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A formula can be any algebraic expression understood by the Emacs
`Calc` package. **Note that **`calc`** has the
non-standard convention that ‘**`/`**’ has lower precedence than
‘**`*`**’, so that ‘**`a/b*c`**’ is interpreted as ‘**`a/(b*c)`**’.** Before
evaluation by `calc-eval`

(see calc-eval),
variable substitution takes place according to the rules described above.
The range vectors can be directly fed into the Calc vector functions
like ‘`vmean`’ and ‘`vsum`’.

A formula can contain an optional mode string after a semicolon. This
string consists of flags to influence Calc and other modes during
execution. By default, Org uses the standard Calc modes (precision
12, angular units degrees, fraction and symbolic modes off). The display
format, however, has been changed to `(float 8)`

to keep tables
compact. The default settings can be configured using the variable
`org-calc-default-modes`

.

p20 set the internal Calc calculation precision to 20 digits n3 s3 e2 f4 Normal, scientific, engineering, or fixed format of the result of Calc passed back to Org. Calc formatting is unlimited in precision as long as the Calc calculation precision is greater. D R angle modes: degrees, radians F S fraction and symbolic modes N interpret all fields as numbers, use 0 for non-numbers E keep empty fields in ranges L literal

Unless you use large integer numbers or high-precision-calculation
and -display for floating point numbers you may alternatively provide a
`printf`

format specifier to reformat the Calc result after it has been
passed back to Org instead of letting Calc already do the
formatting^{1}.
A few examples:

$1+$2 Sum of first and second field $1+$2;%.2f Same, format result to two decimals exp($2)+exp($1) Math functions can be used $0;%.1f Reformat current cell to 1 decimal ($3-32)*5/9 Degrees F -> C conversion $c/$1/$cm Hz -> cm conversion, usingconstants.eltan($1);Dp3s1 Compute in degrees, precision 3, display SCI 1 sin($1);Dp3%.1e Same, but use printf specifier for display vmean($2..$7) Compute column range mean, using vector function vmean($2..$7);EN Same, but treat empty fields as 0 taylor($3,x=7,2) Taylor series of $3, at x=7, second degree

Calc also contains a complete set of logical operations. For example

```
if($1<20,teen,string("")) "teen" if age $1 less than 20, else empty
```

Note that you can also use two org-specific flags `T`

and `t`

for
durations computations Durations and time values.

[1] The `printf`

reformatting is limited in precision
because the value passed to it is converted into an `integer`

or
`double`

. The `integer`

is limited in size by truncating the
signed value to 32 bits. The `double`

is limited in precision to 64
bits overall which leaves approximately 16 significant decimal digits.