Horizon Dip Calculator

How it is calculated

From the height of eye h in metres, the tool computes the dip of the sea horizon in arcminutes as dip = 1.758 × √h, converts it to degrees by dividing by 60, and gives the distance to the horizon as d = 3.57 × √h kilometres. Both grow with the square root of height, so quadrupling the height only doubles them. These are the usual navigation formulas for normal atmospheric refraction, with the horizon taken as open sea level. Height must be above zero and no more than 100,000 m (the small-angle approximation is not meant beyond that); anything else shows no result. It is the height of your eye above the water, not the height of the ship or the deck. Dip is the angle you subtract from a sextant altitude measured to the visible horizon.

Common mistakes

• Entering the height of the deck, mast or the ship instead of the height of the observer's eye above the water.
• Entering feet while the field expects metres. A 33 ft eye height typed as 33 gives a dip of about 10.1 arcminutes instead of the correct 5.6 for 10 m.
• Confusing dip (an angle, in arcminutes) with the distance to the horizon (kilometres). The tool gives both and they are separate numbers.
• Trying very large heights, such as those of an aircraft or a rocket. Anything above 100,000 m, and zero or negative heights, give no result; even at 100,000 m the straight square-root rule is only a rough guide.
• Expecting the distance to tell how far you can see a tall object. It is only the distance to the sea horizon for an observer at that height; a ship's hull or a lighthouse is visible beyond it.