Back to Basics: The “Plus 2 Minus 2” Rule

The “Plus 2, Minus 2” rule (sometimes differently called, or abbreviated as “±2 Rule”) is used to determine the reciprocal of a certain heading. In military simulation context, it is commonly used to determine the reciprocal heading of a bandit (BR), starting from the Bandit Heading (BH).
Other examples include the reciprocal of a runway, or the direction from or to a NAVAID.

This method uses the fact that:

Thus, ignoring the units, adding a “2” in the hundreds and removing a “2” in the tens, results in 180. Moreover, since the sign makes zero difference, the opposite is also true.

This is a mnemonic and simple formula. If you want to use it in a LibreOffice Calc or Google spreadsheet, the modulo is probably the simplest way:

Examples

• HDG 347 → “3” – 2 and “4” + 2. “7” is carried over. Reciprocal: 1 6 7
• HDG 125 → “1” + 2 and “2” – 2. “5” is carried over. Reciprocal: 3 0 5
• HDG 220 → “2” – 2 and “2” + 2. “0” is carried over. Reciprocal: 0 4 0
• HDG 021 → “0” + 2 and “2” – 2. “1” is carried over. Reciprocal: 2 0 1
• HDG 291 → “2” – 2 and “9” + 2. “1” is carried over. Reciprocal: 11 1

If the heading is less than 020, or between 180 and 190, the rule cannot be directly applied.
For example:

1. HDG 019 → 2 -1 9;
2. HDG 188 → 3 6 8;

There are simple workarounds for these cases. In the first, it is easier to simply add 180. Thus, 019 + 180 = 199°. The second case can be solved in multiple ways, but I usually apply the rule then, if the result exceeds 360, I subtract 360. In fact, 368 % 360 = 368 – 360 = 8°.

Variation

Another way to use this rule is looking at two digits at the same time, rather than individually.
To use the rule, action the first digit, adding -2 if the value is either 2 or 3 and adding 2 in the opposite case. Then consider the first and the second digits together, and apply the opposite, either +2 or -2 depending on the previous step.
If the result is greater than 360, modulo or subtracting 360 sorts it.

Examples

Note: the last digit is always carried over, exactly as seen before.

• HDG 347: 3 – 2 → 1 & 4 = 14; 14 + 2 = 16. Reciprocal: 16 7
• HDG 125: 1 + 2 → 3 & 2 = 32; 32 – 2 = 30. Reciprocal: 30 5
• HDG 220: 2 – 2 → 0 & 2 = 02; 02 + 2 = 04. Reciprocal: 04 0
• HDG 021: 0 + 2 → 2 & 2 = 22; 22 – 2 = 20. Reciprocal: 20 1
• HDG 291: 2 – 2 → 0 & 9 = 09; 09 + 2 = 11. Reciprocal: 11 1
• HDG 019: 0 + 2 → 2 & 1 = 21; 21 – 2 = 19. Reciprocal: 19 9
• HDG 188: 1 + 2 → 3 & 8 = 38; 38 – 2 = 36. Reciprocal: 368 – 360 = 008

The output of each variation is the same, as expected. The former is simpler for a beginner, as it “compartmentalise” the figures, the second minimises the intervals where the result is not between 0° and 360°.
Use the one you prefer!