# Minute of Arc Converters > Convert minutes of arc (arcminutes) to and from degrees, radians, seconds of arc, and other angle units **Category:** Conversion **Keywords:** arcminute, minute of arc, moa, angle, degrees, radians, arcsecond, conversion **URL:** https://complete.tools/minute-of-arc-converters ## How it calculates The converter uses the following mathematical relationships to transform arcminutes into other angle units: 1. Degrees: arcminutes / 60 - Since there are exactly 60 arcminutes in one degree, dividing by 60 converts arcminutes to degrees. For example, 90 arcminutes equals 1.5 degrees. 2. Radians: arcminutes × (π / 10800) - A full circle contains 2π radians or 21,600 arcminutes. Therefore, dividing π by 10,800 gives the conversion factor from arcminutes to radians. 3. Arcseconds: arcminutes × 60 - Each arcminute contains exactly 60 arcseconds, so multiplying arcminutes by 60 yields arcseconds. This relationship mirrors the minutes-to-seconds relationship in time measurement. 4. Gradians: arcminutes / 54 - Gradians (also called gons) divide a circle into 400 equal parts. Since one degree equals 10/9 gradians (or 0.9 gradian per degree), and there are 60 arcminutes per degree, the conversion factor is 60 × 0.9 = 54 arcminutes per gradian. 5. Turns: arcminutes / 21,600 - One turn (or revolution) equals a complete 360-degree rotation. Multiplying 360 degrees by 60 arcminutes per degree gives 21,600 arcminutes per turn. 6. Milliradians: arcminutes × (π / 10.8) - Milliradians are simply radians multiplied by 1000, commonly used in military and ballistics applications. For reverse conversions (converting other units to arcminutes), the tool applies the inverse of each formula, multiplying or dividing by the reciprocal of the conversion factor. ## Who should use this Precision shooters and hunters who need to understand and apply MOA adjustments to their rifle scopes. Most rifle scopes use 1/4 MOA or 1/8 MOA click adjustments, and understanding the relationship between MOA and actual distance at various ranges is essential for accurate shooting. Astronomers and astrophotographers working with celestial coordinates, telescope specifications, and angular measurements of celestial objects. The angular sizes of planets, stars, and deep-sky objects are frequently expressed in arcminutes or arcseconds. Navigators and pilots calculating bearings, headings, and course corrections. Aviation and maritime navigation often involve precise angular measurements where understanding arcminutes is crucial for accurate positioning. Surveyors and geodesists measuring angles in land surveying, construction layout, and mapping applications. Theodolites and total stations commonly display readings in degrees, minutes, and seconds. Engineers working with angular tolerances in precision manufacturing, optical systems design, and mechanical engineering applications where tight angular specifications are required. Students and educators studying trigonometry, geometry, astronomy, or navigation who need to convert between different angular measurement systems for coursework and research. Military personnel using fire control systems, artillery calculations, and targeting systems that may use MOA or milliradians interchangeably. ## Worked examples Example 1: Converting 30 arcminutes (half a degree) - Degrees: 30 / 60 = 0.5° - Radians: 30 × (π/10800) = 0.008727 rad - Arcseconds: 30 × 60 = 1800" - Gradians: 30 / 54 = 0.5556 gon - Turns: 30 / 21600 = 0.001389 rev - Milliradians: 0.008727 × 1000 = 8.727 mrad Example 2: Converting 1 arcminute (the base unit) - Degrees: 1 / 60 = 0.01667° (or 1/60 degree) - Radians: 1 × (π/10800) = 0.0002909 rad - Arcseconds: 1 × 60 = 60" - Gradians: 1 / 54 = 0.01852 gon - Turns: 1 / 21600 = 0.0000463 rev - Milliradians: 0.2909 mrad Example 3: Converting 90 arcminutes (1.5 degrees) - Degrees: 90 / 60 = 1.5° - Radians: 90 × (π/10800) = 0.02618 rad - Arcseconds: 90 × 60 = 5400" - Gradians: 90 / 54 = 1.667 gon - Turns: 90 / 21600 = 0.004167 rev - Milliradians: 26.18 mrad Example 4: MOA at 100 yards for shooting applications At 100 yards, 1 MOA subtends approximately 1.047 inches. This is calculated using the formula: arc length = radius × angle (in radians). Converting 1 arcminute to radians gives 0.0002909 rad, and multiplying by 100 yards (3600 inches) yields 1.047 inches. ## Limitations This tool assumes the input is a valid numerical value. Extremely large angles may result in floating-point precision limitations, though the tool uses scientific notation for very large or small values to maintain readability. The converter does not normalize angles to a standard range, so negative values and values greater than 21,600 arcminutes (one full circle) are converted directly without wrapping. For applications requiring normalized angles, additional processing may be needed. The precision of results is limited to approximately 8 significant digits for display purposes. For highly precise scientific calculations, dedicated software with arbitrary precision arithmetic may be required. When using MOA for shooting applications, remember that the 1 MOA = 1 inch at 100 yards approximation has a 4.7% error. The actual value is 1.047 inches, which becomes significant at longer ranges. ## FAQs **Q:** What is the difference between MOA and arcminutes? **A:** MOA (Minute of Angle) and arcminute are the same unit of measurement. MOA is simply a more common abbreviation used in shooting sports and firearms applications, while arcminute is the term more frequently used in astronomy, navigation, and mathematics. Both refer to 1/60 of a degree. **Q:** Why do rifle scopes use MOA adjustments? **A:** MOA provides a convenient angular measurement for adjusting point of impact at various distances. At 100 yards, 1 MOA equals approximately 1 inch, making mental calculations straightforward. At 200 yards, 1 MOA equals about 2 inches, at 300 yards about 3 inches, and so on. This linear relationship makes range estimation and scope adjustment intuitive for shooters. **Q:** How does MOA compare to milliradians (MRAD)? **A:** Both MOA and milliradians are angular units used for precision adjustments. 1 MOA equals approximately 0.291 milliradians. While MOA is more popular in the United States for sporting firearms, milliradians are commonly used in military applications worldwide and are becoming increasingly popular in civilian precision shooting. At 100 yards, 1 MRAD equals 3.6 inches, compared to 1.047 inches for 1 MOA. **Q:** What is the relationship between arcminutes and arcseconds? **A:** Just as there are 60 seconds in a minute of time, there are 60 arcseconds in one arcminute. This subdivision allows for extremely precise angular measurements. Arcseconds are commonly used in astronomy to describe the apparent size of celestial objects and the resolution of telescopes. **Q:** How are arcminutes used in astronomy? **A:** Astronomers use arcminutes (and arcseconds) to describe the apparent angular size of celestial objects. For example, the Moon and Sun each have an apparent diameter of about 30 arcminutes. Planets appear much smaller; Jupiter at opposition has an angular diameter of about 0.8 arcminutes (50 arcseconds). Star charts and telescope eyepiece fields of view are also commonly specified in arcminutes. **Q:** Why are there 21,600 arcminutes in a circle? **A:** A complete circle contains 360 degrees, and each degree contains 60 arcminutes. Multiplying 360 by 60 gives 21,600 arcminutes in a full circle. This number has many useful divisors (including 2, 3, 4, 5, 6, 8, 9, 10, 12, etc.), which made it practical for ancient mathematicians and navigators to work with angular subdivisions before decimal systems became widespread. --- *Generated from [complete.tools/minute-of-arc-converters](https://complete.tools/minute-of-arc-converters)*