Snippet9"::: :::code language="vb" source="./snippets/System/Single/Overview/vb/comparison1.vb" id="Snippet9":::

Calculated values that follow different code paths and that are manipulated in different ways often prove to be unequal. In the following example, one xref:System.Single value is squared, and then the square root is calculated to restore the original value. A second xref:System.Single is multiplied by 3.51 and squared before the square root of the result is divided by 3.51 to restore the original value. Although the two values appear to be identical, a call to the xref:System.Single.Equals%28System.Single%29 method indicates that they are not equal. Using the "G9" standard format string to return a result string that displays all the significant digits of each xref:System.Single value shows that the second value is .0000000000001 less than the first.

:::code language="csharp" source="./snippets/System/Single/Overview/csharp/comparison2.cs" interactive="try-dotnet" id="Snippet10"::: :::code language="fsharp" source="./snippets/System/Single/Overview/fsharp/comparison2.fs" id="Snippet10"::: :::code language="vb" source="./snippets/System/Single/Overview/vb/comparison2.vb" id="Snippet10":::

In cases where a loss of precision is likely to affect the result of a comparison, you can use the following techniques instead of calling the xref:System.Single.Equals%2A or xref:System.Single.CompareTo%2A method:

  • Call the xref:System.Math.Round%2A?displayProperty=nameWithType method to ensure that both values have the same precision. The following example modifies a previous example to use this approach so that two fractional values are equivalent.

    :::code language="csharp" source="./snippets/System/Single/Overview/csharp/comparison3.cs" interactive="try-dotnet" id="Snippet11"::: :::code language="fsharp" source="./snippets/System/Single/Overview/fsharp/comparison3.fs" id="Snippet11"::: :::code language="vb" source="./snippets/System/Single/Overview/vb/comparison3.vb" id="Snippet11":::

    The problem of precision still applies to rounding of midpoint values. For more information, see the xref:System.Math.Round%28System.Double%2CSystem.Int32%2CSystem.MidpointRounding%29?displayProperty=nameWithType method.

  • Test for approximate equality instead of equality. This technique requires that you define either an absolute amount by which the two values can differ but still be equal, or that you define a relative amount by which the smaller value can diverge from the larger value.

    [!WARNING] xref:System.Single.Epsilon?displayProperty=nameWithType is sometimes used as an absolute measure of the distance between two xref:System.Single values when testing for equality. However, xref:System.Single.Epsilon?displayProperty=nameWithType measures the smallest possible value that can be added to, or subtracted from, a xref:System.Single whose value is zero. For most positive and negative xref:System.Single values, the value of xref:System.Single.Epsilon?displayProperty=nameWithType is too small to be detected. Therefore, except for values that are zero, we do not recommend its use in tests for equality.

    The following example uses the latter approach to define an IsApproximatelyEqual method that tests the relative difference between two values. It also contrasts the result of calls to the IsApproximatelyEqual method and the xref:System.Single.Equals%28System.Single%29 method.

    :::code language="csharp" source="./snippets/System/Single/Overview/csharp/comparison4.cs" interactive="try-dotnet" id="Snippet12"::: :::code language="fsharp" source="./snippets/System/Single/Overview/fsharp/comparison4.fs" id="Snippet12"::: :::code language="vb" source="./snippets/System/Single/Overview/vb/comparison4.vb" id="Snippet12":::

Floating-point values and exceptions

Operations with floating-point values do not throw exceptions, unlike operations with integral types, which throw exceptions in cases of illegal operations such as division by zero or overflow. Instead, in these situations, the result of a floating-point operation is zero, positive infinity, negative infinity, or not a number (NaN):

  • If the result of a floating-point operation is too small for the destination format, the result is zero. This can occur when two very small floating-point numbers are multiplied, as the following example shows.

    :::code language="csharp" source="./snippets/System/Single/Overview/csharp/exceptional1.cs" interactive="try-dotnet" id="Snippet1"::: :::code language="fsharp" source="./snippets/System/Single/Overview/fsharp/exceptional1.fs" id="Snippet1"::: :::code language="vb" source="./snippets/System/Single/Overview/vb/exceptional1.vb" id="Snippet1":::

  • If the magnitude of the result of a floating-point operation exceeds the range of the destination format, the result of the operation is xref:System.Single.PositiveInfinity or xref:System.Single.NegativeInfinity, as appropriate for the sign of the result. The result of an operation that overflows xref:System.Single.MaxValue?displayProperty=nameWithType is xref:System.Single.PositiveInfinity, and the result of an operation that overflows xref:System.Single.MinValue?displayProperty=nameWithType is xref:System.Single.NegativeInfinity, as the following example shows.

    :::code language="csharp" source="./snippets/System/Single/Overview/csharp/exceptional2.cs" interactive="try-dotnet" id="Snippet2"::: :::code language="fsharp" source="./snippets/System/Single/Overview/fsharp/exceptional2.fs" id="Snippet2"::: :::code language="vb" source="./snippets/System/Single/Overview/vb/exceptional2.vb" id="Snippet2":::

    xref:System.Single.PositiveInfinity also results from a division by zero with a positive dividend, and xref:System.Single.NegativeInfinity results from a division by zero with a negative dividend.

  • If a floating-point operation is invalid, the result of the operation is xref:System.Single.NaN. For example, xref:System.Single.NaN results from the following operations:

    • Division by zero with a dividend of zero. Note that other cases of division by zero result in either xref:System.Single.PositiveInfinity or xref:System.Single.NegativeInfinity.
    • Any floating-point operation with invalid input. For example, attempting to find the square root of a negative value returns xref:System.Single.NaN.
    • Any operation with an argument whose value is xref:System.Single.NaN?displayProperty=nameWithType.

Type conversions

The xref:System.Single structure does not define any explicit or implicit conversion operators; instead, conversions are implemented by the compiler.

The following table lists the possible conversions of a value of the other primitive numeric types to a xref:System.Single value, It also indicates whether the conversion is widening or narrowing and whether the resulting xref:System.Single may have less precision than the original value.

Conversion from Widening/narrowing Possible loss of precision
xref:System.Byte Widening No
xref:System.Decimal Widening

Note that C# requires a cast operator.		 Yes. xref:System.Decimal supports 29 decimal digits of precision; xref:System.Single supports 9.
xref:System.Double Narrowing; out-of-range values are converted to xref:System.Double.NegativeInfinity?displayProperty=nameWithType or xref:System.Double.PositiveInfinity?displayProperty=nameWithType. Yes. xref:System.Double supports 17 decimal digits of precision; xref:System.Single supports 9.
xref:System.Int16 Widening No
xref:System.Int32 Widening Yes. xref:System.Int32 supports 10 decimal digits of precision; xref:System.Single supports 9.
xref:System.Int64 Widening Yes. xref:System.Int64 supports 19 decimal digits of precision; xref:System.Single supports 9.
xref:System.SByte Widening No
xref:System.UInt16 Widening No
xref:System.UInt32 Widening Yes. xref:System.UInt32 supports 10 decimal digits of precision; xref:System.Single supports 9.
xref:System.UInt64 Widening Yes. xref:System.Int64 supports 20 decimal digits of precision; xref:System.Single supports 9.

The following example converts the minimum or maximum value of other primitive numeric types to a xref:System.Single value.

:::code language="csharp" source="./snippets/System/Single/Overview/csharp/convert1.cs" id="Snippet20"::: :::code language="fsharp" source="./snippets/System/Single/Overview/fsharp/convert1.fs" id="Snippet20"::: :::code language="vb" source="./snippets/System/Single/Overview/vb/convert1.vb" id="Snippet20":::

In addition, the xref:System.Double values xref:System.Double.NaN?displayProperty=nameWithType, xref:System.Double.PositiveInfinity?displayProperty=nameWithType, and xref:System.Double.NegativeInfinity?displayProperty=nameWithType convert to xref:System.Single.NaN?displayProperty=nameWithType, xref:System.Single.PositiveInfinity?displayProperty=nameWithType, and xref:System.Single.NegativeInfinity?displayProperty=nameWithType, respectively.

Note that the conversion of the value of some numeric types to a xref:System.Single value can involve a loss of precision. As the example illustrates, a loss of precision is possible when converting xref:System.Decimal, xref:System.Double, xref:System.Int32, xref:System.Int64, xref:System.UInt32, and xref:System.UInt64 values to xref:System.Single values.

The conversion of a xref:System.Single value to a xref:System.Double is a widening conversion. The conversion may result in a loss of precision if the xref:System.Double type does not have a precise representation for the xref:System.Single value.

The conversion of a xref:System.Single value to a value of any primitive numeric data type other than a xref:System.Double is a narrowing conversion and requires a cast operator (in C#) or a conversion method (in Visual Basic). Values that are outside the range of the target data type, which are defined by the target type's MinValue and MaxValue properties, behave as shown in the following table.

Target type Result
Any integral type An xref:System.OverflowException exception if the conversion occurs in a checked context.

If the conversion occurs in an unchecked context (the default in C#), the conversion operation succeeds but the value overflows.
xref:System.Decimal An xref:System.OverflowException exception,

In addition, xref:System.Single.NaN?displayProperty=nameWithType, xref:System.Single.PositiveInfinity?displayProperty=nameWithType, and xref:System.Single.NegativeInfinity?displayProperty=nameWithType throw an xref:System.OverflowException for conversions to integers in a checked context, but these values overflow when converted to integers in an unchecked context. For conversions to xref:System.Decimal, they always throw an xref:System.OverflowException. For conversions to xref:System.Double, they convert to xref:System.Double.NaN?displayProperty=nameWithType, xref:System.Double.PositiveInfinity?displayProperty=nameWithType, and xref:System.Double.NegativeInfinity?displayProperty=nameWithType, respectively.

Note that a loss of precision may result from converting a xref:System.Single value to another numeric type. In the case of converting non-integral xref:System.Single values, as the output from the example shows, the fractional component is lost when the xref:System.Single value is either rounded (as in Visual Basic) or truncated (as in C# and F#). For conversions to xref:System.Decimal values, the xref:System.Single value may not have a precise representation in the target data type.

The following example converts a number of xref:System.Single values to several other numeric types. The conversions occur in a checked context in Visual Basic (the default), in C# (because of the checked keyword), and in F# (because of the open Checked statement). The output from the example shows the result for conversions in both a checked an unchecked context. You can perform conversions in an unchecked context in Visual Basic by compiling with the /removeintchecks+ compiler switch, in C# by commenting out the checked statement, and in F# by commenting out the open Checked statement.

:::code language="csharp" source="./snippets/System/Single/Overview/csharp/convert2.cs" id="Snippet21"::: :::code language="fsharp" source="./snippets/System/Single/Overview/fsharp/convert2.fs" id="Snippet21"::: :::code language="vb" source="./snippets/System/Single/Overview/vb/convert2.vb" id="Snippet21":::

For more information on the conversion of numeric types, see Type Conversion in .NET and Type Conversion Tables.

Floating-point functionality

The xref:System.Single structure and related types provide methods to perform the following categories of operations:

  • Comparison of values. You can call the xref:System.Single.Equals%2A method to determine whether two xref:System.Single values are equal, or the xref:System.Single.CompareTo%2A method to determine the relationship between two values.

    The xref:System.Single structure also supports a complete set of comparison operators. For example, you can test for equality or inequality, or determine whether one value is greater than or equal to another value. If one of the operands is a xref:System.Double, the xref:System.Single value is converted to a xref:System.Double before performing the comparison. If one of the operands is an integral type, it is converted to a xref:System.Single before performing the comparison. Although these are widening conversions, they may involve a loss of precision.

    [!WARNING] Because of differences in precision, two xref:System.Single values that you expect to be equal may turn out to be unequal, which affects the result of the comparison. See the Test for equality section for more information about comparing two xref:System.Single values.

    You can also call the xref:System.Single.IsNaN%2A, xref:System.Single.IsInfinity%2A, xref:System.Single.IsPositiveInfinity%2A, and xref:System.Single.IsNegativeInfinity%2A methods to test for these special values.

  • Mathematical operations. Common arithmetic operations such as addition, subtraction, multiplication, and division are implemented by language compilers and Common Intermediate Language (CIL) instructions rather than by xref:System.Single methods. If the other operand in a mathematical operation is a xref:System.Double, the xref:System.Single is converted to a xref:System.Double before performing the operation, and the result of the operation is also a xref:System.Double value. If the other operand is an integral type, it is converted to a xref:System.Single before performing the operation, and the result of the operation is also a xref:System.Single value.

    You can perform other mathematical operations by calling static (Shared in Visual Basic) methods in the xref:System.Math?displayProperty=nameWithType class. These include additional methods commonly used for arithmetic (such as xref:System.Math.Abs%2A?displayProperty=nameWithType, xref:System.Math.Sign%2A?displayProperty=nameWithType, and xref:System.Math.Sqrt%2A?displayProperty=nameWithType), geometry (such as xref:System.Math.Cos%2A?displayProperty=nameWithType and xref:System.Math.Sin%2A?displayProperty=nameWithType), and calculus (such as xref:System.Math.Log%2A?displayProperty=nameWithType). In all cases, the xref:System.Single value is converted to a xref:System.Double.

    You can also manipulate the individual bits in a xref:System.Single value. The xref:System.BitConverter.GetBytes%28System.Single%29?displayProperty=nameWithType method returns its bit pattern in a byte array. By passing that byte array to the xref:System.BitConverter.ToInt32%2A?displayProperty=nameWithType method, you can also preserve the xref:System.Single value's bit pattern in a 32-bit integer.

  • Rounding. Rounding is often used as a technique for reducing the impact of differences between values caused by problems of floating-point representation and precision. You can round a xref:System.Single value by calling the xref:System.Math.Round%2A?displayProperty=nameWithType method. However, note that the xref:System.Single value is converted to a xref:System.Double before the method is called, and the conversion can involve a loss of precision.

  • Formatting. You can convert a xref:System.Single value to its string representation by calling the xref:System.Single.ToString%2A method or by using the composite formatting feature. For information about how format strings control the string representation of floating-point values, see the Standard Numeric Format Strings and Custom Numeric Format Strings topics.

  • Parsing strings. You can convert the string representation of a floating-point value to a xref:System.Single value by calling the xref:System.Single.Parse%2A or xref:System.Single.TryParse%2A method. If the parse operation fails, the xref:System.Single.Parse%2A method throws an exception, whereas the xref:System.Single.TryParse%2A method returns false.

  • Type conversion. The xref:System.Single structure provides an explicit interface implementation for the xref:System.IConvertible interface, which supports conversion between any two standard .NET data types. Language compilers also support the implicit conversion of values for all other standard numeric types except for the conversion of xref:System.Double to xref:System.Single values. Conversion of a value of any standard numeric type other than a xref:System.Double to a xref:System.Single is a widening conversion and does not require the use of a casting operator or conversion method.

    However, conversion of 32-bit and 64-bit integer values can involve a loss of precision. The following table lists the differences in precision for 32-bit, 64-bit, and xref:System.Double types:

    Type Maximum precision (in decimal digits) Internal precision (in decimal digits)
    xref:System.Double 15 17
    xref:System.Int32 and xref:System.UInt32 10 10
    xref:System.Int64 and xref:System.UInt64 19 19
    xref:System.Single 7 9

    The problem of precision most frequently affects xref:System.Single values that are converted to xref:System.Double values. In the following example, two values produced by identical division operations are unequal, because one of the values is a single-precision floating point value that is converted to a xref:System.Double.

    :::code language="csharp" source="./snippets/System/Single/Overview/csharp/precisionlist1.cs" interactive="try-dotnet" id="Snippet5"::: :::code language="fsharp" source="./snippets/System/Single/Overview/fsharp/precisionlist1.fs" id="Snippet5"::: :::code language="vb" source="./snippets/System/Single/Overview/vb/precisionlist1.vb" id="Snippet5":::