The Astronomical Angle Subtended (SAF) calculator uses the small angle formula (SAF) to compute the angle subtended (α) of astronomical observations based on the size of the object or separation between objects (S) and the distance (D)
INSTRUCTIONS: Choose units and enter the following:
- (S) Size of Object or the distance of separation between two objects (see diagram)
- (D) Distance to Object
Angle Subtended(α): The calculator returns the angle in arc seconds. However, this can be automatically converted to compatible units via the pull-down menu.

The Math / Science
Use the small angle formula (SAF) to compute the angle subtended by an astronomical object given the size and distance is:
α = S / D
This is an essential step in computing distance with the parallax method. Note: some textbooks show this formula with a coefficient of 2.06 x 105. This is the equivalent to the formula used here, because vCalc makes the appropriate unit conversions from arc-seconds to radians and does not require the 2.06 x 105 coefficient.
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