java.lang.Object
  └ java.lang.Number
      └ java.math.BigDecimal

Immutable, arbitrary-precision signed decimal numbers. A BigDecimal consists of an arbitrary precision integer unscaled value and a 32-bit integer scale. If zero or positive, the scale is the number of digits to the right of the decimal point. If negative, the unscaled value of the number is multiplied by ten to the power of the negation of the scale. The value of the number represented by the BigDecimal is therefore (unscaledValue × 10^-scale).

The BigDecimal class provides operations for arithmetic, scale manipulation, rounding, comparison, hashing, and format conversion. The method provides a canonical representation of a BigDecimal.

The BigDecimal class gives its user complete control over rounding behavior. If no rounding mode is specified and the exact result cannot be represented, an exception is thrown; otherwise, calculations can be carried out to a chosen precision and rounding mode by supplying an appropriate object to the operation. In either case, eight rounding modes are provided for the control of rounding. Using the integer fields in this class (such as ) to represent rounding mode is largely obsolete; the enumeration values of the RoundingMode enum, (such as ) should be used instead.

When a MathContext object is supplied with a precision setting of 0 (for example, ), arithmetic operations are exact, as are the arithmetic methods which take no MathContext object. (This is the only behavior that was supported in releases prior to 5.) As a corollary of computing the exact result, the rounding mode setting of a MathContext object with a precision setting of 0 is not used and thus irrelevant. In the case of divide, the exact quotient could have an infinitely long decimal expansion; for example, 1 divided by 3. If the quotient has a nonterminating decimal expansion and the operation is specified to return an exact result, an ArithmeticException is thrown. Otherwise, the exact result of the division is returned, as done for other operations.

When the precision setting is not 0, the rules of BigDecimal arithmetic are broadly compatible with selected modes of operation of the arithmetic defined in ANSI X3.274-1996 and ANSI X3.274-1996/AM 1-2000 (section 7.4). Unlike those standards, BigDecimal includes many rounding modes, which were mandatory for division in BigDecimal releases prior to 5. Any conflicts between these ANSI standards and the BigDecimal specification are resolved in favor of BigDecimal.

Since the same numerical value can have different representations (with different scales), the rules of arithmetic and rounding must specify both the numerical result and the scale used in the result's representation.

In general the rounding modes and precision setting determine how operations return results with a limited number of digits when the exact result has more digits (perhaps infinitely many in the case of division) than the number of digits returned. First, the total number of digits to return is specified by the MathContext's precision setting; this determines the result's precision. The digit count starts from the leftmost nonzero digit of the exact result. The rounding mode determines how any discarded trailing digits affect the returned result.

For all arithmetic operators , the operation is carried out as though an exact intermediate result were first calculated and then rounded to the number of digits specified by the precision setting (if necessary), using the selected rounding mode. If the exact result is not returned, some digit positions of the exact result are discarded. When rounding increases the magnitude of the returned result, it is possible for a new digit position to be created by a carry propagating to a leading "9" digit. For example, rounding the value 999.9 to three digits rounding up would be numerically equal to one thousand, represented as 100×10¹. In such cases, the new "1" is the leading digit position of the returned result.

Besides a logical exact result, each arithmetic operation has a preferred scale for representing a result. The preferred scale for each operation is listed in the table below.

Preferred Scales for Results of Arithmetic Operations

Operation	Preferred Scale of Result
Add	max(addend.scale(), augend.scale())
Subtract	max(minuend.scale(), subtrahend.scale())
Multiply	multiplier.scale() + multiplicand.scale()
Divide	dividend.scale() - divisor.scale()

These scales are the ones used by the methods which return exact arithmetic results; except that an exact divide may have to use a larger scale since the exact result may have more digits. For example, 1/32 is 0.03125.

Before rounding, the scale of the logical exact intermediate result is the preferred scale for that operation. If the exact numerical result cannot be represented in precision digits, rounding selects the set of digits to return and the scale of the result is reduced from the scale of the intermediate result to the least scale which can represent the precision digits actually returned. If the exact result can be represented with at most precision digits, the representation of the result with the scale closest to the preferred scale is returned. In particular, an exactly representable quotient may be represented in fewer than precision digits by removing trailing zeros and decreasing the scale. For example, rounding to three digits using the {@linkplain RoundingMode#FLOOR floor} rounding mode,
19/100 = 0.19 // integer=19, scale=2
but
21/110 = 0.190 // integer=190, scale=3

Note that for add, subtract, and multiply, the reduction in scale will equal the number of digit positions of the exact result which are discarded. If the rounding causes a carry propagation to create a new high-order digit position, an additional digit of the result is discarded than when no new digit position is created.

Other methods may have slightly different rounding semantics. For example, the result of the pow method using the {@linkplain #pow(int, MathContext) specified algorithm} can occasionally differ from the rounded mathematical result by more than one unit in the last place, one {@linkplain #ulp() ulp}.

Two types of operations are provided for manipulating the scale of a BigDecimal: scaling/rounding operations and decimal point motion operations. Scaling/rounding operations (setScale and round) return a BigDecimal whose value is approximately (or exactly) equal to that of the operand, but whose scale or precision is the specified value; that is, they increase or decrease the precision of the stored number with minimal effect on its value. Decimal point motion operations (movePointLeft and movePointRight) return a BigDecimal created from the operand by moving the decimal point a specified distance in the specified direction.

For the sake of brevity and clarity, pseudo-code is used throughout the descriptions of BigDecimal methods. The pseudo-code expression (i + j) is shorthand for "a BigDecimal whose value is that of the BigDecimal i added to that of the BigDecimal j." The pseudo-code expression (i == j) is shorthand for "true if and only if the BigDecimal i represents the same value as the BigDecimal j." Other pseudo-code expressions are interpreted similarly. Square brackets are used to represent the particular BigInteger and scale pair defining a BigDecimal value; for example [19, 2] is the BigDecimal numerically equal to 0.19 having a scale of 2.

Note: care should be exercised if BigDecimal objects are used as keys in a SortedMap or elements in a SortedSet since BigDecimal's natural ordering is inconsistent with equals. See , or for more information.

All methods and constructors for this class throw NullPointerException when passed a null object reference for any input parameter.