# Engineering

• BASE string of digits representing the number n in base b
• BESSELI Modified Bessel function of the first kind of order α at x
• BESSELJ Bessel function of the first kind of order α at x
• BESSELK Modified Bessel function of the second kind of order α at x
• BESSELY Bessel function of the second kind of order α at x
• BIN2DEC decimal representation of the binary number x
• BIN2HEX hexadecimal representation of the binary number x
• BIN2OCT octal representation of the binary number x
• CONVERT a converted measurement
• DEC2BIN binary representation of the decimal number x
• DEC2HEX hexadecimal representation of the decimal number x
• DEC2OCT octal representation of the decimal number x
• DECIMAL decimal representation of x
• DELTA Kronecker delta function
• ERF Gauss error function
• ERFC Complementary Gauss error function
• GESTEP step function with step at x1 evaluated at x0
• HEX2BIN binary representation of the hexadecimal number x
• HEX2DEC decimal representation of the hexadecimal number x
• HEX2OCT octal representation of the hexadecimal number x
• HEXREP hexadecimal representation of numeric value
• INVSUMINV the reciprocal of the sum of reciprocals of the arguments
• OCT2BIN binary representation of the octal number x
• OCT2DEC decimal representation of the octal number x
• OCT2HEX hexadecimal representation of the octal number x

## BASE

BASE string of digits representing the number n in base b

### Synopsis

`BASE(n,b,length)`

### Arguments

n: integer

b: base (2 ≤ b ≤ 36)

length: minimum length of the resulting string

### Description

BASE converts n to its string representation in base b. Leading zeroes will be added to reach the minimum length given by length.

### OpenDocument Format (ODF) Compatibility

This function is OpenFormula compatible.

## BESSELI

BESSELI Modified Bessel function of the first kind of order α at x

### Synopsis

`BESSELI(X,α)`

### Arguments

X: number

α: order (any non-negative number)

### Note

If x or α are not numeric, #VALUE! is returned. If α < 0, #NUM! is returned.

### Microsoft Excel Compatibility

This function is Excel compatible if only integer orders α are used.

## BESSELJ

BESSELJ Bessel function of the first kind of order α at x

### Synopsis

`BESSELJ(X,α)`

### Arguments

X: number

α: order (any non-negative integer)

### Note

If x or α are not numeric, #VALUE! is returned. If α < 0, #NUM! is returned.

### Microsoft Excel Compatibility

This function is Excel compatible if only integer orders α are used.

## BESSELK

BESSELK Modified Bessel function of the second kind of order α at x

### Synopsis

`BESSELK(X,α)`

### Arguments

X: number

α: order (any non-negative number)

### Note

If x or α are not numeric, #VALUE! is returned. If α < 0, #NUM! is returned.

### Microsoft Excel Compatibility

This function is Excel compatible if only integer orders α are used.

## BESSELY

BESSELY Bessel function of the second kind of order α at x

### Synopsis

`BESSELY(X,α)`

### Arguments

X: number

α: order (any non-negative integer)

### Note

If x or α are not numeric, #VALUE! is returned. If α < 0, #NUM! is returned.

### Microsoft Excel Compatibility

This function is Excel compatible if only integer orders α are used.

## BIN2DEC

BIN2DEC decimal representation of the binary number x

### Synopsis

`BIN2DEC(x)`

### Arguments

x: a binary number, either as a string or as a number involving only the digits 0 and 1

### Microsoft Excel Compatibility

This function is Excel compatible.

## BIN2HEX

BIN2HEX hexadecimal representation of the binary number x

### Synopsis

`BIN2HEX(x,places)`

### Arguments

x: a binary number, either as a string or as a number involving only the digits 0 and 1

places: number of digits

### Description

If places is given, BIN2HEX pads the result with zeros to achieve exactly places digits. If this is not possible, BIN2HEX returns #NUM!

### Microsoft Excel Compatibility

This function is Excel compatible.

## BIN2OCT

BIN2OCT octal representation of the binary number x

### Synopsis

`BIN2OCT(x,places)`

### Arguments

x: a binary number, either as a string or as a number involving only the digits 0 and 1

places: number of digits

### Description

If places is given, BIN2OCT pads the result with zeros to achieve exactly places digits. If this is not possible, BIN2OCT returns #NUM!

### Microsoft Excel Compatibility

This function is Excel compatible.

## CONVERT

CONVERT a converted measurement

### Synopsis

`CONVERT(x,from,to)`

### Arguments

x: number

from: unit (string)

to: unit (string)

### Description

CONVERT returns a conversion from one measurement system to another. x is a value in from units that is to be converted into to units.

from and to can be any of the following:

Weight and mass:

'brton' Imperial ton

'cwt' U.S. (short) hundredweight

'g' Gram

'grain' Grain

'hweight' Imperial (long) hundredweight

'LTON' Imperial ton

'sg' Slug

'shweight' U.S. (short) hundredweight

'lbm' Pound

'lcwt' Imperial (long) hundredweight

'u' U (atomic mass)

'uk_cwt' Imperial (long) hundredweight

'uk_ton' Imperial ton

'ozm' Ounce

'stone' Stone

'ton' Ton

Distance:

'm' Meter

'mi' Statute mile

'survey_mi' U.S. survey mile

'Nmi' Nautical mile

'in' Inch

'ft' Foot

'yd' Yard

'ell' English Ell

'ang' Angstrom

'ly' Light-Year

'pc' Parsec

'parsec' Parsec

'Pica' Pica Points

'Picapt' Pica Points

'picapt' Pica Points

'pica' Pica

Time:

'yr' Year

'day' Day

'hr' Hour

'mn' Minute

'sec' Second

Pressure:

'Pa' Pascal

'psi' PSI

'atm' Atmosphere

'Pa' Pascal

'mmHg' mm of Mercury

'Torr' Torr

Force:

'N' Newton

'dyn' Dyne

'pond' Pond

'lbf' Pound force

Energy:

'J' Joule

'e' Erg

'c' Thermodynamic calorie

'cal' IT calorie

'eV' Electron volt

'HPh' Horsepower-hour

'Wh' Watt-hour

'flb' Foot-pound

'BTU' BTU

Power:

'HP' Horsepower

'PS' Pferdestärke

'W' Watt

Magnetism:

'T' Tesla

'ga' Gauss

Temperature:

'C' Degree Celsius

'F' Degree Fahrenheit

'K' Kelvin

'Rank' Degree Rankine

'Reau' Degree Réaumur

Volume (liquid measure):

'tsp' Teaspoon

'tspm' Teaspoon (modern, metric)

'tbs' Tablespoon

'oz' Fluid ounce

'cup' Cup

'pt' Pint

'us_pt' U.S. pint

'uk_pt' Imperial pint (U.K.)

'qt' Quart

'uk_qt' Imperial quart

'gal' Gallon

'uk_gal' Imperial gallon

'GRT' Registered ton

'regton' Registered ton

'MTON' Measurement ton (freight ton)

'l' Liter

'L' Liter

'lt' Liter

'ang3' Cubic Angstrom

'ang^3' Cubic Angstrom

'barrel' U.S. oil barrel (bbl)

'bushel' U.S. bushel

'ft3' Cubic feet

'ft^3' Cubic feet

'in3' Cubic inch

'in^3' Cubic inch

'ly3' Cubic light-year

'ly^3' Cubic light-year

'm3' Cubic meter

'm^3' Cubic meter

'mi3' Cubic mile

'mi^3' Cubic mile

'yd3' Cubic yard

'yd^3' Cubic yard

'Nmi3' Cubic nautical mile

'Nmi^3' Cubic nautical mile

'Picapt3' Cubic Pica

'Picapt^3' Cubic Pica

'Pica3' Cubic Pica

'Pica^3' Cubic Pica

Area:

'uk_acre' International acre

'us_acre' U.S. survey/statute acre

'ang2' Square angstrom

'ang^2' Square angstrom

'ar' Are

'ha' Hectare

'in2' Square inches

'in^2' Square inches

'ly2' Square light-year

'ly^2' Square light-year

'm2' Square meter

'm^2' Square meter

'Morgen' Morgen (North German Confederation)

'mi2' Square miles

'mi^2' Square miles

'Nmi2' Square nautical miles

'Nmi^2' Square nautical miles

'Picapt2' Square Pica

'Picapt^2' Square Pica

'Pica2' Square Pica

'Pica^2' Square Pica

'yd2' Square yards

'yd^2' Square yards

Bits and Bytes:

'bit' Bit

'byte' Byte

Speed:

'kn' knot

'm/h' Meters per hour

'm/hr' Meters per hour

'm/s' Meters per second

'm/sec' Meters per second

'mph' Miles per hour

For metric units any of the following prefixes can be used:

'Y' yotta 1E+24

'Z' zetta 1E+21

'E' exa 1E+18

'P' peta 1E+15

'T' tera 1E+12

'G' giga 1E+09

'M' mega 1E+06

'k' kilo 1E+03

'h' hecto 1E+02

'e' deca (deka) 1E+01

'd' deci 1E-01

'c' centi 1E-02

'm' milli 1E-03

'u' micro 1E-06

'n' nano 1E-09

'p' pico 1E-12

'f' femto 1E-15

'a' atto 1E-18

'z' zepto 1E-21

'y' yocto 1E-24

For bits and bytes any of the following prefixes can be also be used:

'Yi' yobi 2^80

'Zi' zebi 2^70

'Ei' exbi 2^60

'Pi' pebi 2^50

'Ti' tebi 2^40

'Gi' gibi 2^30

'Mi' mebi 2^20

'ki' kibi 2^10

### Note

If from and to are different types, CONVERT returns #N/A!

### Microsoft Excel Compatibility

This function is Excel compatible (except "picapt").

### OpenDocument Format (ODF) Compatibility

This function is OpenFormula compatible.

## DEC2BIN

DEC2BIN binary representation of the decimal number x

### Synopsis

`DEC2BIN(x,places)`

### Arguments

x: integer (− 513 < x < 512)

places: number of digits

### Description

If places is given and x is non-negative, DEC2BIN pads the result with zeros to achieve exactly places digits. If this is not possible, DEC2BIN returns #NUM!

If places is given and x is negative, places is ignored.

### Note

If x < − 512 or x > 511, DEC2BIN returns #NUM!

### Microsoft Excel Compatibility

This function is Excel compatible.

### OpenDocument Format (ODF) Compatibility

This function is OpenFormula compatible.

## DEC2HEX

DEC2HEX hexadecimal representation of the decimal number x

### Synopsis

`DEC2HEX(x,places)`

### Arguments

x: integer

places: number of digits

### Description

If places is given, DEC2HEX pads the result with zeros to achieve exactly places digits. If this is not possible, DEC2HEX returns #NUM!

### Microsoft Excel Compatibility

This function is Excel compatible.

## DEC2OCT

DEC2OCT octal representation of the decimal number x

### Synopsis

`DEC2OCT(x,places)`

### Arguments

x: integer

places: number of digits

### Description

If places is given, DEC2OCT pads the result with zeros to achieve exactly places digits. If this is not possible, DEC2OCT returns #NUM!

### Microsoft Excel Compatibility

This function is Excel compatible.

## DECIMAL

DECIMAL decimal representation of x

### Synopsis

`DECIMAL(x,base)`

### Arguments

x: number in base base

base: base of x, (2 ≤ base ≤ 36)

### OpenDocument Format (ODF) Compatibility

This function is OpenFormula compatible.

BASE.

## DELTA

DELTA Kronecker delta function

### Synopsis

`DELTA(x0,x1)`

### Arguments

x0: number

x1: number, defaults to 0

### Description

DELTA returns 1 if x1 = x0 and 0 otherwise.

### Note

If either argument is non-numeric, #VALUE! is returned.

### Microsoft Excel Compatibility

This function is Excel compatible.

## ERF

ERF Gauss error function

### Synopsis

`ERF(lower,upper)`

### Arguments

lower: lower limit of the integral, defaults to 0

upper: upper limit of the integral

### Description

ERF returns 2/sqrt(π)* integral from lower to upper of exp(-t*t) dt

### Microsoft Excel Compatibility

This function is Excel compatible if two arguments are supplied and neither is negative.

ERFC.

## ERFC

ERFC Complementary Gauss error function

### Synopsis

`ERFC(x)`

x: number

### Description

ERFC returns 2/sqrt(π)* integral from x to ∞ of exp(-t*t) dt

ERF.

## GESTEP

GESTEP step function with step at x1 evaluated at x0

### Synopsis

`GESTEP(x0,x1)`

### Arguments

x0: number

x1: number, defaults to 0

### Description

GESTEP returns 1 if x1x0 and 0 otherwise.

### Note

If either argument is non-numeric, #VALUE! is returned.

### Microsoft Excel Compatibility

This function is Excel compatible.

## HEX2BIN

HEX2BIN binary representation of the hexadecimal number x

### Synopsis

`HEX2BIN(x,places)`

### Arguments

x: a hexadecimal number, either as a string or as a number if no A to F are needed

places: number of digits

### Description

If places is given, HEX2BIN pads the result with zeros to achieve exactly places digits. If this is not possible, HEX2BIN returns #NUM!

### Microsoft Excel Compatibility

This function is Excel compatible.

## HEX2DEC

HEX2DEC decimal representation of the hexadecimal number x

### Synopsis

`HEX2DEC(x)`

### Arguments

x: a hexadecimal number, either as a string or as a number if no A to F are needed

### Microsoft Excel Compatibility

This function is Excel compatible.

## HEX2OCT

HEX2OCT octal representation of the hexadecimal number x

### Synopsis

`HEX2OCT(x,places)`

### Arguments

x: a hexadecimal number, either as a string or as a number if no A to F are needed

places: number of digits

### Description

If places is given, HEX2OCT pads the result with zeros to achieve exactly places digits. If this is not possible, HEX2OCT returns #NUM!

### Microsoft Excel Compatibility

This function is Excel compatible.

## HEXREP

HEXREP hexadecimal representation of numeric value

### Synopsis

`HEXREP(x)`

x: number

### Description

HEXREP returns a hexadecimal string representation of x.

### Note

This is a function meant for debugging. The layout of the result may change and even depend on how Gnumeric was compiled.

## INVSUMINV

INVSUMINV the reciprocal of the sum of reciprocals of the arguments

### Synopsis

`INVSUMINV(x0,x1,…)`

### Arguments

x0: non-negative number

x1: non-negative number

### Description

INVSUMINV sum calculates the reciprocal (the inverse) of the sum of reciprocals (inverses) of all its arguments.

### Note

If any of the arguments is negative, #VALUE! is returned.

If any argument is zero, the result is zero.

## OCT2BIN

OCT2BIN binary representation of the octal number x

### Synopsis

`OCT2BIN(x,places)`

### Arguments

x: a octal number, either as a string or as a number

places: number of digits

### Description

If places is given, OCT2BIN pads the result with zeros to achieve exactly places digits. If this is not possible, OCT2BIN returns #NUM!

### Microsoft Excel Compatibility

This function is Excel compatible.

## OCT2DEC

OCT2DEC decimal representation of the octal number x

### Synopsis

`OCT2DEC(x)`

### Arguments

x: a octal number, either as a string or as a number

### Microsoft Excel Compatibility

This function is Excel compatible.

## OCT2HEX

OCT2HEX hexadecimal representation of the octal number x

### Synopsis

`OCT2HEX(x,places)`

### Arguments

x: a octal number, either as a string or as a number

places: number of digits

### Description

If places is given, OCT2HEX pads the result with zeros to achieve exactly places digits. If this is not possible, OCT2HEX returns #NUM!

### Microsoft Excel Compatibility

This function is Excel compatible.