Operation	Result	Same as	Result
= 5 & 1	1	0101 & 0001	0001
= 5 | 1	5	0101 | 0001	0101
= ~ 5	10 (4bit unsigned) / -6 (32bit signed)	~0101	1010
= 5 << 1	10	0101 << 1	1010
= 5 ^ 1	4	0101 ^ 0001	0100
= 5 >> 1	2	0101 >> 1	0010
= 5 >>> 1	2	0101 >>> 1	0010

---

Expressions

Our spreadsheet now contains a flexible and easy to use expression parser. The parser supports all data types, functions and constants.

The expression parser is aimed at end users: mathematicians, engineers, students, pupils. The syntax of the expression parser differs from JavaScript and the low-level math.js library.

When writing out an expression, it can be used in two ways:


In its Natural state: Any expression may be entered starting with a "$" sign...

Example 1

$evaluate('sqrt(3^2 + 4^2)')        // 5          Strings don't support cell references
=math.evaluate('sqrt(-4)')          // 2i         Strings don't support cell references

$sqrt(3^2 + 4^2)                    // 5          Doesn't support cell references
=math.sqrt(-4)                      // 2i         Supports cell references

$evaluate('2 inch to cm')           // 5.08 cm    Strings don't support cell references
=math.evaluate('90 km/h to m/s')    // 25m / s    Strings don't support cell references

$evaluate('cos(45 deg)')            // 0.707106   Strings don't support cell references
$evaluate('f(x, y) = x^y')          // f(x, y)    Strings don't support cell references


Algebra (symbolic computation)

$simplify('2x + 3x').toString()     // "5 * x"    Strings don't support cell references
$simplify('x^2 + x + 3 + x^2')      // 2*x^2+x+3  Strings don't support cell references
$simplify('2x + 3x').toString())    // "5 * x"    Strings don't support cell references
$simplify('x * y * -x / (x ^ 2)')   // '-y'       Strings don't support cell references

$derivative('2x^2 + 3x + 4', 'x')   // 4 * x + 3  Strings don't support cell references
$derivative('sin(2x)', 'x')         // 2*cos(2*x) Strings don't support cell references

$rationalize('2x/y - y/(x+1)')      // 2*x^2-y^2  Strings don't support cell references
$rationalize('x+x+x+y',{y:1})       // 3*x+1      Strings don't support cell references

Example 2

Using the standard "=" sign:

A1:3 A2:4

=math.sqrt(3^2 + 4^2)               // 5          supports cell references
=math.sqrt(A1^2 + A2^2)             // 5          supports cell references
=math.evaluate('cos(45 deg)')       // 0.707106   strings don't suppport cell references

Create a currency value:

=math.format(A2,function formatCurrency(value) {return '$'+value.toFixed(2)})
// $4.00 supports cell references

=math.subset([[1, 2], [3, a2]],math.index(0, 1)) // 2 supports cell references

• Evaluate - Syntax describes how to write expressions

  math.evaluate(expr)                       =math.evaluate('(2+3)/4') math.evaluate(expr, scope)                =math.evaluate('a * b',{a:A1,b:A2}) math.evaluate([expr1, expr2, ...])        =math.evaluate(['a=3', 'b=4', 'a*b']) math.evaluate([expr1, expr2, ...], scope) =math.evaluate(['a * b','b/c'],{a:3,b:A2,c:9})

  math.evaluate(expr)                        $evaluate('(2+3)/4') math.evaluate(expr, scope)                 $evaluate('a * b',{a:3,b:4}) math.evaluate([expr1, expr2, ...])         $evaluate(['a=3', 'b=4', 'a*b']) math.evaluate([expr1, expr2, ...], scope)  $evaluate(['a * b','b/c'],{a:3,b:4,c:9})

  
  

  Just remember that string expressions don't support cell references!

---

Simple rules to expressions

Implicit multiplication

The behavior of implicit multiplication can be summarized by these operator precedence rules, listed from highest to lowest precedence:

• Function calls: [symbol] [left paren]
• Explicit division / when the division matches this pattern: [number] / [number] [symbol] or [number] / [number] [left paren]
• Implicit multiplication
• All other division / and multiplication *

Here are some more examples using implicit multiplication:

Expression in Cell	Evaluated as	Result
$(1 + 3) pi	(1 + 3) * pi	12.566370614359172
$(4 - 1) 2	(4 - 1) * 2	6
$3 / 4 mm	(3 / 4) * mm	0.75 mm
$2 + 3 i	2 + (3 * i)	2 + 3i
$(1 + 2) (4 - 2)	(1 + 2) * (4 - 2)	6
$sqrt(4) (1 + 2)	sqrt(4) * (1 + 2)	6
$8 pi / 2 pi	(8 * pi) / (2 * pi)	4
$pi / 2 pi	pi / (2 * pi)	0.5
$1 / 2i	(1 / 2) * i	0.5 i
$8.314 J / mol K	8.314 J / (mol * K)	8.314 J / (mol * K)

The following operators are available with the "$" prefix:

Operator	Name	Syntax	Associativity	Example	Result
(, )	Grouping	(x)	None	2 * (3 + 4)	14
[, ]	Matrix, Index	[...]	None	[[1,2],[3,4]]	[[1,2],[3,4]]
{, }	Object	{...}	None	{a: 1, b: 2}	{a: 1, b: 2}
,	Parameter separator	x, y	Left to right	max(2, 1, 5)	5
.	Property accessor	obj.prop	Left to right	obj={a: 12}; obj.a	12
;	Statement separator	x; y	Left to right	a=2; b=3; a*b	[6]
;	Row separator	[x; y]	Left to right	[1,2;3,4]	[[1,2],[3,4]]
\n	Statement separator	x \n y	Left to right	a=2 \n b=3 \n a*b	[2,3,6]
+	Add	x + y	Left to right	4 + 5	9
+	Unary plus	+y	Right to left	+4	4
-	Subtract	x - y	Left to right	7 - 3	4
-	Unary minus	-y	Right to left	-4	-4
*	Multiply	x * y	Left to right	2 * 3	6
.*	Element-wise multiply	x .* y	Left to right	[1,2,3] .* [1,2,3]	[1,4,9]
/	Divide	x / y	Left to right	6 / 2	3
./	Element-wise divide	x ./ y	Left to right	[9,6,4] ./ [3,2,2]	[3,3,2]
%, mod	Modulus	x % y	Left to right	8 % 3	2
^	Power	x ^ y	Right to left	2 ^ 3	8
.^	Element-wise power	x .^ y	Right to left	[2,3] .^ [3,3]	[8,27]
'	Transpose	y'	Left to right	[[1,2],[3,4]]'	[[1,3],[2,4]]
!	Factorial	y!	Left to right	5!	120
&	Bitwise and	x & y	Left to right	5 & 3	1
~	Bitwise not	~x	Right to left	~2	-3
|	Bitwise or	x | y	Left to right	5 | 3	7
^|	Bitwise xor	x ^| y	Left to right	5 ^| 2	7
<<	Left shift	x << y	Left to right	4 << 1	8
>>	Right arithmetic shift	x >> y	Left to right	8 >> 1	4
>>>	Right logical shift	x >>> y	Left to right	-8 >>> 1	2147483644
and	Logical and	x and y	Left to right	true and false	false
not	Logical not	not y	Right to left	not true	false
or	Logical or	x or y	Left to right	true or false	true
xor	Logical xor	x xor y	Left to right	true xor true	false
=	Assignment	x = y	Right to left	a = 5	5
? :	Conditional expression	x ? y : z	Right to left	15 > 100 ? 1 : -1	-1
:	Range	x : y	Right to left	1:4	[1,2,3,4]
to, in	Unit conversion	x to y	Left to right	2 inch to cm	5.08 cm
==	Equal	x == y	Left to right	2 == 4 - 2	true
!=	Unequal	x != y	Left to right	2 != 3	true
<	Smaller	x < y	Left to right	2 < 3	true
>	Larger	x > y	Left to right	2 > 3	false
<=	Smallereq	x <= y	Left to right	4 <= 3	false
>=	Largereq	x >= y	Left to right	2 + 4 >= 6	true

Precedence

These operators have the following precedence, from highest to lowest when used with the "$" prefix:

Operators	Description
(...) [...] {...}	Grouping Matrix Object
x(...) x[...] obj.prop :	Function call Matrix index Property accessor Key/value separator
'	Matrix transpose
!	Factorial
^, .^	Exponentiation
+, -, ~, not	Unary plus, unary minus, bitwise not, logical not
See section below	Implicit multiplication
*, /, .*, ./, %, mod	Multiply, divide, modulus
+, -	Add, subtract
:	Range
to, in	Unit conversion
<<, >>, >>>	Bitwise left shift, bitwise right arithmetic shift, bitwise right logical shift
==, !=, <, >, <=, >=	Relational
&	Bitwise and
^|	Bitwise xor
|	Bitwise or
and	Logical and
xor	Logical xor
or	Logical or
?, :	Conditional expression
=	Assignment
,	Parameter and column separator
;	Row separator
\n, ;	Statement separators

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Functions from our Custom Math unit...

Algebra functions #

Function	Description
derivative(expr, variable)	Takes the derivative of an expression expressed in parser Nodes.
math.lsolve(L, b)	Finds one solution of a linear equation system by forwards substitution.
math.lsolve(L, b)	Finds all solutions of a linear equation system by forwards substitution.
math.lup(A)	Calculate the Matrix LU decomposition with partial pivoting.
math.lusolve(A, b)	Solves the linear system A * x = b where A is an [n x n] matrix and b is a [n] column vector.
math.qr(A)	Calculate the Matrix QR decomposition.
rationalize(expr)	Transform a rationalizable expression in a rational fraction.
simplify(expr)	Simplify an expression tree.
math.slu(A, order, threshold)	Calculate the Sparse Matrix LU decomposition with full pivoting.
math.usolve(U, b)	Finds one solution of a linear equation system by backward substitution.
math.usolve(U, b)	Finds all solutions of a linear equation system by backward substitution.

Arithmetic functions #

Function	Description
math.abs(x)	Calculate the absolute value of a number.
math.add(x, y)	Add two or more values, x + y.
math.cbrt(x [, allRoots])	Calculate the cubic root of a value.
math.ceil(x)	Round a value towards plus infinity If x is complex, both real and imaginary part are rounded towards plus infinity.
math.cube(x)	Compute the cube of a value, x * x * x.
math.divide(x, y)	Divide two values, x / y.
math.dotDivide(x, y)	Divide two matrices element wise.
math.dotMultiply(x, y)	Multiply two matrices element wise.
math.dotPow(x, y)	Calculates the power of x to y element wise.
math.exp(x)	Calculate the exponent of a value.
math.expm1(x)	Calculate the value of subtracting 1 from the exponential value.
math.fix(x)	Round a value towards zero.
math.floor(x)	Round a value towards minus infinity.
math.gcd(a, b)	Calculate the greatest common divisor for two or more values or arrays.
math.hypot(a, b, …)	Calculate the hypotenusa of a list with values.
math.lcm(a, b)	Calculate the least common multiple for two or more values or arrays.
math.log(x [, base])	Calculate the logarithm of a value.
math.log10(x)	Calculate the 10-base logarithm of a value.
math.log1p(x)	Calculate the logarithm of a value+1.
math.log2(x)	Calculate the 2-base of a value.
math.mod(x, y)	Calculates the modulus, the remainder of an integer division.
math.multiply(x, y)	Multiply two or more values, x * y.
math.norm(x [, p])	Calculate the norm of a number, vector or matrix.
math.nthRoot(a)	Calculate the nth root of a value.
math.nthRoots(x)	Calculate the nth roots of a value.
math.pow(x, y)	Calculates the power of x to y, x ^ y.
math.round(x [, n])	Round a value towards the nearest integer.
math.sign(x)	Compute the sign of a value.
math.sqrt(x)	Calculate the square root of a value.
math.square(x)	Compute the square of a value, x * x.
math.subtract(x, y)	Subtract two values, x - y.
math.unaryMinus(x)	Inverse the sign of a value, apply a unary minus operation.
math.unaryPlus(x)	Unary plus operation.
math.xgcd(a, b)	Calculate the extended greatest common divisor for two values.

Bitwise functions #

Function	Description
math.bitAnd(x, y)	Bitwise AND two values, x & y.
math.bitNot(x)	Bitwise NOT value, ~x.
math.bitOr(x, y)	Bitwise OR two values, x | y.
math.bitXor(x, y)	Bitwise XOR two values, x ^ y.
math.leftShift(x, y)	Bitwise left logical shift of a value x by y number of bits, x << y.
math.rightArithShift(x, y)	Bitwise right arithmetic shift of a value x by y number of bits, x >> y.
math.rightLogShift(x, y)	Bitwise right logical shift of value x by y number of bits, x >>> y.

Combinatorics functions #

Function	Description
math.bellNumbers(n)	The Bell Numbers count the number of partitions of a set.
math.catalan(n)	The Catalan Numbers enumerate combinatorial structures of many different types.
math.composition(n, k)	The composition counts of n into k parts.
math.stirlingS2(n, k)	The Stirling numbers of the second kind, counts the number of ways to partition a set of n labelled objects into k nonempty unlabelled subsets.

Complex functions #

Function	Description
math.arg(x)	Compute the argument of a complex value.
math.conj(x)	Compute the complex conjugate of a complex value.
math.im(x)	Get the imaginary part of a complex number.
math.re(x)	Get the real part of a complex number.

Geometry functions #

Function	Description
math.distance([x1, y1], [x2, y2])	Calculates: The eucledian distance between two points in N-dimensional spaces.
math.intersect(endPoint1Line1, endPoint2Line1, endPoint1Line2, endPoint2Line2)	Calculates the point of intersection of two lines in two or three dimensions and of a line and a plane in three dimensions.

Logical functions #

Function	Description
math.and(x, y)	Logical and.
math.not(x)	Logical not.
math.or(x, y)	Logical or.
math.xor(x, y)	Logical xor.

Matrix functions #

Function	Description
math.apply(A, dim, callback)	Apply a function that maps an array to a scalar along a given axis of a matrix or array.
math.column(value, index)	Return a column from a Matrix.
math.concat(a, b, c, … [, dim])	Concatenate two or more matrices.
math.cross(x, y)	Calculate the cross product for two vectors in three dimensional space.
math.ctranspose(x)	Transpose and complex conjugate a matrix.
math.det(x)	Calculate the determinant of a matrix.
math.diag(X)	Create a diagonal matrix or retrieve the diagonal of a matrix When x is a vector, a matrix with vector x on the diagonal will be returned.
math.diff(arr)	Create a new matrix or array of the difference between elements of the given array The optional dim parameter lets you specify the dimension to evaluate the difference of If no dimension parameter is passed it is assumed as dimension 0 Dimension is zero-based in javascript and one-based in the parser and can be a number or bignumber Arrays must be ‘rectangular’ meaning arrays like [1, 2] If something is passed as a matrix it will be returned as a matrix but other than that all matrices are converted to arrays.
math.dot(x, y)	Calculate the dot product of two vectors.
math.eigs(x)	Compute eigenvalue and eigenvector of a real symmetric matrix.
math.expm(x)	Compute the matrix exponential, expm(A) = e^A.
math.filter(x, test)	Filter the items in an array or one dimensional matrix.
math.flatten(x)	Flatten a multi dimensional matrix into a single dimensional matrix.
math.forEach(x, callback)	Iterate over all elements of a matrix/array, and executes the given callback function.
math.getMatrixDataType(x)	Find the data type of all elements in a matrix or array, for example ‘number’ if all items are a number and ‘Complex’ if all values are complex numbers.
math.identity(n)	Create a 2-dimensional identity matrix with size m x n or n x n.
math.inv(x)	Calculate the inverse of a square matrix.
math.kron(x, y)	Calculates the kronecker product of 2 matrices or vectors.
math.map(x, callback)	Create a new matrix or array with the results of the callback function executed on each entry of the matrix/array.
math.ones(m, n, p, …)	Create a matrix filled with ones.
math.partitionSelect(x, k)	Partition-based selection of an array or 1D matrix.
math.range(start, end [, step])	Create an array from a range.
math.reshape(x, sizes)	Reshape a multi dimensional array to fit the specified dimensions.
math.resize(x, size [, defaultValue])	Resize a matrix.
math.rotate(w, theta)	Rotate a vector of size 1x2 counter-clockwise by a given angle Rotate a vector of size 1x3 counter-clockwise by a given angle around the given axis.
math.rotationMatrix(theta)	Create a 2-dimensional counter-clockwise rotation matrix (2x2) for a given angle (expressed in radians).
math.row(value, index)	Return a row from a Matrix.
math.size(x)	Calculate the size of a matrix or scalar.
math.sort(x)	Sort the items in a matrix.
X = math.sqrtm(A)	Calculate the principal square root of a square matrix.
math.squeeze(x)	Squeeze a matrix, remove inner and outer singleton dimensions from a matrix.
math.subset(x, index [, replacement])	Get or set a subset of a matrix or string.
math.trace(x)	Calculate the trace of a matrix: the sum of the elements on the main diagonal of a square matrix.
math.transpose(x)	Transpose a matrix.
math.zeros(m, n, p, …)	Create a matrix filled with zeros.

Probability functions #

Function	Description
math.combinations(n, k)	Compute the number of ways of picking k unordered outcomes from n possibilities.
math.combinationsWithRep(n, k)	Compute the number of ways of picking k unordered outcomes from n possibilities, allowing individual outcomes to be repeated more than once.
math.factorial(n)	Compute the factorial of a value Factorial only supports an integer value as argument.
math.gamma(n)	Compute the gamma function of a value using Lanczos approximation for small values, and an extended Stirling approximation for large values.
math.kldivergence(x, y)	Calculate the Kullback-Leibler (KL) divergence between two distributions.
math.multinomial(a)	Multinomial Coefficients compute the number of ways of picking a1, a2, .
math.permutations(n [, k])	Compute the number of ways of obtaining an ordered subset of k elements from a set of n elements.
math.pickRandom(array)	Random pick one or more values from a one dimensional array.
math.random([min, max])	Return a random number larger or equal to min and smaller than max using a uniform distribution.
math.randomInt([min, max])	Return a random integer number larger or equal to min and smaller than max using a uniform distribution.

Relational functions #

Function	Description
math.compare(x, y)	Compare two values.
math.compareNatural(x, y)	Compare two values of any type in a deterministic, natural way.
math.compareText(x, y)	Compare two strings lexically.
math.deepEqual(x, y)	Test element wise whether two matrices are equal.
math.equal(x, y)	Test whether two values are equal.
math.equalText(x, y)	Check equality of two strings.
math.larger(x, y)	Test whether value x is larger than y.
math.largerEq(x, y)	Test whether value x is larger or equal to y.
math.smaller(x, y)	Test whether value x is smaller than y.
math.smallerEq(x, y)	Test whether value x is smaller or equal to y.
math.unequal(x, y)	Test whether two values are unequal.

Set functions #

Function	Description
math.setCartesian(set1, set2)	Create the cartesian product of two (multi)sets.
math.setDifference(set1, set2)	Create the difference of two (multi)sets: every element of set1, that is not the element of set2.
math.setDistinct(set)	Collect the distinct elements of a multiset.
math.setIntersect(set1, set2)	Create the intersection of two (multi)sets.
math.setIsSubset(set1, set2)	Check whether a (multi)set is a subset of another (multi)set.
math.setMultiplicity(element, set)	Count the multiplicity of an element in a multiset.
math.setPowerset(set)	Create the powerset of a (multi)set.
math.setSize(set)	Count the number of elements of a (multi)set.
math.setSymDifference(set1, set2)	Create the symmetric difference of two (multi)sets.
math.setUnion(set1, set2)	Create the union of two (multi)sets.

Special functions #

Function	Description
math.erf(x)	Compute the erf function of a value using a rational Chebyshev approximations for different intervals of x.

Statistics functions #

Function	Description
math.mad(a, b, c, …)	Compute the median absolute deviation of a matrix or a list with values.
math.max(a, b, c, …)	Compute the maximum value of a matrix or a list with values.
math.mean(a, b, c, …)	Compute the mean value of matrix or a list with values.
math.median(a, b, c, …)	Compute the median of a matrix or a list with values.
math.min(a, b, c, …)	Compute the minimum value of a matrix or a list of values.
math.mode(a, b, c, …)	Computes the mode of a set of numbers or a list with values(numbers or characters).
math.prod(a, b, c, …)	Compute the product of a matrix or a list with values.
math.quantileSeq(A, prob[, sorted])	Compute the prob order quantile of a matrix or a list with values.
math.std(a, b, c, …)	Compute the standard deviation of a matrix or a list with values.
math.sum(a, b, c, …)	Compute the sum of a matrix or a list with values.
math.variance(a, b, c, …)	Compute the variance of a matrix or a list with values.

String functions #

Function	Description
math.bin(value)	Format a number as binary.
math.format(value [, precision])	Format a value of any type into a string.
math.hex(value)	Format a number as hexadecimal.
math.oct(value)	Format a number as octal.
math.print(template, values [, precision])	Interpolate values into a string template.

Trigonometry functions #

Function	Description
math.acos(x)	Calculate the inverse cosine of a value.
math.acosh(x)	Calculate the hyperbolic arccos of a value, defined as acosh(x) = ln(sqrt(x^2 - 1) + x).
math.acot(x)	Calculate the inverse cotangent of a value, defined as acot(x) = atan(1/x).
math.acoth(x)	Calculate the hyperbolic arccotangent of a value, defined as acoth(x) = atanh(1/x) = (ln((x+1)/x) + ln(x/(x-1))) / 2.
math.acsc(x)	Calculate the inverse cosecant of a value, defined as acsc(x) = asin(1/x).
math.acsch(x)	Calculate the hyperbolic arccosecant of a value, defined as acsch(x) = asinh(1/x) = ln(1/x + sqrt(1/x^2 + 1)).
math.asec(x)	Calculate the inverse secant of a value.
math.asech(x)	Calculate the hyperbolic arcsecant of a value, defined as asech(x) = acosh(1/x) = ln(sqrt(1/x^2 - 1) + 1/x).
math.asin(x)	Calculate the inverse sine of a value.
math.asinh(x)	Calculate the hyperbolic arcsine of a value, defined as asinh(x) = ln(x + sqrt(x^2 + 1)).
math.atan(x)	Calculate the inverse tangent of a value.
math.atan2(y, x)	Calculate the inverse tangent function with two arguments, y/x.
math.atanh(x)	Calculate the hyperbolic arctangent of a value, defined as atanh(x) = ln((1 + x)/(1 - x)) / 2.
math.cos(x)	Calculate the cosine of a value.
math.cosh(x)	Calculate the hyperbolic cosine of a value, defined as cosh(x) = 1/2 * (exp(x) + exp(-x)).
math.cot(x)	Calculate the cotangent of a value.
math.coth(x)	Calculate the hyperbolic cotangent of a value, defined as coth(x) = 1 / tanh(x).
math.csc(x)	Calculate the cosecant of a value, defined as csc(x) = 1/sin(x).
math.csch(x)	Calculate the hyperbolic cosecant of a value, defined as csch(x) = 1 / sinh(x).
math.sec(x)	Calculate the secant of a value, defined as sec(x) = 1/cos(x).
math.sech(x)	Calculate the hyperbolic secant of a value, defined as sech(x) = 1 / cosh(x).
math.sin(x)	Calculate the sine of a value.
math.sinh(x)	Calculate the hyperbolic sine of a value, defined as sinh(x) = 1/2 * (exp(x) - exp(-x)).
math.tan(x)	Calculate the tangent of a value.
math.tanh(x)	Calculate the hyperbolic tangent of a value, defined as tanh(x) = (exp(2 * x) - 1) / (exp(2 * x) + 1).

Unit functions #

Function	Description
math.to(x, unit)	Change the unit of a value.

Utils functions #

Function	Description
math.clone(x)	Clone an object.
math.hasNumericValue(x)	Test whether a value is an numeric value.
math.isInteger(x)	Test whether a value is an integer number.
math.isNaN(x)	Test whether a value is NaN (not a number).
math.isNegative(x)	Test whether a value is negative: smaller than zero.
math.isNumeric(x)	Test whether a value is an numeric value.
math.isPositive(x)	Test whether a value is positive: larger than zero.
math.isPrime(x)	Test whether a value is prime: has no divisors other than itself and one.
math.isZero(x)	Test whether a value is zero.
math.numeric(x)	Convert a numeric input to a specific numeric type: number, BigNumber, or Fraction.
math.typeOf(x)	Determine the type of a variable.

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Quick Conversions

Some examples of unit conversions: (units must be in lowercase)

• $26 fahrenheit to celsius            // Returns -3.3333 celcius
• $18 mile to km                       // Returns 28.968 km / kilometer
• $25 ounce to gram                    // Returns 708.74 gram
• $25 ounce to gram to kg              // Returns 0.70874 kg / kilogram
• $88 inch to cm                       // Returns 223.52 cm / centimeter
• $88 inch to m                        // Returns 2.2352 m / meter
• $8 fluidounce to milliliter          // Returns 236,59 milliliter / ml
• $18 poundmass to kg                  // Returns 8.1647 kg / kilogram

foot, link, angstrom, ft, mil, sqft, sqrd, acre, hectare, mile, inch, chain, sqin, sqmi, litre, milliliter, cuin, cuyd, gill, pint, gallon, oilbarrel,floz, pt, tonne, poundforce, grain, gram, ounce, fluidounce, hundredweight, min, sec, hour, day, year, millennium, hertz, deg, gradian, arcmin, celsius, fahrenheit, kelvin, candela, cd, mole, newton, joule, kip, BTU, eV, electronvolt, psi, Pa, bar, atm, torr, cmH2O, mmhg, mmh2o farad, V, ohm, henry, siemens, tesla, weber, bits, bytes, meters, coulomb, ampere, volt . . .

Complete List of Units

meters:"meter" inches:"inch" feet:"foot" yards:"yard" miles:"mile" links:"link" rods:"rod" chains:"chain" angstroms:"angstrom" lt:"l" litres:"litre" liter:"litre" liters:"litre" teaspoons:"teaspoon" tablespoons:"tablespoon" minims:"minim" fluiddrams:"fluiddram" fluidounces:"fluidounce" gills:"gill" cups:"cup" pints:"pint" quarts:"quart" gallons:"gallon" beerbarrels:"beerbarrel" oilbarrels:"oilbarrel" hogsheads:"hogshead" gtts:"gtt" grams:"gram" tons:"ton" tonnes:"tonne" grains:"grain" drams:"dram" ounces:"ounce" poundmasses:"poundmass" hundredweights:"hundredweight" sticks:"stick" lb:"lbm" lbs:"lbm" kips:"kip" kgf:"kilogramforce" acres:"acre" hectares:"hectare" sqfeet:"sqft" sqyard:"sqyd" sqmile:"sqmi" sqmiles:"sqmi" mmhg:"mmHg" mmh2o:"mmH2O" cmh2o:"cmH2O" seconds:"second" secs:"second" minutes:"minute" mins:"minute" hours:"hour" hr:"hour" hrs:"hour" days:"day" weeks:"week" months:"month" years:"year" decades:"decade" centuries:"century" millennia:"millennium" hertz:"hertz" radians:"radian" degrees:"degree" gradians:"gradian" cycles:"cycle" arcsecond:"arcsec" arcseconds:"arcsec" arcminute:"arcmin" arcminutes:"arcmin" BTUs:"BTU" watts:"watt" joules:"joule" amperes:"ampere" coulombs:"coulomb" volts:"volt" ohms:"ohm" farads:"farad" webers:"weber" teslas:"tesla" electronvolts:"electronvolt" moles:"mole" bit:"bits" byte:"bytes"

Universal Constants e.g. $speedOfLight >> 2.9979e+8 m/s

gravitationConstant planckConstant reducedPlanckConstant magneticConstant electricConstant vacuumImpedance coulomb elementaryCharge bohrMagneton conductanceQuantum inverseConductanceQuantum magneticFluxQuantum nuclearMagneton klitzing bohrRadius classicalElectronRadius electronMass fermiCoupling

fineStructure hartreeEnergy protonMass deuteronMass neutronMass quantumOfCirculation rydberg thomsonCrossSection weakMixingAngle efimovFactor atomicMass avogadro boltzmann faraday firstRadiation loschmidt gasConstant molarPlanckConstant

molarVolume sackurTetrode secondRadiation stefanBoltzmann wienDisplacement molarMass molarMassC12 gravity planckLength planckMass planckTime planckCharge planckTemperature speedOfLight

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Esoteric Functions       Works only with the "=" sign prefix

numbers.generate.fibonacci(n)

Calculates the nth Fibonacci number.
Parameters
n:Int | Desired Fibonacci number to calculate.

Returns num:Int The nth Fibonacci number.

numbers.random.bates(n, b, a)

Generates a random number according to a Bates distribution inside the interval [a,b]. Both arguments are optional.

Parameters
n : Int Number of times to sum.
b : Number, optional Right endpoint of interval.Default value is 1.
a : Number, optional Left endpoint of the interal. Default value is 0.

Returns num : Number Random number according to a Bates distribution on [a,b].

numbers.random.irwinHall(n, sub)

Generates a random number according to an Irwin-Hall distribution, given a maximum sum, n, and a number to subtract, sub.

Parameters
n : Number Maximum sum.
sub : Number Number to subtract.

Returns num : Number Random number according to an Irwin-Hall distribution.

numbers.prime.coprime(a, b)

Determine if two integers are coprime.

Parameters
a : Int First integer.
b : Int Second integer

Returns bool : Boolean true if a, b are coprime, false otherwise.

numbers.prime.millerRabin(n, k)

Determines if an integer, n, is prime in polynomial time using the Miller-Rabin primality test, with an accuracy rate (number of trials) k.

Parameters
n : Int The number to test for primality.
k : Int The accuracy rate.

Returns bool : Boolean true if n is prime, false otherwise.

numbers.prime.simple(n)

Determines if an integer, n, is prime using brute force.

Parameters
n : Int The number to test for primality.
Returns bool : Boolean true if n is prime, false otherwise.

numbers.calculus.LanczosGamma(n)

Lanczos' approximation to the gamma function of a number, n.

Parameters
n : Number A number

Returns num : Number Gamma of n.

numbers.calculus.StirlingGamma(n)

Striling's approximation to the gamma function of a number, n.

Parameters
n : Number A number.
Returns num : Number Gamma of n.

numbers.basic.binomial(n, k)

Calculates the binomial coefficient of n,k (n choose k).

Parameters
n : Int Number of available choices.
k : Int Number of choices selected.

Returns num : Int The number of combinations of choices, n choose k.

numbers.basic.factorial(n)

Calculates the factorial of a positive integer, n.

Parameters
n : Int A positive integer.
Returns num : Int Factorial of n

numbers.basic.fallingFactorial(n, k)

Calculates the falling factorial of a positive integer n with k steps: n!/(n-k)!

Parameters
n : Int A positive integer.
k : Int The number of steps to fall.

Returns r : Int Falling factorial of n with k steps. If k > n then 0 is returned.

numbers.basic.gcd(a, b)

Calculates the greatest common divisor (gcd) amongst two integers.

Parameters
a : Int First integer.
b : Int Second integer.

Returns num : Int The gcd of a,b. If a or b are Infinity or -Infinity, then Infinity is returned. If a or b are not numbers, then NaN is returned.

numbers.basic.lcm(a, b)

Calculates the lowest common multiple (lcm) amongst two integers.

Parameters
a : Int First integer.
b : Int Second integer.

Returns num : Int The lcm of a,b. If a or b are Infinity or -Infinity, then 0 is returned. If a or b are not numbers, then NaN is returned.

numbers.basic.modInverse(a, m)

Calculates the modular multiplicative inverse x of an integer a and modulus m, ax = 1 (mod m).

Parameters
a : Int An integer.
m : Int Modulus.

Returns x : Int An integer such that ax = 1 (mod m).

numbers.basic.numbersEqual(a, b, epsilon)

Determines if two numbers, a,b, are equal within a given margin of precision, epsilon.

Parameters
a : Number First number.
b : Number Second number.
epsilon : Number Precision.

Returns bool : Boolean

numbers.basic.permutation(n, k)

Calculate the permutation (n choose k)

Parameters
n : Int Number of total elements
k : Int Fixed number of elements

Returns num : Number Number of ordered variations

Errors: An error is thrown if:
n cannot be less than or equal to 0.
k cannot be greater than n.

numbers.basic.subtraction(arr)

Calculates the differences of elements of an array, using the first element as the starting point.

Parameters
arr : Array An array of numbers.
Returns num : Number The difference of the elements of arr.

Errors
An error is thrown if:
not all elements of arr are numbers
arr is not an array

numbers.basic.sum(arr)

Calculates the sum of the elements of an array.

Parameters
arr : Array An array of numbers.
Returns num : Number The sum of the elements of arr.

Errors
An error is thrown if:
not all elements of arr are numbers
arr is not an array

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