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For a precise answer, it would have to be worked out mathematically, but a rough rule of thumb is "the rule of 1 in 60" which says that each degree of variance in heading will result in being one mile off for each 60 miles out. For instance, if you were 2 degrees off heading (assuming no wind conditions), you would be 2 miles off at 60 miles out, or 4 miles off at 120 miles out, and so forth. In your case, if you divide 1000 by 60, you find that you would be 16.7 miles off at 1000 miles out for each degree you were off heading. To do it accurately, simply use the formula for the circumference of a circle (Pi times the diameter). So, if your "circle" has a radius of 1000 miles, it has a diameter of 2000 miles. Multiply that by 3.14 and divide the result (6280) by 360 degrees and you find that each degree at that distance would equal approximately 17.4 miles off. Our "rule of 1 in 60" gave us 16.7, so that's pretty close for our rule of thumb.

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Q: If you are 1 degree off heading how far would you be off 1000 miles away?
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