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Angular Size Calculator

The Angular Size Calculator helps determine the apparent size of an object as seen from a specific distance. It is useful for astronomers, photographers, and anyone dealing with visual measurements. By inputting the object’s actual size and the distance to the observer, the calculator provides the angular size in degrees or arcminutes, helping assess how large the object will appear from a given viewpoint.

Angular Size Calculator

Input Fields
If enabled, the result will update automatically when you change any value.

Angular Size Formula

Formula
$$\theta = 2 \cdot \arctan\left(\frac{d}{2D}\right)$$

Where:

  • $$\theta$$ = angular size in radians
  • $$d$$ = actual size of the object
  • $$D$$ = distance from the observer to the object

Explanation:
This formula calculates the angle subtended by the object at the observer’s eye. It assumes a simple triangle where the object lies perpendicular to the line of sight.

The angular size is a measure of how large an object appears from a specific viewing point, not how large it actually is. This concept is widely used in astronomy (e.g., measuring the Moon or planets), optics, and photography. For example, the Moon and the Sun have roughly the same angular size when viewed from Earth, even though their actual sizes differ greatly. This calculator simplifies the process by providing a quick estimation based on object size and distance. For best results, ensure consistent units (e.g., meters for both size and distance).

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