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Precision, scale, and length (Transact-SQL)

  • Article

Applies to: SQL Server Azure SQL Database Azure SQL Managed Instance Azure Synapse Analytics Analytics Platform System (PDW) SQL analytics endpoint in Microsoft Fabric Warehouse in Microsoft Fabric SQL database in Microsoft Fabric

Precision is the number of digits in a number. Scale is the number of digits to the right of the decimal point in a number. For example, the number 123.45 has a precision of 5 and a scale of 2.

In SQL Server, the default maximum precision of numeric and decimal data types is 38.

Length for a numeric data type is the number of bytes that are used to store the number. For varchar and char, the length of a character string is the number of bytes. For nvarchar and nchar, the length of the character string is the number of byte-pairs. The length for binary, varbinary, and image data types is the number of bytes. For example, an int data type can hold 10 digits, is stored in 4 bytes, and doesn't accept decimal points. The int data type has a precision of 10, a length of 4, and a scale of 0.

  • When you concatenate two char, varchar, binary, or varbinary expressions, the length of the resulting expression is the sum of the lengths of the two source expressions, up to 8,000 bytes.

  • When you concatenate two nchar or nvarchar expressions, the length of the resulting expression is the sum of the lengths of the two source expressions, up to 4,000 byte-pairs.

  • When you compare two expressions of the same data type but different lengths by using UNION, EXCEPT, or INTERSECT, the resulting length is the longer of the two expressions.

Remarks

The precision and scale of the numeric data types besides decimal are fixed. When an arithmetic operator has two expressions of the same type, the result has the same data type with the precision and scale defined for that type. If an operator has two expressions with different numeric data types, the rules of data type precedence define the data type of the result. The result has the precision and scale defined for its data type.

The following table defines how the precision and scale of the result are calculated when the result of an operation is of type decimal. The result is decimal when either:

  • Both expressions are decimal.
  • One expression is decimal and the other is a data type with a lower precedence than decimal.

The operand expressions are denoted as expression e1, with precision p1 and scale s1, and expression e2, with precision p2 and scale s2. The precision and scale for any expression that isn't decimal is the precision and scale defined for the data type of the expression. The function max(a, b) indicates to take the greater value of a or b. Similarly, min(a, b) indicates to take the smaller value of a or b.

Operation Result precision Result scale 1
e1 + e2 max(s1, s2) + max(p1 - s1, p2 - s2) + 1 max(s1, s2)
e1 - e2 max(s1, s2) + max(p1 - s1, p2 - s2) + 1 max(s1, s2)
e1 * e2 p1 + p2 + 1 s1 + s2
e1 / e2 p1 - s1 + s2 + max(6, s1 + p2 + 1) max(6, s1 + p2 + 1)
e1 { UNION | EXCEPT | INTERSECT } e2 max(s1, s2) + max(p1 - s1, p2 - s2) max(s1, s2)
e1 % e2 min(p1 - s1, p2 - s2) + max(s1, s2) max(s1, s2)

1 The result precision and scale have an absolute maximum of 38. When a result precision is greater than 38, it's reduced to 38, and the corresponding scale is reduced to try to prevent truncating the integral part of a result. In some cases such as multiplication or division, scale factor isn't reduced, to maintain decimal precision, although the overflow error can be raised.

In addition and subtraction operations, we need max(p1 - s1, p2 - s2) places to store the integral part of the decimal number. If there isn't enough space to store them (that is, max(p1 - s1, p2 - s2) < min(38, precision) - scale), the scale is reduced to provide enough space for the integral part. The resulting scale is min(precision, 38) - max(p1 - s1, p2 - s2), so the fractional part might be rounded to fit into the resulting scale.

In multiplication and division operations, we need precision - scale places to store the integral part of the result. The scale might be reduced using the following rules:

  1. The resulting scale is reduced to min(scale, 38 - (precision-scale)) if the integral part is less than 32, because it can't be greater than 38 - (precision-scale). The result might be rounded in this case.
  2. The scale isn't changed if it's less than 6 and if the integral part is greater than 32. In this case, an overflow error might be raised if it can't fit into decimal(38, scale).
  3. The scale is set to 6 if it's greater than 6 and if the integral part is greater than 32. In this case, both the integral part and scale would be reduced and resulting type is decimal(38, 6). The result might be rounded to 7 decimal places, or the overflow error is thrown if the integral part can't fit into 32 digits.

Examples

The following expression returns result 0.00000090000000000 without rounding, because the result can fit into decimal(38, 17):

SELECT CAST(0.0000009000 AS DECIMAL(30, 20)) * CAST(1.0000000000 AS DECIMAL(30, 20)) [decimal(38, 17)];

In this case precision is 61, and scale is 40.

The integral part (precision-scale = 21) is less than 32, so this case is the first case in the multiplication rules, and scale is calculated as min(scale, 38 - (precision-scale)) = min(40, 38 - (61-40)) = 17. Result type is decimal(38, 17).

The following expression returns result 0.000001 to fit into decimal(38, 6):

SELECT CAST(0.0000009000 AS DECIMAL(30, 10)) * CAST(1.0000000000 AS DECIMAL(30, 10)) [decimal(38, 6)];

In this case precision is 61, and scale is 20.

Scale is greater than 6 and the integral part (precision-scale = 41) is greater than 32. This case is the third case in the multiplication rules, and the result type is decimal(38, 6).

See also