GNUCalc Reference Card                                            Arithmetic                                                            Scientific Functions
                      (for GNU Emacs version 28)
                                                                            add, subtract, multiply, divide               +, -, *, /              ln, log10, logb                               L, H L, B
                                                                                                                                                               x    x
     Starting and Stopping                                                  raise to a power, nth root                    ^, I ^                  exponential e , 10                            E, H E
                                                                            change sign                                   n                       sin, cos, tan                                 S, C, T
                                                                            reciprocal 1/x                                &                       arcsin, arccos, arctan                        I S, I C, I T
     start/stop standard Calc                      C-x * c                  square root √x                                Q                       inverse, hyperbolic prefix keys                I, H
     start/stop X keypad Calc                      C-x * k                  set precision                                 p                       two-argument arctan                           f T
        start/stop either: C-x * *                                          round off last two digits                      c 2                     degrees, radians modes                        m d, m r
     stop standard Calc                            q                        convert to fraction, float                     c F, c f                pi (π)                                        P
     Calc tutorial                                 C-x * t                  enter using algebraic notation                ’ 2+3*4                 factorial, double factorial                   !, k d
     run Calc in other window                      C-x * o                  refer to previous result                      ’ 3*$^2                 combinations, permutations                    k c, H k c
     quick calculation in minibuffer                C-x * q                  refer to higher stack entries                 ’ $1*$2^2               prime factorization                           k f
                                                                            finish alg entry without evaluating            LFD                     next prime, previous prime                    k n, I k n
     Getting Help                                                           set mode where alg entry used by default      m a                     GCD, LCM                                      k g, k l
                                                                                                                                                  random number, shuffle                          k r, k h
     The h prefix key is Calc’s analogue of C-h in Emacs.                    Stack Commands                                                        minimum, maximum                              f n, f x
     quick summary of keys                         ?                                                                                              error functions erf, erfc                     f e, I f e
     describe key briefly                           h c                      Here S is the nth stack entry, and N is the size of the stack.        gamma, beta functions                         f g, f b
                                                                                  n
     describe key fully                            h k                        key       no prefix         prefix n          prefix −n                incomplete gamma, beta functions              f G, f B
     describe function or command                  h f                                                                                            Bessel J , Y  functions                       f j, f y
                                                                              RET       copy S           copy S           copy S                          ν   ν
                                                                                               1               1..n             n
     read Info manual                              h i or C-x * i             LFD       copy S           copy S           copy S                  complex magnitude, arg, conjugate             A, G, J
                                                                                               2               n                1..n
     read full Calc summary                        h s or C-x * s             DEL       delete S         delete S         delete S                real, imaginary parts                         f r, f i
                                                                                                1                1..n             n
                                                                              M-DEL     delete S         delete S         delete S                convert polar/rectangular                     c p
                                                                                                2                n                1..n
                                                                              TAB       swap S ↔S        roll S to S      roll S to S
     Error Recovery                                                                            1    2         1     n          n     N
                                                                              M-TAB     roll S to S      roll S to S      roll S  to S
                                                                                             3     1          n     1          N      n           Financial Functions
     abort command in progress                     C-g                      With a 0 prefix, these copy, delete, or reverse the entire stack.
     display recent error messages                 w                                                                                              enter percentage                              M-%
     undo last operation                           U                        Display                                                               convert to percentage                         c %
     redo last operation                           D                                                                                              percentage change                             b %
     recall last arguments                         M-RET                    scroll horizontally, vertically               < >, { }
     edit top of stack                             ‘                                                                                              present value                                 b P
     reset Calc to initial state                   C-x * 0 (zero)           home cursor                                   o                       future value                                  b F
                                                                            line numbers on/off                            d l                     rate of return                                b T
                                                                            trail display on/off                           t d                     number of payments                            b #
     Transferring Data                                                      scientific notation                            d s                     size of payments                              b M
                                                                            fixed-point notation                           d f                     net present value, int. rate of return        b N, b I
     grab region from a buffer                      C-x * g                  floating-point (normal) notation               d n                     Above computations assume payments at end of period. Use I
     grab rectangle from a buffer                   C-x * r                  group digits with commas                      d g                     prefix for beginning of period, or H for a lump sum investment.
     grab rectangle, summing columns               C-x * :                  For display mode commands, H prefix prevents screen redraw
     grab rectangle, summing rows                  C-x * _                                                                                        straight-line depreciation                    b S
                                                                            and I prefix temporarily redraws top of stack.                         sum-of-years’-digits                          b Y
     yank data to a buffer                          C-x * y                                                                                        double declining balance                      b D
     Also, try C-k/C-y or X cut and paste.                                  Notations
                                                                                                                                                  Units
     Examples                                                               scientific notation                            6.02e23
     In RPN, enter numbers first, separated by RET if necessary,             minus sign in numeric entry                   _23 or 23 n             enter with units                              ’ 55 mi/hr
     then type the operator. To enter a calculation in algebraic            fractions                                     3:4                     convert to new units, base units              u c, u b
     form, press the apostrophe first.                                       complex numbers                               (x, y)                  convert temperature units                     u t
                                                                            polar complex numbers                         (r; θ)                  simplify units expression                     u s
                    RPNstyle:               algebraic style:                vectors (commas optional)                     [1, 2, 3]               view units table                              u v
        Example:    2 RET 3 +               ’ 2+3 RET                       matrices (or nested vectors)                  [1, 2; 3, 4]            Common units:
        Example:    2 RET 3 + 4 *           ’ (2+3)*4 RET                   error forms (p key)                           100 +/- 0.5               distance: m, cm, mm, km; in, ft, mi, mfi; point, lyr
        Example:    2 RET 3 RET 4 + *       ’ 2*(3+4) RET                   interval forms                                [2 .. 5)                  volume: l or L, ml; gal, qt, pt, cup, floz, tbsp, tsp
        Example:    3 RET 6 + Q 3 ^         ’ sqrt(3+6)^3 RET               modulo forms (M key)                          6 mod 24                  mass: g, mg, kg, t; lb, oz, ton
        Example:    P 3 / n S               ’ sin(-pi/3) RET =              HMSforms                                      5@ 30’ 0"                 time: s or sec, ms, us, ns, min, hr, day, wk
                                                                            date forms                                                 temperature: degC, degF, K
          c                                                                 infinity, indeterminate                        inf, nan
          
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          GNUCalc Reference Card                                           Algebra                                                               Selections
     Programmer’s Functions                                                enter an algebraic formula                    ’ 2x+3y^2               select subformula under cursor                j s
                                                                           enter an equation                             ’ 2x^2=18               select nth subformula                         j n
                                                                           symbolic (vs. numeric) mode                   m s                     select more                                   j m
     binary, octal, hex display                    d 2, d 8, d 6           fractions (vs. float) mode                     m f                     unselect this, all formulas                   j u, j c
     decimal, other radix display                  d 0, d r                suppress evaluation of formulas               m O                     copy indicated subformula                     j RET
     display leading zeros                         d z                     return to default evaluation rules            m D                     delete indicated subformula                   j DEL
     entering non-decimal numbers                  16#7FFF
     binary word size                              b w                     “Big” display mode                            d B                     commute selected terms                        j C
     binary AND, OR, XOR                           b a, b o, b x           C, Pascal, FORTRAN modes                      d C, d P, d F           commute term leftward, rightward              j L, j R
                                                                           T X, LaT X, eqn modes                         d T, d L, d E           distribute, merge selection                   j D, j M
     binary DIFF, NOT                              b d, b n                 E       E
     left shift                                    b l                     Maxima                                        d X                     isolate selected term in equation             j I
     logical right shift                           b r                     Unformatted mode                              d U                     negate, invert term in context                j N, j &
     arithmetic right shift                        b R                     Normal language mode                          d N                     rewrite selected term                         j r
     integer quotient, remainder                   \, %                    simplify formula                              a s
     integer square root, logarithm                f Q, f I                put formula into rational form                a n                     Graphics
     floor, ceiling, round to integer               F, I F, R               evaluate variables in formula                 =
                                                                           evaluate numerically                          N                       graph function or data                        g f
                                                                           let variable equal a value in formula         s l x=val               graph 3D function or data                     g F
     Variables                                                             declare properties of variable                s d                     replot current graph                          g p
     Variable names are single digits or whole words.                        Common decls: pos, int, real, scalar, [a..b].                       print current graph                           g P
     store to variable                             s t                     expand, collect terms                         a x, a c                add curve to graph                            g a
     store and keep on stack                       s s                     factor, partial fractions                     a f, a a                set number of data points                     g N
     recall from variable                          s r                     polynomial quotient, remainder, GCD           a \, a %, a g           set line, point styles                        g s, g S
     shorthands for digit variables                t n, s n, r n           derivative, integral                          a d, a i                set log vs. linear x, y axis                  g l, g L
     unstore, exchange variable                    s u, s x                taylor series                                 a t                     set range for x, y axis                       g r, g R
     edit variable                                 s e                     principal solution to equation(s)             a S                     close graphics window                         g q
                                                                           list of solutions                             a P
     Vector Operations                                                     generic solution                              H a S                   Programming
                                                                           apply function to both sides of eqn           a M
     vector of 1, 2, ..., n                        v x n                   rewrite formula                               a r                     begin, end recording a macro                  C-x (, C-x )
     vector of n counts from a by b                C-u v x                   Example: a r a*b + a*c := a*(b+c)                                   replay keyboard macro                         X
     vector of copies of a value                   v b                       Example: a r sin(x)^2 := 1-cos(x)^2                                 read region as written-out macro              C-x * m
     concatenate into vector                       |                         Example: a r cos(n pi) := 1 :: integer(n) :: n%2 = 0                if, else, endif                               Z [, Z :, Z ]
     pack many stack items into vector             v p                       Example: a r [f(0) := 1, f(n) := n f(n-1) :: n > 0]                 equal to, less than, member of                a =, a <, a {
     unpack vector or object                       v u                       Put rules in EvalRules to have them apply automatically.            repeat n times, break from loop               Z <, Z >, Z /
                                                                             Put rules in AlgSimpRules to apply during a s command.              “for” loop: start, end; body, step            Z (, Z )
     length of vector (list)                       v l                       Common markers: opt, plain, quote, eval, let, remember.             save, restore mode settings                   Z ‘, Z ’
     reverse vector                                v v                                                                                           query user during macro                       Z #
     sort, grade vector                            V S, V G                Numerical Computations                                                put finished macro on a key                    Z K
     histogram of vector data                      V H                                                                                           define function with formula                   Z F
     extract vector element                        v r                                                                                           edit definition                                Z E
     matrix determinant, inverse                   V D, &                  sum formula over a range                      a +
     matrix transpose, trace                       v t, V T                product of formula over a range               a *                     record user-defined command permanently        Z P
     cross, dot products                           V C, *                  tabulate formula over a range                 a T                     record variable value permanently             s p
     identity matrix                               v i                     integrate numerically over a range            a I                     record mode settings permanently              m m
     extract matrix row, column                    v r, v c                find zero of formula or equation               a R
                                                                           find local min, max of formula                 a N, a X
     intersection, union, diff of sets              V ^, V V, V -           fit data to line or curve                      a F
     cardinality of set                            V #
                                                                                                                                                                    c
                                                                           mean of data in vector or variable            u M                              Copyright 
 2022 Free Software Foundation, Inc.
     add vectors elementwise (i.e., map +)         V M +                   median of data                                H u M                             designed by Dave Gillespie and Stephen Gildea,
     sum elements in vector (i.e., reduce +)       V R +                   geometric mean of data                        u G                                          for GNU Emacs Calc.
     sum rows in matrix                            V R _ +                 sum, product of data                          u +, u *                Released under the terms of the GNU General Public License version 3
     sum columns in matrix                         V R : +                 minimum, maximum of data                      u N, u X                or later.
     sum elements, accumulate results              V U +                                                                                         For more Emacs documentation, and the T X source for this card, see
                                                                           sample, pop. standard deviation               u S, I u S                                                   E
                                                                                                                                                 the Emacs distribution, or https://www.gnu.org/software/emacs