Minutes of arc

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Created by: Team Physics - Examples.com, Last Updated: April 25, 2024

Minutes of arc

What is Minutes of arc?

Minutes of arc, also known as arc minutes or MOA, are a unit of angular measurement used especially in astronomy, navigation, and shooting. One minute of arc is defined as one-sixtieth of a degree (1°/360). Since a full circle consists of 360 degrees, there are 21,600 minutes of arc in a full circle(360°× 60).

Minutes of arc = Degrees × 60

This formula stems from the fact that each degree is divided into 60 minutes of arc. So, multiplying the number of degrees by 60 gives you the equivalent number of minutes of arc.

SI Multiples of Minutes of arc

SI PrefixUnit NameMultipleEquivalent in Minutes of ArcDescription
KilominuteKilominute of arc10³1 kilominute = 1,000 minutes of arcUsed for larger angular measurements, not commonly employed.
DeciminuteDeciminute of arc10−¹1 deciminute = 0.1 minutes of arcProvides finer precision for detailed measurements.
CentiminuteCentiminute of arc10−²1 centiminute = 0.01 minutes of arcOffers greater precision for extremely detailed adjustments.
MicrominuteMicrominute of arc10−³1 microminute = 0.001 minutes of arcUsed in highly specialized or theoretical applications.

Conversion of Minutes of arc into other Units

Conversion of Minutes of arc into other Units
From Minutes of ArcTo UnitConversion FormulaDescription
Minutes of ArcDegreesDegrees = Minutes of Arc/60Each degree consists of 60 minutes of arc.
Minutes of ArcSeconds of ArcSeconds of Arc = Minutes of Arc×60Each minute of arc consists of 60 seconds of arc.
Minutes of ArcRadiansRadians=Minutes of Arc×c/180×60​Converting minutes to degrees and then to radians.
Minutes of ArcMilliradiansMilliradians=Minutes of Arc×1000×π/180×60​Milliradians are a smaller unit, allowing finer precision.

Converting minutes of arc into other units of angular measurement is essential in fields like astronomy, navigation, and mapping. Here are some key conversions:

From Minutes of Arc to Degrees:

Conversion: Degrees = Minutes of Arc/60

Since there are 60 minutes in a degree, dividing the number of minutes of arc by 60 gives the equivalent degrees.

From Minutes of Arc to Seconds of Arc:

Conversion :Seconds of Arc = Minutes of Arc × 60

Each minute of arc consists of 60 seconds, so multiplying minutes of arc by 60 converts them into seconds.

From Minutes of Arc to Radians:

Conversion: Radians=Minutes of Arc × c/(180×60​)

This conversion uses the fact that there are π radians in 180 degrees, with each degree containing 60 minutes.
π radians in 180 degrees, with each degree containing 60 minutes.

From Minutes of Arc to Milliradians:

Conversion: Milliradians=Minutes of Arc × (1000×π)/(180×60​)

This formula converts minutes of arc to milliradians by using the conversion factor between

Uses of Minutes of arc

Uses of Minutes of arc

Minutes of arc are a widely used unit of angular measurement due to their precision and utility in various fields. Here are some of the key uses of minutes of arc:

Astronomers use minutes of arc to measure the angular size of celestial bodies and the distances between stars or other astronomical objects. This precise unit helps in calculating the positions and movements of objects in the sky accurately.

In maritime and aerial navigation, minutes of arc are crucial for determining latitude and longitude, allowing navigators to pinpoint locations accurately on earth. This precision affects course plotting and ensures safe and efficient travel.

Surveyors rely on minutes of arc for measuring and mapping land. Precise angular measurements are necessary for property delineation, construction planning, and infrastructure development.

4.Photography and Film:
In panoramic photography and film, minutes of arc are used to calculate the necessary camera pan or tilt to capture images with the desired field of view.

5.Shooting and Ballistics:
In shooting sports and ballistics, minutes of arc help in adjusting rifle scopes for better accuracy over distances. Understanding the angular spread of shots is crucial for targeting at varying ranges.

6.Optics and Lens Design:
Designers of optical instruments like telescopes, binoculars, and cameras use minutes of arc to describe and measure the field of view provided by lenses, enabling the creation of devices suited for specific observational purposes.

These uses highlight the versatility and importance of minutes of arc as a unit of measurement across diverse disciplines, showcasing their role in ensuring accuracy and precision in both theoretical calculations and practical applications.


What is the relationship between minutes of arc and seconds of arc?

One minute of arc is composed of 60 seconds of arc. Therefore, to convert minutes of arc to seconds of arc, multiply by 60.

How precise are minutes of arc in measurements?

Minutes of arc provide a medium level of precision, suitable for tasks where angular measurements are needed to be finer than degrees but do not require the extreme precision of seconds of arc or milliradians.

Are there smaller units than minutes of arc?

Yes, seconds of arc are smaller units, where each minute of arc contains 60 seconds of arc. Even finer measurements can be made using milli arc seconds, particularly in scientific and astronomical contexts.

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