Arithmetic functions

Overview

Arithmetic functions work for any two operands of type UInt8, UInt16, UInt32, UInt64, Int8, Int16, Int32, Int64, Float32, or Float64. Before performing the operation, both operands are cast to the result type. The result type is determined as follows (unless specified differently in the function documentation below):

If both operands are up to 32 bits wide, the size of the result type will be the size of the next bigger type following the bigger of the two operands (integer size promotion). For example, UInt8 + UInt16 = UInt32 or Float32 * Float32 = Float64.
If one of the operands has 64 or more bits, the size of the result type will be the same size as the bigger of the two operands. For example, UInt32 + UInt128 = UInt128 or Float32 * Float64 = Float64.
If one of the operands is signed, the result type will also be signed, otherwise it will be unsigned. For example, UInt32 * Int32 = Int64 or UInt32 * UInt32 = UInt64.

These rules make sure that the result type will be the smallest type which can represent all possible results. While this introduces a risk of overflows around the value range boundary, it ensures that calculations are performed quickly using the maximum native integer width of 64 bit. This behavior also guarantees compatibility with many other databases which provide 64 bit integers (BIGINT) as the biggest integer type. Example:

SELECT toTypeName(0), toTypeName(0 + 0), toTypeName(0 + 0 + 0), toTypeName(0 + 0 + 0 + 0)

┌─toTypeName(0)─┬─toTypeName(plus(0, 0))─┬─toTypeName(plus(plus(0, 0), 0))─┬─toTypeName(plus(plus(plus(0, 0), 0), 0))─┐
│ UInt8         │ UInt16                 │ UInt32                          │ UInt64                                   │
└───────────────┴────────────────────────┴─────────────────────────────────┴──────────────────────────────────────────┘

Overflows are produced the same way as in C++.

abs

Introduced in: v1.1.0 Calculates the absolute value of x. Has no effect if x is of an unsigned type. If x is of a signed type, it returns an unsigned number. Syntax

abs(x)

Arguments

x — Value to get the absolute value of

Returned value The absolute value of x Examples Usage example

Query

SELECT abs(-0.5)

Response

0.5

avg2

Introduced in: v25.11.0 Computes and returns the average value of the provided arguments. Supports numerical and temporal types. Syntax

avg2(x1, x2])

Arguments

x1, x2] — Accepts two values for averaging.

Returned value Returns the average value of the provided arguments, promoted to the largest compatible type. Examples Numeric types

Query

SELECT avg2(toUInt8(3), 1.0) AS result, toTypeName(result) AS type;
-- The type returned is a Float64 as the UInt8 must be promoted to 64 bit for the comparison.

Response

┌─result─┬─type────┐
│      2 │ Float64 │
└────────┴─────────┘

Decimal types

Query

SELECT avg2(toDecimal32(1, 2), 2) AS result, toTypeName(result) AS type;

Response

┌─result─┬─type──────────┐
│    1.5 │ Decimal(9, 2) │
└────────┴───────────────┘

Date types

Query

SELECT avg2(toDate('2025-01-01'), toDate('2025-01-05')) AS result, toTypeName(result) AS type;

Response

┌─────result─┬─type─┐
│ 2025-01-03 │ Date │
└────────────┴──────┘

DateTime types

Query

SELECT avg2(toDateTime('2025-01-01 00:00:00'), toDateTime('2025-01-03 12:00:00')) AS result, toTypeName(result) AS type;

Response

┌──────────────result─┬─type─────┐
│ 2025-01-02 06:00:00 │ DateTime │
└─────────────────────┴──────────┘

Time64 types

Query

SELECT avg2(toTime64('12:00:00', 0), toTime64('14:00:00', 0)) AS result, toTypeName(result) AS type;

Response

┌───result─┬─type──────┐
│ 13:00:00 │ Time64(0) │
└──────────┴───────────┘

byteSwap

Introduced in: v23.10.0 Reverses the bytes of an integer, i.e. changes its endianness. The below example can be worked out in the following manner:

Convert the base-10 integer to its equivalent hexadecimal format in big-endian format, i.e. 3351772109 -> C7 C7 FB CD (4 bytes)
Reverse the bytes, i.e. C7 C7 FB CD -> CD FB C7 C7
Convert the result back to an integer assuming big-endian, i.e. CD FB C7 C7 -> 3455829959 One use case of this function is reversing IPv4s:

┌─toIPv4(byteSwap(toUInt32(toIPv4('205.251.199.199'))))─┐
│ 199.199.251.205                                       │
└───────────────────────────────────────────────────────┘

Syntax

byteSwap(x)

Arguments

x — An integer value. (U)Int*

Returned value Returns x with bytes reversed. (U)Int* Examples Usage example

Query

SELECT byteSwap(3351772109)

Response

3455829959

8-bit

Query

SELECT byteSwap(54)

Response

16-bit

Query

SELECT byteSwap(4135)

Response

32-bit

Query

SELECT byteSwap(3351772109)

Response

3455829959

64-bit

Query

SELECT byteSwap(123294967295)

Response

18439412204227788800

divide

Introduced in: v1.1.0 Calculates the quotient of two values a and b. The result type is always Float64. Integer division is provided by the intDiv function.

Division by 0 returns inf, -inf, or nan.

Syntax

divide(x, y)

Arguments

x — Dividend - y — Divisor

Returned value The quotient of x and y Examples Dividing two numbers

Query

SELECT divide(25,5) AS quotient, toTypeName(quotient)

Response

5 Float64

Dividing by zero

Query

SELECT divide(25,0)

Response

inf

divideDecimal

Introduced in: v22.12.0 Performs division on two decimals. Result value will be of type Decimal256. Result scale can be explicitly specified by result_scale argument (const Integer in range [0, 76]). If not specified, the result scale is the max scale of given arguments.

These function work significantly slower than usual divide. In case you don’t really need controlled precision and/or need fast computation, consider using divide.

Syntax

divideDecimal(x, y[, result_scale])

Arguments

x — First value: Decimal. - y — Second value: Decimal. - result_scale — Scale of result. Type Int/UInt.

Returned value The result of division with given scale. Decimal256 Examples Example 1

Query

divideDecimal(toDecimal256(-12, 0), toDecimal32(2.1, 1), 10)

Response

┌─divideDecimal(toDecimal256(-12, 0), toDecimal32(2.1, 1), 10)─┐
│                                                -5.7142857142 │
└──────────────────────────────────────────────────────────────┘

Example 2

Query

SELECT toDecimal64(-12, 1) / toDecimal32(2.1, 1);
SELECT toDecimal64(-12, 1) as a, toDecimal32(2.1, 1) as b, divideDecimal(a, b, 1), divideDecimal(a, b, 5);

Response

┌─divide(toDecimal64(-12, 1), toDecimal32(2.1, 1))─┐
│                                             -5.7 │
└──────────────────────────────────────────────────┘
┌───a─┬───b─┬─divideDecimal(toDecimal64(-12, 1), toDecimal32(2.1, 1), 1)─┬─divideDecimal(toDecimal64(-12, 1), toDecimal32(2.1, 1), 5)─┐
│ -12 │ 2.1 │                                                       -5.7 │                                                   -5.71428 │
└─────┴─────┴────────────────────────────────────────────────────────────┴────────────────────────────────────────────────────────────┘

divideOrNull

Introduced in: v25.5.0 Same as divide but returns NULL when dividing by zero. Syntax

divideOrNull(x, y)

Arguments

x — Dividend - y — Divisor

Returned value The quotient of x and y, or NULL. Examples Dividing by zero

Query

SELECT divideOrNull(25, 0)

Response

\N

gcd

Introduced in: v1.1.0 Returns the greatest common divisor of two values a and b. An exception is thrown when dividing by zero or when dividing a minimal negative number by minus one. Syntax

gcd(x, y)

Arguments

x — First integer - y — Second integer

Returned value The greatest common divisor of x and y. Examples Usage example

Query

SELECT gcd(12, 18)

Response

ifNotFinite

Introduced in: v20.3.0 Checks whether a floating point value is finite. You can get a similar result by using the ternary operator: isFinite(x) ? x : y. Syntax

ifNotFinite(x,y)

Arguments

x — Value to check if infinite. Float*
y — Fallback value. Float*

Returned value

x if x is finite.
y if x is not finite.

Examples Usage example

Query

SELECT 1/0 AS infimum, ifNotFinite(infimum,42)

Response

inf  42

intDiv

Introduced in: v1.1.0 Performs an integer division of two values x by y. In other words it computes the quotient rounded down to the next smallest integer. The result has the same width as the dividend (the first parameter). An exception is thrown when dividing by zero, when the quotient does not fit in the range of the dividend, or when dividing a minimal negative number by minus one. Syntax

intDiv(x, y)

Arguments

x — Left hand operand. - y — Right hand operand.

Returned value Result of integer division of x and y Examples Integer division of two floats

Query

SELECT intDiv(toFloat64(1), 0.001) AS res, toTypeName(res)

Response

┌──res─┬─toTypeName(intDiv(toFloat64(1), 0.001))─┐
│ 1000 │ Int64                                   │
└──────┴─────────────────────────────────────────┘

Quotient does not fit in the range of the dividend

Query

SELECT
intDiv(1, 0.001) AS res,
toTypeName(res)

Response

Received exception from server (version 23.2.1):
Code: 153. DB::Exception: Received from localhost:9000. DB::Exception:
Cannot perform integer division, because it will produce infinite or too
large number: While processing intDiv(1, 0.001) AS res, toTypeName(res).
(ILLEGAL_DIVISION)

intDivOrNull

Introduced in: v25.5.0 Same as intDiv but returns NULL when dividing by zero or when dividing a minimal negative number by minus one. Syntax

intDivOrNull(x, y)

Arguments

x — Left hand operand. (U)Int*
y — Right hand operand. (U)Int*

Returned value Result of integer division of x and y, or NULL. Examples Integer division by zero

Query

SELECT intDivOrNull(1, 0)

Response

\N

Dividing a minimal negative number by minus 1

Query

SELECT intDivOrNull(-9223372036854775808, -1)

Response

\N

intDivOrZero

Introduced in: v1.1.0 Same as intDiv but returns zero when dividing by zero or when dividing a minimal negative number by minus one. Syntax

intDivOrZero(a, b)

Arguments

a — Left hand operand. (U)Int*
b — Right hand operand. (U)Int*

Returned value Result of integer division of a and b, or zero. Examples Integer division by zero

Query

SELECT intDivOrZero(1, 0)

Response

Dividing a minimal negative number by minus 1

Query

SELECT intDivOrZero(0.05, -1)

Response

isFinite

Introduced in: v1.1.0 Returns 1 if the Float32 or Float64 argument not infinite and not a NaN, otherwise this function returns 0. Syntax

isFinite(x)

Arguments

x — Number to check for finiteness. Float*

Returned value 1 if x is not infinite and not NaN, otherwise 0. Examples Test if a number is finite

Query

SELECT isFinite(inf)

Response

isInfinite

Introduced in: v1.1.0 Returns 1 if the Float32 or Float64 argument is infinite, otherwise this function returns 0. Note that 0 is returned for a NaN. Syntax

isInfinite(x)

Arguments

x — Number to check for infiniteness. Float*

Returned value 1 if x is infinite, otherwise 0 (including for NaN). Examples Test if a number is infinite

Query

SELECT isInfinite(inf), isInfinite(NaN), isInfinite(10))

Response

1 0 0

isNaN

Introduced in: v1.1.0 Returns 1 if the Float32 and Float64 argument is NaN, otherwise returns 0. Syntax

isNaN(x)

Arguments

x — Argument to evaluate for if it is NaN. Float*

Returned value 1 if NaN, otherwise 0 Examples Usage example

Query

SELECT isNaN(NaN)

Response

lcm

Introduced in: v1.1.0 Returns the least common multiple of two values x and y. An exception is thrown when dividing by zero or when dividing a minimal negative number by minus one. Syntax

lcm(x, y)

Arguments

x — First integer. (U)Int*
y — Second integer. (U)Int*

Returned value Returns the least common multiple of x and y. (U)Int* Examples Usage example

Query

SELECT lcm(6, 8)

Response

max2

Introduced in: v21.11.0 Returns the bigger of two numeric values x and y. Syntax

max2(x, y)

Arguments

x — First value (U)Int8/16/32/64 or Float* or Decimal
y — Second value (U)Int8/16/32/64 or Float* or Decimal

Returned value Returns the bigger value of x and y. Float64 Examples Usage example

Query

SELECT max2(-1, 2)

Response

midpoint

Introduced in: v25.11.0 Computes and returns the average value of the provided arguments. Supports numerical and temporal types. Syntax

midpoint(x1[, x2, ...])

Arguments

x1[, x2, ...] — Accepts a single value or multiple values for averaging.

Returned value Returns the average value of the provided arguments, promoted to the largest compatible type. Examples Numeric types

Query

SELECT midpoint(1, toUInt8(3), 0.5) AS result, toTypeName(result) AS type;
-- The type returned is a Float64 as the UInt8 must be promoted to 64 bit for the comparison.

Response

┌─result─┬─type────┐
│    1.5 │ Float64 │
└────────┴─────────┘

Decimal types

Query

SELECT midpoint(toDecimal32(1.5, 2), toDecimal32(1, 1), 2) AS result, toTypeName(result) AS type;

Response

┌─result─┬─type──────────┐
│    1.5 │ Decimal(9, 2) │
└────────┴───────────────┘

Date types

Query

SELECT midpoint(toDate('2025-01-01'), toDate('2025-01-05')) AS result, toTypeName(result) AS type;

Response

┌─────result─┬─type─┐
│ 2025-01-03 │ Date │
└────────────┴──────┘

DateTime types

Query

SELECT midpoint(toDateTime('2025-01-01 00:00:00'), toDateTime('2025-01-03 12:00:00')) AS result, toTypeName(result) AS type;

Response

┌──────────────result─┬─type─────┐
│ 2025-01-02 06:00:00 │ DateTime │
└─────────────────────┴──────────┘

Time64 types

Query

SELECT midpoint(toTime64('12:00:00', 0), toTime64('14:00:00', 0)) AS result, toTypeName(result) AS type;

Response

┌───result─┬─type──────┐
│ 13:00:00 │ Time64(0) │
└──────────┴───────────┘

min2

Introduced in: v21.11.0 Returns the smaller of two numeric values x and y. Syntax

min2(x, y)

Arguments

x — First value (U)Int8/16/32/64 or Float* or Decimal
y — Second value (U)Int8/16/32/64 or Float* or Decimal

Returned value Returns the smaller value of x and y. Float64 Examples Usage example

Query

SELECT min2(-1, 2)

Response

-1

minus

Introduced in: v1.1.0 Calculates the difference of two values a and b. The result is always signed. Similar to plus, it is possible to subtract an integer from a date or date with time. Additionally, subtraction between date with time is supported, resulting in the time difference between them. Syntax

minus(x, y)

Arguments

x — Minuend. - y — Subtrahend.

Returned value x minus y Examples Subtracting two numbers

Query

SELECT minus(10, 5)

Response

Subtracting an integer and a date

Query

SELECT minus(toDate('2025-01-01'),5)

Response

2024-12-27

modulo

Introduced in: v1.1.0 Calculates the remainder of the division of two values a by b. The result type is an integer if both inputs are integers. If one of the inputs is a floating-point number, the result type is Float64. The remainder is computed like in C++. Truncated division is used for negative numbers. An exception is thrown when dividing by zero or when dividing a minimal negative number by minus one. Syntax

modulo(a, b)

Aliases: mod Arguments

a — The dividend - b — The divisor (modulus)

Returned value The remainder of a % b Examples Usage example

Query

SELECT modulo(5, 2)

Response

moduloLegacy

Introduced in: v1.1.0 Calculates the remainder of a division. This is the legacy modulo implementation that uses the C++ % operator, which may produce negative results for negative arguments. This function exists for backward compatibility with old table partitioning logic. Use modulo or positiveModulo for standard behavior. Syntax

moduloLegacy(a, b)

Arguments

a — The dividend. (U)Int* or Float*
b — The divisor. (U)Int* or Float*

Returned value Returns the remainder of the division. (U)Int* or Float* Examples Basic usage

Query

SELECT moduloLegacy(10, 3)

Response

moduloOrNull

Introduced in: v25.5.0 Calculates the remainder when dividing a by b. Similar to function modulo except that moduloOrNull will return NULL if the right argument is 0. Syntax

moduloOrNull(x, y)

Aliases: modOrNull Arguments

x — The dividend. (U)Int* or Float*
y — The divisor (modulus). (U)Int* or Float*

Returned value Returns the remainder of the division of x by y, or null when the divisor is zero. Examples moduloOrNull by zero

Query

SELECT moduloOrNull(5, 0)

Response

\N

moduloOrZero

Introduced in: v20.3.0 Like modulo but returns zero when the divisor is zero, as opposed to an exception with the modulo function. Syntax

moduloOrZero(a, b)

Arguments

a — The dividend. (U)Int* or Float*
b — The divisor (modulus). (U)Int* or Float*

Returned value Returns the remainder of a % b, or 0 when the divisor is 0. Examples Usage example

Query

SELECT moduloOrZero(5, 0)

Response

multiply

Introduced in: v1.1.0 Calculates the product of two values x and y. Syntax

multiply(x, y)

Arguments

x — factor. (U)Int* or Float* or Decimal
y — factor. (U)Int* or Float* or Decimal

Returned value Returns the product of x and y Examples Multiplying two numbers

Query

SELECT multiply(5,5)

Response

multiplyDecimal

Introduced in: v22.12.0 Performs multiplication on two decimals. Result value will be of type Decimal256. Result scale can be explicitly specified by result_scale argument (const Integer in range [0, 76]). If not specified, the result scale is the max scale of given arguments.

These functions work significantly slower than usual multiply. In case you don’t really need controlled precision and/or need fast computation, consider using multiply

Syntax

multiplyDecimal(a, b[, result_scale])

Arguments

a — First value. Decimal
b — Second value. Decimal
result_scale — Scale of result. (U)Int*

Returned value The result of multiplication with the given scale. Type: Decimal256 Examples Usage example

Query

SELECT multiplyDecimal(toDecimal256(-12, 0), toDecimal32(-2.1, 1), 1)

Response

25.2

Difference with regular multiplication

Query

SELECT multiplyDecimal(toDecimal256(-12, 0), toDecimal32(-2.1, 1), 1)

Response

┌─multiply(toDecimal64(-12.647, 3), toDecimal32(2.1239, 4))─┐
│                                               -26.8609633 │
└───────────────────────────────────────────────────────────┘
┌─multiplyDecimal(toDecimal64(-12.647, 3), toDecimal32(2.1239, 4))─┐
│                                                         -26.8609 │
└──────────────────────────────────────────────────────────────────┘

Decimal overflow

Query

SELECT
    toDecimal64(-12.647987876, 9) AS a,
    toDecimal64(123.967645643, 9) AS b,
    multiplyDecimal(a, b);
SELECT
    toDecimal64(-12.647987876, 9) AS a,
    toDecimal64(123.967645643, 9) AS b,
    a * b;

Response

┌─────────────a─┬─────────────b─┬─multiplyDecimal(toDecimal64(-12.647987876, 9), toDecimal64(123.967645643, 9))─┐
│ -12.647987876 │ 123.967645643 │                                                               -1567.941279108 │
└───────────────┴───────────────┴───────────────────────────────────────────────────────────────────────────────┘
Received exception from server (version 22.11.1):
Code: 407. DB::Exception: Received from localhost:9000. DB::Exception: Decimal math overflow:
While processing toDecimal64(-12.647987876, 9) AS a, toDecimal64(123.967645643, 9) AS b, a * b. (DECIMAL_OVERFLOW)

negate

Introduced in: v1.1.0 Negates the argument x. The result is always signed. Syntax

negate(x)

Arguments

x — The value to negate.

Returned value Returns -x from x Examples Usage example

Query

SELECT negate(10)

Response

-10

plus

Introduced in: v1.1.0 Calculates the sum of two values x and y. Alias: x + y (operator). It is possible to add an integer and a date or date with time. The former operation increments the number of days in the date, the latter operation increments the number of seconds in the date with time. It is also possible to add a date and a time. Adding a Date and a Time produces a DateTime. Adding a Date and a Time64, or a Date32 and a Time or Time64, produces a DateTime64. Syntax

plus(x, y)

Arguments

x — Left hand operand. - y — Right hand operand.

Returned value Returns the sum of x and y Examples Adding two numbers

Query

SELECT plus(5,5)

Response

Adding an integer and a date

Query

SELECT plus(toDate('2025-01-01'),5)

Response

2025-01-06

Adding a date and time

Query

SELECT toDate('2025-01-01') + CAST('14:30:25', 'Time')

Response

2025-01-01 14:30:25

positiveModulo

Introduced in: v22.11.0 Calculates the remainder when dividing x by y. Similar to function modulo except that positiveModulo always return non-negative number. Syntax

positiveModulo(x, y)

Aliases: positive_modulo, pmod Arguments

x — The dividend. (U)Int* or Float* or Decimal
y — The divisor (modulus). (U)Int* or Float* or Decimal

Returned value Returns the difference between x and the nearest integer not greater than x divisible by y. Examples Usage example

Query

SELECT positiveModulo(-1, 10)

Response

positiveModuloOrNull

Introduced in: v25.5.0 Calculates the remainder when dividing a by b. Similar to function positiveModulo except that positiveModuloOrNull will return NULL if the right argument is 0. Syntax

positiveModuloOrNull(x, y)

Aliases: positive_modulo_or_null, pmodOrNull Arguments

x — The dividend. (U)Int*/Float32/64. - x — The divisor (modulus). (U)Int*/Float32/64.

Returned value Returns the difference between x and the nearest integer not greater than x divisible by y, null when the divisor is zero. Examples positiveModuloOrNull

Query

SELECT positiveModuloOrNull(5, 0)

Response

\N

SQL Reference

Arithmetic Functions

Arithmetic functions

Overview

abs

avg2

byteSwap

divide

divideDecimal

divideOrNull

gcd

ifNotFinite

intDiv

intDivOrNull

intDivOrZero

isFinite

isInfinite

isNaN

lcm

max2

midpoint

min2

minus

modulo

moduloLegacy

moduloOrNull

moduloOrZero

multiply

multiplyDecimal

negate

plus

positiveModulo

positiveModuloOrNull

SQL Reference

Documentation Index

​Arithmetic functions

​Overview

​abs

​avg2

​byteSwap

​divide

​divideDecimal

​divideOrNull

​gcd

​ifNotFinite

​intDiv

​intDivOrNull

​intDivOrZero

​isFinite

​isInfinite

​isNaN

​lcm

​max2

​midpoint

​min2

​minus

​modulo

​moduloLegacy

​moduloOrNull

​moduloOrZero

​multiply

​multiplyDecimal

​negate

​plus

​positiveModulo

​positiveModuloOrNull

Arithmetic functions

Overview

abs

avg2

byteSwap

divide

divideDecimal

divideOrNull

gcd

ifNotFinite

intDiv

intDivOrNull

intDivOrZero

isFinite

isInfinite

isNaN

lcm

max2

midpoint

min2

minus

modulo

moduloLegacy

moduloOrNull

moduloOrZero

multiply

multiplyDecimal

negate

plus

positiveModulo

positiveModuloOrNull