How to Compute Your Reciprocal Heading

“Twin Cessna 543MT, fly present heading, join the Graham 230 radial direct Graham.”

In order to fly the 230 radial inbound, you will need to tune your CDI needle to the opposite of 230°.¹ How do you compute the opposite heading? Read on.

The Trick Version 1:
Add 200, then subtract 20:
230 + 200 = 430
430 + 20 = 450

You might have noticed that a course of 450º does not make a whole lot of sense (unless you’re an engineer). Well, lets try again shall we?

The Trick Version 2:
Subtract 200, then add 20:
230 – 200 = 30
30 + 20 = 50

Notice that we did just the opposite this time. We added 20 instead of subtracting, and we subtracted 200 instead of adding. The result makes  a lot more sense too. The reciprocal course of 230° is 50°.

Why it Works
Because there are 360° in your heading indicator, the reciprocal heading will always be 180° away. If you add or subtract 180, you will always wind up with the opposite heading.

By subtracting 200, then adding 20, we are actually subtracting 180 in a more human-friendly way. Notice that 200 – 20 = 180. We break it up to make the math a little easier on the head.

The two versions of “the trick,” are there to provide a means to subtract 180 (for headings greater than 180º, and a method to add 180 (for headings less than 180°).

¹ For those of you having trouble understanding why you must fly the opposite of 230, recall that radials extend outward from a VOR. In order to track inbound, one must fly the radial’s reciprocal heading to the station.

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About the author
Pat Flannigan is a professional pilot and aviation blogger. He has been flying for fifteen years and is currently working as an airline pilot in the United States.

2 Replies to How to Compute Your Reciprocal Heading

  1. Nice refresher for me, Patrick.

    I’ve always used the +2,-2 trick or vice versa.

    Example: Reciprocal of 360 : subtract 2 from 3 which is 1, then add 2 to 6 which is 8 and and always keep the last digit which is 0, therefore = 180 degrees.

    Example 2: Reciprocal of 270 : subtract 2 from 2 which is 0, then add 2 to 7 which is 9 and keep the last digit of 0, therefore = 090 degrees.

    Example 3: Reciprocal of 010: add 2 to 0 which is 2, subtract 2 from 1 (kinda weird, I know), but is 9, keep last digit which is 0 = 190 degrees

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