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Astronomy & optics

Angular size from size and distance

Calculate the angle subtended by a length perpendicular to the line of sight.

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01

Your inputs

The starting values are an example.

Decimals: 12.5 · Thousands: 1,234.56. Follow the field instructions for lists.

02

Your result

Enter your values and select Calculate.

Your calculation will appear here.

Your result will include the relevant values and units.

Understand the calculation

Formula and example

How it is calculated

Angle = 2 × arctan(size ÷ (2 × distance))

Worked example

A width of 1 m viewed from a distance of 100 m subtends an angle of approximately 0.573°.

Things to check

  • Size and distance must use the same length unit, making their ratio dimensionless.
  • The apparent edge of a nearby sphere requires a different geometric model.