Template:Calculate increment

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Usage[change source]

This template takes two numbers and calculates a suitable increment for {{scalemarkers}} based on the difference between these numbers. Increments are 1, 2 or 5 times an appropriate power of 10.

These numbers, the from value and the to value, are input as unnamed parameters.

{{calculate increment|p1|p2}}

The absolute value, d, of the difference between these is calculated.

d = | p1p2 |

This can be expressed in scientific notation as follows.

d = a × 10n

Where 1 ≤ a < 10 and n is an integer.

The output of the template is as follows.

For 1 ≤ a < 1.35 the output is the number 1 × 10n − 1
For 1.35 ≤ a < 3.45 the output is the number 2 × 10n − 1
For 3.45 ≤ a < 6.95 the output is the number 5 × 10n − 1
For 6.95 ≤ a < 10 the output is the number 1 × 10n
Note
  • The values are returned as ordinary numbers (for use in other templates) not in scientific notation (e.g. 5000 not 5 × 103).
  • The template code actually uses 1.4, 3.5 and 7 as cut offs but these are reduced by 0.05 due to rounding.
Examples
  • "{{calculate increment|1|5}}" gives "0.5


" [1]

  • "{{calculate increment|10|20}}" gives "1


" [2]

  • "{{calculate increment|10|50}}" gives "5


" [3]

  • "{{calculate increment|100|250}}" gives "20


" [4]

  • "{{calculate increment|1000|2000}}" gives "100


" [5]

  • "{{calculate increment|2000|7500}}" gives "500


" [6]

  • "{{calculate increment|100000|750000}}" gives "50000


" [7]

Technical details

The main template page calculates d, the absolute value of the difference between the two inputs. Using {{order of magnitude}} the order of magnitude, n, of d is calculated. d and 10n − 1 are sent as parameters 1 and 2 respectively to a subpage, {{calculate increment/calc}}. This subtemplate uses a #switch to determine the correct factor, 1, 2, 5 or 10, then multiplies by 10n − 1.