Template:Calculate increment

Template Documentation view

Usage

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 = | p₁ − p₂ |

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"
• {{calculate increment|10|23}} gives "1"
• {{calculate increment|10|23.5}} gives "2"
• {{calculate increment|100|300}} gives "20"
• {{calculate increment|1010|1030}} gives "2"
• {{calculate increment|3550|7450}} gives "500"
• {{calculate increment|101000|889330}} gives "100000"

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 10^{n − 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 10^{n − 1}.