1QALC(1) General Commands Manual QALC(1)
2
6 qalc - Powerful and easy to use command line calculator
7
9 qalc [options] [expression]
10
12 Qalculate! is a multi-purpose cross-platform desktop calculator. It is
13 simple to use but provides power and versatility normally reserved for
14 complicated math packages, as well as useful tools for everyday needs
15 (such as currency conversion and percent calculation). Features include
16 a large library of customizable functions, unit calculations and con‐
17 version, physical constants, symbolic calculations (including integrals
18 and equations), arbitrary precision, uncertainty propagation, interval
19 arithmetic, plotting, and a user-friendly interface. qalc is the com‐
20 mand line interface of Qalculate!.
21
23 -b, --base base
24 set the number base for results and, optionally, expressions
25 -c, --color
27 use colors to hightlight different elements of expressions and
28 results
29 -e, --exrates
31 update exchange rates
32 -f, --file file
34 execute commands from a file first
35 -h, --help
37 display this help and exits
38 -i, --interactive
40 start in interactive mode
41 -l, --list [search term]
43 displays a list of all user-defined or matching variables,
44 functions, units, and prefixes.
45 --list-functions [search term]
47 displays a list of all or matching functions.
48 --list-prefixes [search term]
50 displays a list of all or matching prefixes.
51 --list-units [search term]
53 displays a list of all or matching units.
54 --list-variables [search term]
56 displays a list of all or matching variables.
57 -m, --time milliseconds
59 terminate calculation and display of result after specified
60 amount of time
61 -n, --nodefs
63 do not load any functions, units, or variables from file
64 --nocurrencies
66 do not load any global currencies from file
67 --nodatasets
69 do not load any global data sets from file
70 --nofunctions
72 do not load any global functions from file
73 --nounits
75 do not load any global units from file
76 --novariables
78 do not load any global variables from file
79 -p [base]
81 start in programming mode (same as -b "base base" -s "xor^",
82 with base conversion)
83 -s, --set "option value"
85 as set command in interactive program session (ex. --set "base
86 16")
87 -t, --terse
89 reduce output to just the result of the input expression
90 -/+u8 switch unicode support on/off
92 -v, --version
94 show application version and exit
95 The program will start in interactive mode if no expression and no file
97 is specified (or interactive mode is explicitly selected).
98
100 approximate
101 Equivalent to set approximation try exact.
102 assume assumptions
104 Set default assumptions for unknown variables (unknown, non-
105 zero, positive, negative, non-positive, non-negative + number,
106 real, rational, integer).
107 base base
109 Sets the result number base (equivalent to set base).
110 delete name
112 Removes the user-defined variable or function with the speci‐
113 fied name.
114 Example: delete var1.
115 exact Equivalent to set approximation exact.
117 expand Expands the current result.
119 exrates Downloads current exchange rates from the Internet.
121 factor Factorizes the current result.
123 find, list [name]
125 Displays a list of variables, functions and units. Enter with
126 argument 'currencies', 'functions', 'variables', 'units', or
127 'prefixes' to show a list of all currencies, functions, vari‐
128 ables, units, or prefixes. Enter a search term to find matching
129 variables, functions, units, and/or prefixes. If command is
130 called with no argument all user-definied objects are listed.
131 Example: list functions.
132 Example: find dinar.
133 Example: find variables planck.
134 function name expression
136 Creates a function with the specified name and expression. Use
137 '\x', '\y', '\z', '\a', etc. for arguments in the expression.
138 Example: function func1 5*\x.
139 help [command]
141 info Displays information about a function, variable, unit, or pre‐
143 fix.
144 Example: info sin.
145 MC/MS/M+/M-
147 Memory operations (memory clear, memory store, memory plus,
148 memory minus). Recall the memory using the MR/MRC variable.
149 mode Displays the current mode.
151 partial fraction
153 Applies partial fraction decomposition to the current result.
154 save, store name [category] [title]
156 Saves the current result in a variable with the specified name.
157 You may optionally also provide a category (default "Tempo‐
158 rary") and a title. If name equals "mode" or "definitions",
159 the current mode and definitions, respectively, will be saved.
160 Example: store var1.
161 save definitions
163 save mode
165 set option value
167 to, convert, -> unit/"to"-command
169 Converts the previous result. Equivalent to using "to" at the
170 end of an expression. Example: to m/s
171 Example: to bin
172 variable name expression
174 Create a variables with the specified name and expression.
175 Example: variable var1 pi / 2.
176 quit/exit
178 Terminates the program.
179 Commands for RPN mode:
181 rpn state
183 (De)activates the Reverse Polish Notation stack and syntax.
184 "syntax" activates only the RPN syntax and "stack" enables the
185 RPN stack.
186 stack Displays the RPN stack.
188 clear stack
190 Clears the entire RPN stack.
191 copy [index]
193 Duplicates a value on the RPN stack to the top of the stack. If
194 no index is specified, the top of the stack is duplicated.
195 Index 1 is the top of stack and negative index values counts
196 from the bottom of the stack.
197 move index 1 index 2
199 Changes the position of a value on the RPN stack. Index 1 is
200 the top of stack and negative index values counts from the bot‐
201 tom of the stack.
202 Example: move 2 4
203 pop [index]
205 Removes the top of the RPN stack or the value at the specified
206 index. Index 1 is the top of stack and negative index values
207 counts from the bottom of the stack.
208 rotate [direction]
210 Rotates the RPN stack up (default) or down.
211 swap [index 1] [index 2]
213 Swaps position of values on the RPN stack. If no index is spec‐
214 ified, the values on the top of the stack (index 1 and index 2)
215 will be swapped and if only one index is specified, the value
216 at this index will be swapped with the top value. Index 1 is
217 the top of stack and negative index values counts from the bot‐
218 tom of the stack.
219 Example: swap 2 4
220 When a line begins with '/', the text that follows is always inter‐
222 preted as a command.
223
225 Tab shows a list of functions, variables, and units that matches
226 the last object in the current expression
227 Ctrl+D terminates the program
229 Ctrl+E switches between approximation modes (exact, try exact, auto)
231 Ctrl+F switches between fraction modes (simple, decimal, auto)
233 Ctrl+A saves the current result in a temporary variable
235
237 These settings are changed using the set command (e.g. set base 16) or
238 the -s, --set command line option (e.g. qalc -s "base 16"). Possible
239 values are shown in parenthesis. 1 and 0 can be used instead of on and
240 off. If the value is left out, a value of 1 is generally assumed. The
241 default value is marked with '*'.
242 Algebraic mode:
244 algebra mode, alg (1* = expand, 2 = factorize)
246 Determines if the expression is factorized or not after calcu‐
247 lation.
248 assume nonzero denominators, nzd (on*, off)
250 Determines if unknown values will be assumed non-zero (x/x=1).
251 warn nonzero denominators, warnnzd (on*, off)
253 Display a message after a value has been assumed non-zero.
254 assumptions, ass (unknown*, non-zero, positive, negative, non-positive,
256 non-negative + number, real*, rational, integer)
257 Default assumptions for unknown variables.
258 Calculation:
260 angle unit, angle (0 = none, 1* = radians, 2 = degrees, 3 = gradians)
262 Default angle unit for trigonometric functions.
263 approximation, appr (-1* = auto, 0 = exact, 1 = try exact, 2 = approxi‐
265 mate, 3 = dual)
266 How approximate variables and calculations are handled. In
267 exact mode approximate values will not be calculated.
268 interval arithmetic, ia (on*, off)
270 If activated, interval arithmetic determines the final preci‐
271 sion of calculations (avoids wrong results after loss of sig‐
272 nificance) with approximate functions and/or irrational num‐
273 bers.
274 interval calculation, ic (1* = variance formula, 2 = interval arith‐
276 metic)
277 Determines the method used for interval calculation / uncer‐
278 tainty propagation.
279 precision, prec (> 0) 10*
281 Specifies the default number of significant digits displayed
282 and determines the precision used for approximate calculations.
283 Enabled objects:
285 calculate functions, calcfunc (on*, off)
287 calculate variables, calcvar (on*, off)
289 complex numbers, cplx (on*, off)
291 functions, func (on*, off)
293 infinite numbers, inf (on*, off)
295 units (on*, off)
297 unknowns (on, off*)
299 Interprete undefined symbols in expressions as unknown vari‐
300 ables.
301 variables, var (on*, off)
303 variable units, varunit (on*, off)
305 If activated physical constants include units (e.g. c =
306 299 792 458 m∕s).
307 Generic display options:
309 abbreviations, abbr (on*, off)
311 Use abbreviated names for units and variables.
312 color (0 = off, 1* = default, 2 = light)
314 Use colors to highlight different elements of expressions and
315 results.
316 division sign, divsign (0* = /, 1 = division slash, 2 = division sign)
318 excessive parentheses, expar (on, off*)
320 minus last, minlast (on, off*)
322 Always place negative values last.
323 multiplication sign, mulsign (0 = *, 1 = multiplication dot, 2* = mul‐
325 tiplication x, 3 = middle dot)
326 short multiplication, shortmul (on*, off)
328 spacious, space (on*, off)
330 Add extra space around operators.
331 spell out logical, spellout (on*, off)
333 unicode, uni (on*, off)
335 Display Unicode characters.
336 Numerical display:
338 base (-1114112 - 1114112, bin, oct, dec*, hex, sexa, time, roman)
340 base display, basedisp (0 = none, 1* = normal, 2 = alternative)
342 complex form, cplxform (0* = rectangular, 1 = exponential, 2 = polar, 3
344 = cis, 4 = angle)
345 decimal comma (locale*, off, on)
347 Determines the default decimal separator.
348 digit grouping, group (0* = off, 1 = standard, 2 = locale)
350 fractions, fr (-1* = auto, 0 = off, 1 = exact, 2 = on, 3 = mixed, 4 =
352 long, 5 = dual)
353 Determines how rational numbers are displayed (e.g. 5/4 = 1 +
354 1/4 = 1.25). 'long' removes limits on the size of the numerator
355 and denonimator.
356 hexadecimal two's, hextwos (on, off*)
358 Enables two's complement representation for display of negative
359 hexadecimal numbers.
360 imaginary j, imgj (on, off*)
362 Use 'j' (instead of 'i') as default symbol for the imaginary
363 unit.
364 interval display, ivdisp (0* = adaptive, 1 = significant, 2 = interval,
366 3 = plusminus, 4 = midpoint, 5 = upper, 6 = lower)
367 lowercase e, lowe (on, off*)
369 Use lowercase e for E-notation (5e2 = 5 * 10^2).
370 lowercase numbers, lownum (on, off*)
372 Use lowercase letters for number bases > 10.
373 max decimals, maxdeci (off*, >= 0)
375 min decimals, mindeci (off*, >= 0)
377 round to even, rndeven (on, off*)
379 Determines whether halfway numbers are rounded upwards or
380 towards the nearest even integer.
381 scientific notation, exp (0 = off, -1 = auto*, -3 = engineering, 1 =
383 pure, 3 = scientific, >= 0)
384 Determines how scientific notation are used (e.g. 5 543 000 =
385 5.543E6).
386 show ending zeroes, zeroes (on*, off)
388 If actived, zeroes are kept at the end of approximate numbers.
389 two's complement, twos (on*, off)
391 Enables two's complement representation for display of negative
392 binary numbers.
393 Parsing:
395 caret as xor, xor^ (on, off*)
397 Use ^ as bitwise exclusive OR operator.
398 decimal comma (locale*, off, on)
400 Determines the default decimal separator.
401 ignore comma (on, off*)
403 Allows use of ',' as thousands separator.
404 ignore dot (on, off*)
406 Allows use of '.' as thousands separator.
407 imaginary j, imgj (on, off*)
409 Use 'j' (instead of 'i') as default symbol for the imaginary
410 unit.
411 input base, inbase (-1114112 - 1114112, bin, oct, dec*, hex, roman)
413 limit implicit multiplication, limimpl (on, off*)
415 parsing mode, syntax (0* = adaptive, 1 = implicit first, 2 = conven‐
417 tional, 3 = chain, 4 = rpn)
418 See syntax section.
419 read precision, readprec (0* = off, 1 = always, 2 = when decimals)
421 If activated, numbers be interpreted as approximate with preci‐
422 sion equal to the number of significant digits (3.20 =
423 3.20+/-0.005).
424 Units:
426 all prefixes, allpref (on, off*)
428 Enables automatic use of hecto, deca, deci, and centi.
429 autoconversion, conv (none, optimal*, base, optimalsi, mixed)
431 Controls automatic unit conversion of the result. 'optimalsi'
432 always converts non-SI units, while 'optimal' only converts to
433 more optimal unit expressions, with less units and exponents.
434 binary prefixes, binpref (on, off*)
436 If activated, binary prefixes are used by default for informa‐
437 tion units.
438 currency conversion, curconv (on*, off)
440 Enables automatic conversion to the local currency when optimal
441 unit conversion is enabled.
442 denominator prefixes, denpref (on*, off)
444 Enables automatic use of prefixes in the denominator of unit
445 expressions.
446 place units separately, unitsep (on*, off)
448 If activated, units are separated from variables at the end of
449 the result.
450 prefixes, pref (on*, off)
452 Enables automatic use of prefixes in the result.
453 show negative exponents, negexp (on, off*)
455 Use negative exponents instead of division for units in result
456 (m/s = m*s^-1).
457 sync units, sync (on*, off)
459 temperature units, temp (hybrid*, absolute, relative)
461 Determines how expressions with temperature units are calcu‐
462 lated (hybrid acts as absolute if the expression contains dif‐
463 ferent temperature units, otherwise as relative).
464 update exchange rates, upxrates (-1 = ask*, 0 = never, > 0 = days)
466 Other:
468 ignore locale (yes, no*)
470 Ignore system language and use English (requires restart).
471 rpn (on, off*)
473 Activates the Reverse Polish Notation stack.
474 save definitions (yes*, no)
476 Save functions, units, and variables on exit.
477 save mode (yes*, no)
479 Save settings on exit.
480
482 Mathematical entities:
483 Numbers
485 These are the regular numbers composed by digits 0-9 and a deci‐
486 mal sign — a dot, or a comma if it is the default decimal point
487 in the locale/language used. If comma is used as decimal sign,
488 the dot is still kept as an alternative decimal sign, if not
489 explicitely deactivated. Numbers include integers, real numbers,
490 and complex numbers. The imaginary part of complex numbers are
491 written with as regular number followed by the special variable
492 "i" (can be changed to a "j"), which represents the square root
493 of -1. Spaces between digits are ignored ("5 5 = 55"). "E" (or
494 "e") can be considered as a shortcut for writing many zeroes and
495 is equivalent to multiplication by 10 raised to the power of the
496 right-hand value (e.g. "5E3 = 5000"). Sexagesimal numbers (and
497 time) can be entered directly using colons (e.g. "5:30 = 5.5").
498 A number immediately preceeded "0b", "0o", "0d" or "0x" are
499 interpreted as a number with base 2, 8, 12 or 16, respectively
500 (e.g. "0x3f = 63").
501 Intervals
503 A number interval can be entered using the interval() function,
504 the uncertainty() function, or using "±" or "+/-" (e.g. 5±1 =
505 uncertainty(5, 0.2) = interval(4, 6)). If the read precision
506 option is activated, decimal numbers are interpreted as an
507 interval between the numbers that are normally rounded to the
508 entered number (e.g. 1.1 = 1.1±0.05). If interval calculation
509 using variance formula is activated (default), the interval rep‐
510 resents the standard uncertainty (deviation) of the value.
511 Vectors and Matrices
513 A matrix is a two-dimensional rectangular array of mathematical
514 objects. Vectors are matrices with only one row or column, and
515 thus one-dimensional sequences of objects. Vectors and matrices
516 are generated by various functions, or using syntax in the form
517 of [1, 2, 3, 4] and [[1, 2], [3, 4]].
518 Variables/Constants
520 See the list of variables in the GUI manual or using the command
521 .I list variables
522 Functions
524 See the list of functions in the GUI manual or using the command
525 .I list functions
526 Units and Prefixes
528 See the list of units and prefixes in the GUI manual or using
529 the command .I list units. Abbreviated, plural and singular
530 forms of unit names and prefixes are generally allowed. Prefixes
531 must be put immediately before the unit to be interpreted as
532 prefixes (eg. 5 mm = 0.005 m, but 5 m m = 5 m^2). For conve‐
533 nience units allow the power operator to be left out (e.g. 5 m2
534 = 5 m^2), with currencies excluded.
535 Unknowns
537 Unknowns are text strings without any associated value. These
538 are temporary unknown variables with default assumptions.
539 Unknowns can also be explicitly entered by placing a backslash
540 (\) before a single character (e.g. 5\a + 2\b) or using quota‐
541 tion mark before and after a text string (e.g. 5 "apples" + 2
542 "bananas"). If unknowns are activated characters without any
543 associated variable, function or unit in an expression, will be
544 regarded as an unknown variable.
545 Date and Time
547 Date/time values are specified using quoted text string (quota‐
548 tion marks are not needed for function arguments), using stan‐
549 dard date and time format (YYYY-MM-DDTHH:MM:SS). Some local for‐
550 mats are also supported, but not recommended. The local time
551 zone are used, unless a time zone is specified at the end of the
552 time string (Z/UTC/GMT or +/-HH:MM). Date/time supports a small
553 subset of arithmetic operations. The time units represents cal‐
554 ender time, instead of average values, when added or subtracted
555 to a date.
556 Text
558 This category represent a number of different function argument
559 types, such as regular text and file names. They can, but do not
560 need to be put in quotes except when containing the argument
561 separator.
562 Comments
564 All text after a hashtag (e.g. (5*2)/2 #calculating triangle
565 area) is treated as a comment, which are added to the history.
566 Operations and operators (word operators such as AND must be surrounded
568 by space):
569 Addition (+)
571 Subtraction (-)
573 Multiplication (*)
575 Division (/)
577 Modulo (%, mod)
579 Returns the remainder after division.
580 Integer Division (//, div)
582 Rounds the result of division towards zero.
583 Exponentiation (^, **)
585 Note that x^y^z equals x^(y^z), and not (x^y)^z. Note also that
586 for non-integer exponents with negative bases, the principal
587 root is returned and not the real root ((-8)^(1/3) equals 1 +
588 1.73i, and not -2). To calculate the real root for negative val‐
589 ues, use the cbrt() and root() functions.
590 10^x (E)
592 Parenthesis ((, ))
594 Logical operators (!, ||, OR, &&, AND)
596 Primarily used in conjunction with comparisons.
597 Bitwise operators (~, |, &, <<, >>, XOR)
599 Comparison operators (=, !=, <, <=, >, >=)
601 Returns 1 if expression is true and 0 if false. The x variable
602 is isolated if the expression does not evaluate as true or
603 false. Primarily used for equations and inequalities.
604 Evaluation priority order: parenthesis, 10^x, exponentiation, func‐
606 tions, bitwise NOT, logical NOT, multiplication/division/modulo, addi‐
607 tion/subtraction, bitwise NOT, bitwise shift, comparisons, bitwise AND,
608 bitwise XOR, bitwise OR, logical AND, logical OR.
609 The evaluation of short/implicit multiplication without any multiplica‐
611 tion sign (e.g. 5x, 5(2+3)), differs depending on the parsing mode. In
612 the conventional mode implicit multiplication does not differ from
613 explicit multiplication (12/2(1+2) = 12/2*3 = 18, 5x/5y = 5 * x/5 * y =
614 xy). In the parse implicit multiplication first mode, implicit multi‐
615 plication is parsed before explicit multiplication (12/2(1+2) = 12/(2 *
616 3) = 2, 5x/5y = (5 * x)/(5 * y) = x/y). The default adaptive mode works
617 as the parse implicit multiplication first mode, unless spaces are
618 found (1/5x = 1/(5 * x), but 1/5 x = (1/5) * x). In the adaptive mode
619 unit expressions are parsed separately (5 m/5 m/s = (5 * m)/(5 * (m/s))
620 = 1 s). Function arguments without parentheses are an exception, where
621 implicit multiplication in front of variables and units is parsed first
622 regardless of mode (sqrt 2x = sqrt(2x)).
623 In chain mode, expressions are calculated from left to right, ignoring
625 standard order of operations, as the immediate execution mode of a tra‐
626 ditional calculator (1+2*3 = (1+2)*3 = 9).
627 The "to"-operator is used for unit conversion and manipulation of how
629 the result is presented. Place " to " or a right arrow (e.g. "->") fol‐
630 lowed by one of expressions/commands the below, at the end of an
631 expression.
632 Unit conversion
634 - a unit or unit expression (e.g. meter or km/h)
635 prepend with ? to request the optimal prefix
636 prepend with b? to request the optimal binary prefix
637 prepend with + or - to force/disable use of mixed units
638 - a variable or physical constant (e.g. c)
639 - base (convert to base units)
640 - optimal (convert to optimal unit)
641 - mixed (convert to mixed units, e.g. hours + minutes)
642 Number base conversion
644 - bin, binary (show as binary number)
645 - bin# (show as binary number with specified number of bits)
646 - oct, octal (show as octal number)
647 - duo, duodecimal (show as duodecimal number)
648 - hex, hexadecimal (show as hexadecimal number)
649 - hex# (show as hexadecimal number with specified number of
650 bits)
651 - sex, sexagesimal (show as sexagesimal number)
652 - bijective (shown in bijective base-26)
653 - fp16, fp32, fp64, fp80, fp128 (show in binary floating-point
654 format)
655 - roman (show as roman numerals)
656 - time (show in time format)
657 - unicode
658 - base # (show in specified number base)
659 - bases (show as binary, octal, decimal and hexadecimal number)
660 Complex format
662 - rectangular, cartesian (show complex numbers in rectangular
663 form)
664 - exponential (show complex numbers in exponential form)
665 - polar (show complex numbers in polar form)
666 - cis (show complex numbers in cis form)
667 - angle, phasor (show complex numbers in angle/phasor notation)
668 Time and date conversion
670 - UTC (show date and time in UTC time zone)
671 - UTC+/-hh[:mm] (show date and time in specified time zone)
672 - calendars
673 Other conversion commands
675 - fraction (show result as mixed fraction)
676 - factors (factorize result)
677 Similarily where (or alternatively "/.") can be used at the end (but
679 before "to"), for variable assignments, function replacements, etc.
680 (e.g. "x+y where x=1 and y=2", "x^2=4 where x>0", and "sin(5) where
681 sin()=cos()").
682
684 Note that semicolon can be replaced with comma, if comma is not used as
685 decimal or thousands separator.
686 Basic functions and operators
688 sqrt 4 = sqrt(4)
690 = 4^(0.5)
691 = 4^(1/2)
692 = 2
693 sqrt(25; 16; 9; 4)
695 = [5; 4; 3; 2]
696 sqrt(32)
698 = 4 * sqrt(2) (in exact mode)
699 cbrt(-27)
701 = root(-27; 3)
702 = -3 (real root)
703 (-27)^(1/3)
705 = 1.5 + 2.5980762i (principal root)
706 ln 25 = log(25; e)
708 = 3.2188758
709 log2(4)/log10(100)
711 = log(4; 2)/log(100; 10)
712 = 1
713 5! = 1 * 2 * 3 * 4 * 5
715 = 120
716 5\2 (integer division)
718 = 5//2
719 = trunc(5/2)
720 = 2
721 5 mod 3 = mod(5; 3)
723 = 2
724 52 to factors
726 = 2^2 * 13
727 25/4 * 3/5 to fraction
729 = 3 + 3/4
730 gcd(63; 27)
732 = 9
733 sin(pi/2) - cos(pi)
735 = sin(90 deg) - cos(180 deg)
736 = 2
737 sum(x; 1; 5)
739 = 1 + 2 + 3 + 4 + 5 = 15
740 sum(i^2+sin(i); 1; 5; i)
742 = 1^2 + sin(1) + 2^2 + sin(2) + ... = 55.176162
743 product(x; 1; 5)
745 = 1 * 2 * 3 * 4 * 5 = 120
746 var1:=5 store value 5 in variable var1
748 5^2 #this is a comment
750 = 25
751 sinh(0.5) where sinh()=cosh()
753 = cosh(0.5) = 1.1276260
754 plot(x^2; -5; 5)
756 plots the function y=x^2 from -5 to 5
757 Units
759 5 dm3 to L
761 = 25 dm^3 to L
762 = 5 L
763 20 miles / 2h to km/h
765 = 16.09344 km/h
766 1.74 to ft = 1.74 m to ft
768 = 5 ft + 8.5039370 in
769 1.74 m to -ft
771 = 5.7086614 ft
772 100 lbf * 60 mph to hp
774 = 16 hp
775 50 Ω * 2 A
777 = 100 V
778 50 Ω * 2 A to base
780 = 100 kg*m^2*s^-3*A^-1
781 10 N / 5 Pa
783 = (10 N)/(5 Pa) = 2 m^2
784 5 m/s to s/m
786 = 0.2 s/m
787 500 EUR - 20% to USD
789 = 451.04 USD
790 500 megabit/s * 2 h to b?byte
792 = 419.09516 gibibytes
793 Physical constants
795 k_e / G * a_0
797 = (coulombs_constant / newtonian_constant) * bohr_radius
798 = 7.126e9 kg*H*m^-1
799 planck ∕ (compton_wavelength * c)
801 = 9.1093837e-31 kg
802 5 ns * rydberg to c
804 = 6.0793194E-8c
805 atom(Hg; weight) + atom(C; weight) * 4 to g
807 = 4.129e-22 g
808 (G * planet(earth; mass) * planet(mars; mass))/(54.6e6 km)^2
810 = 8.58e16 N (gravitational attraction between earth and mars)
811 Uncertainty and interval arithmetic
813 result with interval arithmetic activated is shown in parenthesis
814 sin(5+/-0.2)^2/2+/-0.3
816 = 0.460±0.088 (0.46+/-0.12)
817 (2+/-0.02 J)/(523+/-5 W)
819 = 3.824+/-0.053 ms (3.82+/-±0.075 ms)
820 interval(-2; 5)^2
822 = intervall(-8.2500000; 12.750000) (intervall(0; 25))
823 Algebra
825 (5x^2 + 2)/(x - 3)
827 = 5x + 15 + 47/(x - 3)
828 (\a + \b)(\a - \b) = ("a" + "b")("a" - "b")
830 = 'a'^2 - 'b'^2
831 (x + 2)(x - 3)^3
833 = x^4 - 7x^3 + 9x^2 + 27x - 54
834 factorize x^4 - 7x^3 + 9x^2 + 27x - 54
836 = x^4 - 7x^3 + 9x^2 + 27x - 54 to factors
837 = (x + 2)(x - 3)^3
838 cos(x)+3y^2 where x=pi and y=2
840 = 11
841 gcd(25x; 5x^2)
843 = 5x
844 1/(x^2+2x-3) to partial fraction
846 = 1/(4x - 4) - 1/(4x + 12)
847 x+x^2+4 = 16
849 x = 3 or x = -4
850 x^2/(5 m) - hypot(x; 4 m) = 2 m where x>0
852 x = 7.1340411 m
853 cylinder(20cm; x) = 20L
855 x = (1 / (2pi)) m
856 x = 16 cm (height of 20 L cylinder with radius 20 cm)
857 asin(sqrt(x)) = 0.2
859 x = sin(0.2)^2
860 x = 0.039469503
861 x^2 > 25x
863 = x > 25 or x < 0
864 solve(x = y+ln(y); y)
866 = lambertw(e^x)
867 solve2(5x=2y^2; sqrt(y)=2; x; y)
869 = 32/5
870 multisolve([5x=2y+32; y=2z; z=2x]; [x; y; z])
872 = [-32/3; -128/3; -64/3]
873 dsolve(diff(y; x) - 2y = 4x; 5)
875 = 6e^(2x) - 2x - 1
876 Calculus
878 diff(6x^2)
880 = 12x
881 diff(sinh(x^2)/(5x) + 3xy/sqrt(x))
883 = (2/5) * cosh(x^2) - sinh(x^2)/(5x^2) + (3y)/(2 * sqrt(x))
884 integrate(6x^2)
886 = 2x^3 + C
887 integrate(6x^2; 1; 5)
889 = 248
890 integrate(sinh(x^2)/(5x) + 3xy/sqrt(x))
892 = 2x * sqrt(x) * y + Shi(x^2) / 10 + C
893 integrate(sinh(x^2)/(5x) + 3xy/sqrt(x); 1; 2)
895 = 3.6568542y + 0.87600760
896 limit(ln(1 + 4x)/(3^x - 1); 0)
898 = 4 / ln(3)
899 Matrices and vectors
901 ((1; 2; 3); (4; 5; 6))
903 = [[1; 2; 3]; [4; 5; 6]] (2x3 matrix)
904 (1; 2; 3) * 2 - 2
906 = [1 * 2 - 2; 2 * 2 - 2; 3 * 2 - 2]
907 = [0; 2; 4]
908 (1; 2; 3) * (4; 5; 6)
910 = 32 (dot product)
911 cross((1; 2; 3); (4; 5; 6))
913 = [-3; 6; -3] (cross product)
914 ((1; 2; 3); (4; 5; 6)) * ((7; 8); (9; 10); (11; 12))
916 = [[58; 64]; [139; 154]]
917 hadamard([[1; 2; 3]; [4; 5; 6]]; [[7; 8; 9]; [10; 11; 12]])
919 = [[7; 16; 27]; [40; 55; 72]] (hadamard product)
920 ((1; 2); (3; 4))^-1
922 = inverse([[1; 2]; [3; 4]])
923 = [[-2; 1]; [1.5; -0.5]]
924 Statistics
926 mean(5; 6; 4; 2; 3; 7)
928 = 4.5
929 stdev(5; 6; 4; 2; 3; 7)
931 = 1.87
932 quartile((5; 6; 4; 2; 3; 7); 1)
934 = percentile([5; 6; 4; 2; 3; 7]; 25)
935 = 2.9166667
936 normdist(7; 5)
938 = 0.053990967
939 spearman(column(load(test.csv); 1); column(load(test.csv); 2))
941 = -0.33737388 (depends on the data in the CSV file)
942 Time and date
944 10:31 + 8:30 to time
946 = 19:01
947 10h 31min + 8h 30min to time
949 = 19:01
950 now to utc
952 = "2020-07-10T07:50:40Z"
953 "2020-07-10T07:50CET" to utc+8
955 = "2020-07-10T14:50:00+08:00"
956 "2020-05-20" + 523d
958 = addDays(2020-05-20; 523)
959 = "2021-10-25"
960 today - 5 days
962 = "2020-07-05"
963 "2020-10-05" - today
965 = days(today; 2020-10-05)
966 = 87
967 timestamp(2020-05-20)
969 = 1 589 925 600
970 stamptodate(1 589 925 600)
972 = "2020-05-20T00:00:00"
973 "2020-05-20" to calendars
975 returns date in Hebrew, Islamic, Persian, Indian, Chinese,
976 Julian, Coptic, and Ethiopian calendars
977 Number bases
979 52 to bin
981 = 0011 0100
982 52 to bin16
984 = 0000 0000 0011 0100
985 52 to oct
987 = 064
988 52 to hex
990 = 0x34
991 0x34 = hex(34)
993 = base(34; 16)
994 = 52
995 523<<2&250 to bin
997 = 0010 1000
998 52.345 to float
1000 = 0100 0010 0101 0001 0110 0001 0100 1000
1001 float(01000010010100010110000101001000)
1003 = 1715241/32768
1004 = 52.345001
1005 floatError(52.345)
1007 = 1.2207031e-6
1008 52.34 to sexa
1010 = 52°20'24"
1011 1978 to roman
1013 = MCMLXXVIII
1014 52 to base 32
1016 = 1K
1017 sqrt(32) to base sqrt(2)
1019 = 100000
1020
1022 The manual of the graphical user interface at https://qalcu‐
1023 late.github.io/manual/index.html (includes more details about the syn‐
1024 tax and elements supported in mathematical expressions, and various
1025 options, and includes a complete list of functions, variables, and
1026 units)
1027
1029 Please report any bugs at https://github.com/Qalculate/libqalcu‐
1030 late/issues
1031
1033 Hanna Knutsson <hanna.knutsson@protonmail.com>.
1034 13 July 2020 QALC(1)