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Linear Size Calculator

This Linear Size Calculator helps determine the actual linear dimension of an object based on its distance and angular size. It’s useful for optical calculations, astronomy, photography, and any field involving angular measurement. Simply input the distance to the object (L) and the angular size (α), and the tool will compute the linear size (D).

Linear Size Calculator

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

Linear Size Formula

Formula
$$D = 2 \cdot L \cdot \tan\left(\frac{\alpha}{2}\right)$$

Where:

  • $$D$$ is the linear size
  • $$L$$ is the distance to the object
  • $$\alpha$$ is the angular size (in degrees or radians)

This formula calculates the actual size of an object given the angle it subtends and the distance from the observer. It assumes a simple isosceles triangle geometry.

The linear size formula is widely used in physics, astronomy, and imaging. For example, if you know how wide a mountain appears in your field of view and how far away it is, you can calculate its actual width. The angle must be in radians when using standard mathematical functions unless otherwise specified. Typical applications include calculating the diameter of celestial objects, estimating object size in photos, or designing projection systems.

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Angular Size

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