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

This topic has often been mentioned on this site. For simplicity of reference, this rule has now its own dedicated article, part of the "Back to Basics" series.
Back to Basics” Disclaimer

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:

BR = BH + 180° = BH + 200 – 020

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:

BR = (BH + 180) % 360

#### 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!

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