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`s = alpha * d`

Enter a value for all fields

The **Astronomical Size (SAF) **calculator uses the small angle formula (SAF) to compute the size of an astronomical body based on the distance to the object (D) and the angle subtended (α).

**INSTRUCTIONS**: Choose units and enter the following:

- (
**D**) Distance to Object - (
**α**) Angle Subtended

**Size (S):** The calculator returns the size in Astronomical Units (ua). However, this can be automatically converted to compatible units via the pull-down menu.

Use the small angle formula (SAF) to compute the size of an astronomical body or separation between astronomical bodies (e.g. planet and a moon) given the distance and angle subtended:

S = α • D

where:

**S**is the Small Angle Formula size of the object.**D**is the distance to 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 10^{5}. 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 10^{5} coefficient.

- Hubble's Law
- Kepler's 3
^{rd}Law formula T² = (4π • R³)/(G • M) - Small Angle Formula
*Small Angle Formula**α = S / D* - Flux and Magnitude formulas
- Telescope formulas
- Mass formulas
- Relative Size Formulas
- Wavelength Formulas
- Luminosity and other Formulas

**Related Astro Calculators:**

- Hubble's Law
- Kepler's 3
^{rd}Law Calc has Kepler's 3^{rd}law solved for each parameter. - Astronomy Calculator contains basic formulas for a college level Introduction to Astronomy
- Exoplanet Calculator contains formulas for studying planets outside of our Solar System.
- 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.
- Ellipse Calculator
- 3D Vector Calculator:
- Drake Equation Calculator
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- Exoplanet Calculator contains formulas for studying planets outside of our Solar System.
- 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.
- Radius of Perigee
- Radius of Apogee

Dr. Spicklemire has an instructional YouTube video on the using the Small Angle Equation (CLICK HERE).