Help:Calculation

Calculation is the determination of something by using mathematics. One can evaluate an expression on the Scratch Wiki using the parser function #expr. There is a 14 digit limit for rational and irrational digits; rational numbers will show up as scientific notation as it passes the 14th digit.

Usage

To use this function, simply use the syntax {{#expr:expression}}. For example, {{#expr:2+2}} is equal to 4, but {{#expr:5/0}} will result in an error (division by zero is undefined), similar to an error produced by the template {{error}}. This function also accepts wiki variables in it; {{#expr:{{CURRENTDAY}}^2}} is equal to 1. Common supported operators include -,+,*,/,^,brackets and common functions include sin( ), cos( ), tan( ), ln( ), abs( ), ceil( ), floor( ), mod( ). Irrational numbers are also supported, such as pi and e. Note the trigonometric functions are based in radians and not in degrees.

Operators

Note:

In logic gate functions (not, and, or), 0 equals false, 1 equals true. Other values always equal true.

Operators

Operator	Explanation	Example
+	Adds two operands together or a unary operator	{{#expr:5+5}} = 10 Five plus five is equal to ten. {{#expr:+7}} = 7 (Positive) seven is equal to (positive) seven.
-	Subtracts two operands or a unary operator	{{#expr:10-3}} = 7 Ten minus three equals to seven. {{#expr:+-8}} = -8 (Positive) negative eight is equal to negative eight.
*	Multiplies two operands together	{{#expr:2*9}} = 18 Two multiplied by nine equals to eighteen.
/	Divides two operands	{{#expr:35/7}} = 5 Thirty-five divided by seven is equal to five.
^	Exponent, Multiplies the number x times	{{#expr:4^3}} = 64 Four to the power of three is equal to sixty-four.
!=	Inequality	{{#expr:2!=6}} = 1 Two is unequal (True(1)) to six. {{#expr:3+2^2!=7}} = 0 Two to the power of two (four) plus three (seven) is not unequal (False(0)) to seven.
=	Equality	{{#expr:(4-2)^2=4}} = 1 Four minus two (two) to the power of two (four) is equal (True(1)) to four. {{#expr:9+3^2=144}} = 0 Three to the power of two (nine) plus nine (eighteen) is not equal (False(0)) to one hundred and forty-four.
>	Greater than	{{#expr:2>1}} = 1 Two is greater than (True(1)) one. {{#expr:e>e}} = 0 The Euler number (2.71828...) is not greater than (False(0)) itself.
>=	Greater than or equal to	{{#expr:7>=7}} = 1 Seven is equal to (True(1)) seven. {{#expr:2>=0}} = 1 Two is not greater than (False(0)) zero.
<	Less than	{{#expr:1<{{#expr:4/3}}}} = 1 One is less than (True(1)) four-thirds (1.333...). {{#expr:abs-50<22}} = 0 The absolute value of negative fifty (fifty) is not less than (False(0)) twenty-two.
<=	Less than or equal to	{{#expr:9<=(8+({{#expr:1/3}}+{{#expr:2/3}}))}} = 1 Nine is equal to (True(1)) one third added to two thirds. {{#expr:2<=1}} = 0 Two is not less than (False(0)) one.
abs	Absolute value	{{#expr:abs-6}} = 6 The absolute value of negative six is equal to (positive) six.
acos	Inverse of cos function	{{#expr:acos1}} = 0 The arccosine of one is zero. {{#expr:acos(sqrt(2)/2)}} = 0.78539816339745 The arccosine of √2 halved is pi/4 (~0.785).
and	Logical AND	{{#expr:5 and 4}} = 1 True(5) and True(4) is equal to True(1). {{#expr:0 and 0}} = 0 False(0) and False(0) is equal to False(0).
asin	Inverse of sine function	{{#expr:asin0}} = 0 The arcsine of zero is zero. {{#expr:asin(0.5)}} = 0.5235987755983 The arcsine of one half is pi/6 (~0.524)
atan	Inverse of tan function	{{#expr:atan1}} = 0.78539816339745 The arctangent of one is pi/4 (~0.785). {{#expr:atan(sqrt(3))}} = 1.0471975511966 The arctangent of √3 is pi/3 (~1.05).
ceil	Raises the decimal to the next integer	{{#expr:ceil-3.9}} = -3 The ceiling of negative three and nine tenths is equal to negative three.
cos	Cosine function in radians	{{#expr:cos0}} = 1 The cosine of zero radians is one. {{#expr:cos(45*pi/180)}} = 0.70710678118655 The cosine of 45 degrees is √2/2 (~0.707).
div	Same as division	{{#expr:6 div 2}} = 3 Six divided by two is equal to three.
exp	Irrational number e (euler number) to x power	{{#expr:exp5}} = 148.41315910258 The Euler number to the power of five is about one hundred and forty-eight.
floor	Lowers the decimal to the next integer	{{#expr:floor-6.79}} = -7 The floor of negative six and seventy-nine hundredths is equal to negative seven.
ln	Natural logarithm	{{#expr:ln(e^5)}} = 5 The (natural) logarithm for e to the power of five is five. {{#expr:ln pi/ln10}} = 0.49714987269413 The base ten (natural) algorithm for pi is about zero and five tenths.
mod	Modulo, remainder	{{#expr:19 mod 7}} = 5 The remainder of nineteen divided by seven is five.
not	Logical NOT	{{#expr:not 4}} = 0 Not True(4) is equal to False(0). {{#expr:not 0}} = 1 Not False(0) is equal to True(1).
or	Logical OR	{{#expr:0 or 0}} = 0 False(0) or False(0) is equal to False(0). {{#expr:0 or 5}} = 1 False(0) or True(5) is equal to True(1).
round	Rounds the number to the xth digit after the decimal	{{#expr:1.4757027 round 3}} = 1.476 One and four million, seven hundred fifty-seven thousand, twenty-seven ten-millionths rounded to the third digit after the decimal point is equal to one and four hundred seventy-six thousandths. {{#expr:82978 round -2}} = 83000 Eighty-two thousand, nine hundred and seventy-eight rounded to the second digit before the decimal point is equal to eighty-three thousand.
sin	Sine function in radians	{{#expr:sin1}} = 0.8414709848079 The sine of one radian is about zero and eight tenths. {{#expr:sin(30*pi/180)}} = 0.5 The sine of thirty degrees is equal to one half.
tan	Tangent function in radians	{{#expr:tan0}} = 0 The tangent of zero is zero. {{#expr:tan(45*pi/180)}} = 1 The tangent of 45 degrees is equal to one.
trunc	'Truncates' x into an integer without rounding	{{#expr:trunc-7.8}} = -7 Truncated negative seven and eight tenths is equal to negative seven.

Therefore,

• {{#expr:(0or1)+1}} = 2
• {{#expr:0or not1}} = 0
• {{#expr:------5}} = 5
• {{#expr:not not 1}} = 1
• {{#expr:not0 or not0 and not1}} = 1
• {{#expr:pi/pi and pi*pi/pi}} = 1
• {{#expr:.}} = 0
• {{#expr:.1}} = 0.1
• {{#expr:e-6}} = -3.281718171541
• {{#expr:1e-6}} = 1.0E-6

Errors

An error will result if:

• An operator is missing a parameter.
  • {{#expr:2+}} gives
• There is an unexpected number or operator.
  • {{#expr:2 3}} gives
  • {{#expr:=}} gives
• An unsupported word or character is used.
  • {{#expr:what}} gives
  • {{#expr:%}} gives
• A mathematical error occurs.
  • {{#expr:1/0}} gives
  • {{#expr:ln-1}} gives

If a number is too large, it returns INF (positive infinity) or -INF (negative infinity).

• {{#expr:1e309}} gives INF
• {{#expr:-1e309}} gives -INF

See Also

• Help:Magic words
• Truth Table
• Trigonometry