Angular Size Calculator

How it is calculated

The apparent angle is θ = 2 × arctan(size ÷ (2 × distance)). size is the true diameter or width of the object and distance is how far away it is. Both can be in any unit as long as they are the same one: the unit cancels and only the ratio matters. The result is shown in degrees (four decimals), arcminutes (θ × 60) and arcseconds (θ × 3600). The exact arctangent form is used, not the small-angle shortcut, so it stays correct for large angles too. Both numbers must be greater than zero, otherwise there is no result. The distance is measured from the observer to the centre of the object, and the object is treated as a flat disc or a line facing you.

Common mistakes

• Entering size and distance in different units, for example a diameter in kilometres and a distance in metres or miles. The ratio is then off by the conversion factor and the angle is wrong by the same amount.
• Using the radius instead of the diameter. The tool expects the full width of the object; a radius gives an angle half as large.
• Entering the distance from the Earth's surface or from an orbit's altitude instead of the distance to the object itself. For nearby objects such as a satellite, the difference matters.
• Mixing up arcminutes and arcseconds. One degree is 60 arcminutes and 3600 arcseconds, so read the line that matches the unit your eyepiece or chart uses.
• Using an average distance for objects whose distance changes a lot, like the Moon or a planet. The size on the sky changes with the distance you enter, so use the distance for the date you care about.