Calculate the Angular Ratio
Calculator for ratios of angles in degrees, arc minutes, arc seconds or decimal degrees. Enter two angles, when entering decimal degrees, arc minutes and arc seconds can be omitted. The ratio of the two angles will be calculated in one and in two dimensions, as integer ratio and in relation to 1 (rounded to 5 decimal places).
Example: the Sun has an average diameter of approximately 32 arc minutes. Mercury has a diameter of approximately 11 arc seconds at a transit. At a transit of Mercury, the planet has about 1/175 of the solar width and occults about 1/30466 of Sun's surface.
The difference between an integer ratio and a ratio in relation to 1 can be seen when entering angles that are coprime. For example, for angles of 11 and 17 degrees, the integer ratio of the angles is of course 11 to 17, the ratio to one is 1 : 1.54545. The integer ratio of the area is 121 : 289, the ratio to one is 1 : 2.38843. When referring to 1, the other value is always greater than 1, the ratio is written in the corresponding order. This is the usual specification for such ratios.
The area refers to the apparent surface area of an object that has a corresponding angular size. This apparent surface area is the projection of this object along the bisector of the two legs onto a vertical plane and corresponds to how we perceive the object. The ratio of the areas is the square of the ratio of the angles. The two surfaces are comparable using this calculation if they are geometrically similar to each other, i.e. if they look the same apart from their size. The angles of the two objects must therefore always be in the same ratio, no matter in which direction they are applied to the surface of the objects.
