Wikipedia:About valid routine calculations

The policy WP:CALC express, in general terms, when an editor can add some calculations (to an article) that are not in the sources, but are an obvious and acceptable interpretation of the source data:


 * Routine calculations do not count as original research. Basic arithmetic, such as adding numbers, converting units, or calculating a person's age, is allowed provided there is consensus among editors that the calculation is an obvious, correct, and meaningful reflection of the sources.

This essay supports both, a detailed review of "Routine calculations" at Wikipedia, and a natural extension to this policy:


 * The recursive use of routine calculations, such as summation, products of sequences, or the calculation of averages, also do not count as original research, when interpreted by the article's reader as a summary of numerical data &mdash; i.e. when used for well-known (and consensual) forms of "numerical synthesis". In this context, the synthesis of numerical data is not original research by synthesis.

Working definitions and examples
More formal and detailed definitions, to support Wikipedians that are discussing the policy WP:CALC and similar ones.

Routine calculations
A routine calculation consists of Any of these formulas must applied into a valid context of units,  dimension, precision, etc. and are valid as "routine calculation (WP:CALC)" when there is (implicit or discussed) consensus  among editors that the calculation is an obvious, correct, and meaningful reflection of the sources.
 * Basic arithmetic (single) operation: addition, subtraction, multiplication and division.
 * Well-known function: like unit conversion (between well-known units), numeral system conversion (between well-known systems), etc. The function needs a "tradition of use" and consensus in the Wikipedia.
 * Wikipedia well-known templates: that calculates automatically (and consensually). See list of conversion templates.

Round and precision
Using automatic conversion, it is easy and secure to convert units, like  to feet by the template:Convert,  , that results in. But, unfortunately, the work does not stop here. Quality work takes into account context and interprets precision: "5300 meters" often means something like "5300±100 meters". So the correct translation is with some round in the outcome:.

Numerical treatment and representation
When sources have complex or technical data, and editors need to reproduce data at Wikipedia for normal people, some numerical treatment can be made. Examples:
 * Use of error propagation rules when applying "routine calculation" on quantities with error values (ex. multiply 4.26 ± 0.02 by two).
 * Recursive use of routine calculation over a list of numbers.
 * Graphic representation of data.

Summary of numerical data
The repeated (recursive) use of routine operations, such as summation, "products of sequences", or the calculation of averages, are valid when used for well-known (and consensual) forms of "numerical synthesis", and can be interpreted by the article's reader as summaries of numerical data. Example:


 * {|class="wikitable"

!title="A"| quant. A !title="B"| quant. B !title="100*A/B"|Perc. of A !title="Difference between lines"| Diff.
 * 20  ||   123
 * style="background-color:#BCC"| 16.3% ||style="background-color:#BCC"|
 * 40  ||   234
 * style="background-color:#BCC"| 17.1% ||style="background-color:#BCC"| 0.8%
 * 55  ||   300
 * style="background-color:#BCC"| 18.3% ||style="background-color:#BCC"| 1.2%
 * style="background-color:#DBB" title="Total"|Total: 115     ||style="background-color:#DBB" title="Total"|Total: 657
 * style="background-color:#DBB" title="Average"|Average: 17.2% ||style="background-color:#DBB" title="Average of not-NULL"|Average: 1.0%
 * colspan="5"| (without background) Source data
 * colspan="5" style="background-color:#BCC"| (this background) Calculated by an editor
 * colspan="5" style="background-color:#DBB"| (this background) Summarized by an editor
 * }
 * colspan="5"| (without background) Source data
 * colspan="5" style="background-color:#BCC"| (this background) Calculated by an editor
 * colspan="5" style="background-color:#DBB"| (this background) Summarized by an editor
 * }
 * colspan="5" style="background-color:#DBB"| (this background) Summarized by an editor
 * }
 * }

The table above illustrates an encyclopedic issue produced with source data and NOTOR Simple calculations. It "translates and synthesizes" the source data, with accuracy and neutral point of view; preserving "the truth" of the source. A "new truth" can be produced by some statistical methods, such when interpreting an average as an expected value.

Recommendations
Guidance kernel. It is not a Wikipedia policy or guideline, though it may be consulted for assistance and advice.

Routine calculations
General rules: in case of doubt about two or more alternatives for calculations, prefer Wikipedia-tradition-of-use to non-traditional-uses, a template-made to a hand-made, a standard to a non-standard, simple to complex. The table below shows contexts and methods for routine calculations. Each method is an editor's option for calculation, or strategy to express the result of your calculations.

Customary justifications for "valid routine calculations". It is not a full systematic list, but can be used as reference and to inductive reasoning:


 * Really usual calculations:
 * Sum of quantities. Example: source says "two jumps of 2 and 3 meters", editor writes "the two jumps totaled 5 meters".
 * Percentuals. Based on division, using also round function and multiplication. . Example: "120 of 200 (60%)". See Template:Percentage.
 * ... many others ... see Category:Mathematical function templates...


 * "Real time" calculations:
 * Age calculation. Use subtraction of dates, . Example: source say "born in 2001" and Wikipedia write (by templating, calculates currentDate-bornDate=2013-2001=12) the age today, "12 years old". See Template:Age.
 * (... any other? ...)


 * Translations:
 * Metric system translations. Example: " " converted to " ". See template:Convert/lengthcalc, etc.
 * Translation of numeric representation. Examples: source say " " and page needs to show it in binary,, or in roman, . See template:Binary, template:Roman, Module:BaseConvert, etc.
 * ... many others ... see Category:Smart_conversion_templates, ...



Round, precision and other treatment procedures
...

Summary of numerical data
...