Reciprocal Runway Math Made Easy

Reciprocal Runways – 180 Degree Opposites

Runway Numbering
The diagram shown here displays a 4,000 foot long (75 foot wide) runway with two ends. Each end of the runway is labelled with a large number. The actual pavement would have these large numbers painted on the runway at the threshold for each end of the runway. In this example, we see the Runway Numbers 3 and 21.

Magnetic Direction
The runway number represent the first two digits of the runway’s actual three digit magnetic direction. Runways are oriented or pointed at angles with respect to the magnetic north pole. The magnetic north pole is where your compass points, and not the true north pole. The Runway Numbers are essentially the runway direction, rounded off to the nearest 10 degrees.

Reciprocal Runways
By now, you have probably figured out that the Runway Diagram shown here identifies two runways sharing the same pavement. There are two ends to the pavement, and each end is a Reciprocal Runway of its opposite end of the pavement. For instance, Runway 3 and Runway 21 on the diagram point in opposite directions. Runway 3 is at a 30 degree angle in relationship to the magnetic north pole, and Runway 21 is at a 210 degree angle. The difference between these two angles is 180 degrees. 30 + 180 = 210.

180 Degrees
When you are on a Runway, you can calculate the opposite direction (Reciprocal Runway) by adding or subtracting 180 degrees. Every circle has 360 degrees, and therefore 180 degrees is exactly half of the full rotation of a circle. As you see, Runway 3 (30 degrees) is paired with Runway 21 (210 degrees), and these two runways are 180 degree opposites.

Runway 28
Here we see Runway 28. As only the first two digits of the three digit magnetic direction are used for Runway Numbering, we realize this Runway is aligned at 280 degrees from Magnetic North.

Reciprocal of Runway 28?
You could calculate the Reciprocal of Runway 28 (280 degrees) by subtracting 180 degrees. This would be 100 degrees, or Runway 10. If a Runway is between 0 and 180 degrees, then add 180 degrees to calculate the Reciprocal runway. However, if the runway is above 180 degrees, simply subtract 180 degrees to calculate the reciprocal runway angle.

Math Made Easy!

Here’s a little trick…
If you love math, then you can continue to do it the old way, and mathematically add or subtract 180 degrees to calculate the Reciprocal Runway. However, for everyone else, here is a great way to quickly calculate reciprocal numbers in an instant, with very easy math! No more struggling with the addition or subtraction of 180 degrees. Now, you only need to be able to add or subtract by 2.

Shift by Two
It’s really easy. Just remember to shift each digit in the runway number by two. You must start with the Runway Number in 2 digit format (i.e. Runway 3 would be 03)

Now, you just shift each digit by 2. Basically, you add or subtract 2 for each digit in the number. One number in the pair will go up by two, and the other will go down by two.

Don’t worry, it’s not as difficult as it sounds
Just remember, you can’t exceed 360 degrees, so you need to be careful determining which digit goes up by two, and which digit goes down by two. But, both digits will need to be adjusted (shifted) by two.

A Step by Step Example
Starting with Runway 21. Subtract 2 from the first digit, and add 2 to the second digit. Each digit is shifted by two. The result will be 03 or Runway 3. Notice, we subtracted 2 from the first digit. If we added 2, the result would exceed 360 degrees, so we know the first digit must be reduced, and the second digit is therefore increased.

Reverse Example
This time, let’s try Runway 3. Remember, we must always start with a two digit number, so we use 03 as our starting number. We can’t subtract 2 from the first digit (0), or we will go negative. So this time we add two to the first digit, and then subtract two from the second digit. The result is 21. Pretty easy huh?

Just add 2 to one number, and subtract 2 from the other digit. Sometimes, you add to the first digit, but other times you need the reverse. As you practice, you will see how easy it becomes.

Some More Examples

• Runway 9 (Start with 09, add 2 to the first digit, and subtract 2 from the second digit) Result is 27
• Runway 27 (Subtract 2 from the first digit, and add 2 to the second digit) Result is 09 or Runway 9
• Runway 30 (Subtract 2 from the first digit, and add 2 to the second digit) Result is 12
• Runway 33 (Subtract 2 from the first digit, and add 2 to the second digit) Result is 15
• Runway 10 (This is a tricky one. If we subtract 2 from either digit, we will have a negative result) This is an exception, and you may want to use the old school math of adding 180 degrees for a result of Runway 28)
• Runway 15 (Add 2 to the first digit, and subtract 2 from the second digit) Result is 33

Easy, Fast and Fun!
Just shift the numbers by two, and you will be quickly calculating Reciprocal Runway Numbers with ease. Just remember these quick tips:

• Start with a 2 digit number (i.e. Runway 9 would be 09)
• Add 2 to one digit, and subtract 2 from the other digit (i.e. Shift one digit up by two, and the other down by 2)
• Don’t allow either digit to go negative, or to exceed 360 degrees. This helps you determine which digit needs to go up by 2, and which digit goes down by 2)

It’s either:
Add 2, Subtract 2 OR Subtract 2, Add 2.

Adding and subtracting 2 is always easier than adding or subtracting 180. Reciprocal Math calculations just became very easy.