`\alpha = ( s / d )`

Enter a value for all fields

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   

• D is the Small Angle Formula Distance to the object.
• S is the size of the object.
• α is the angle subtended.

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.  

Astronomy Calculators

• Hubble's Law
• Kepler's 3^rd Law formula T² = (4π • R³)/(G • M)
  • (M) - mass of the system. 
  • (T) - period of the orbit.
  • (R) - separation distance between the two objects.
  • (G) - universal gravity constant
• Small Angle Formula        Small Angle Formula    α = S / D
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  • (D) - distance to astronomical object
  • (S) - size or diameter of astronomical object
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  • Magnification of a Telescope
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  • Mass from Acceleration and Radius
  • Mass from Speed and Separation
  • Mass of extra-solar planet from mass of star, radius of star orbit and radius of exoplanet orbit
  • Mass of extra-solar planet from mass and velocity of star and velocity of planet
• Relative Size Formulas
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  • Wavelength Shift from Wavelength and Speed
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• Luminosity and other Formulas
  • Distance from absolute and apparent magnitude
  • Radius from Speed and Period
  • Speed of Circular Motion
  • Hubble Time
  • Luminosity from Mass

Related Astro Calculators:

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• Astronomy Calculator contains basic formulas for a college level Introduction to Astronomy
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• Ellipse Calculator
• 3D Vector Calculator:
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• Astronomical Distance Calculator provides the distance from the Earth to numerous astronomical bodies (e.g. Sun, Moon, planets, stars, Milky Way's Center and Edge, Andromeda Galaxy)
• Astronomical Distance Travel Time Calculator computes the time to travel to distant parts of space at different velocities.
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