Degree to Arcminute Converter
Convert degree to arcminute instantly. 1 degree = 60.0 arcminute.
Degree to Arcminute Table
| Degree | Arcminute |
|---|---|
| 1 ° | 60.0 ' |
| 5 ° | 300.0 ' |
| 10 ° | 600.0 ' |
| 30 ° | 1800.0 ' |
| 45 ° | 2700.0 ' |
| 90 ° | 5400.0 ' |
| 180 ° | 10800.0 ' |
| 360 ° | 21600.0 ' |
Related Conversions
Quick Answer
Formula: Arcminute = Degree × 60
Multiply any degree value by 60 to get arcminute.
Reverse: Degree = Arcminute × 0.01667
Worked Examples
Degree to Arcminute Conversion Table
Common degree values — factor: 1 ° = 60 ′
| Degree (°) | Arcminute (′) | Context |
|---|---|---|
| 1 ° | 60 ′ | 1° |
| 5 ° | 300 ′ | 5° |
| 10 ° | 600 ′ | 10° |
| 15 ° | 900 ′ | Clock hour |
| 30 ° | 1800 ′ | Clock half-hour |
| 45 ° | 2700 ′ | Half right angle |
| 60 ° | 3600 ′ | Equilateral triangle |
| 90 ° | 5400 ′ | Right angle |
| 120 ° | 7200 ′ | Obtuse |
| 135 ° | 8100 ′ | 3/8 turn |
| 180 ° | 1.08e+04 ′ | Straight line |
| 270 ° | 1.62e+04 ′ | 3/4 turn |
| 360 ° | 2.16e+04 ′ | Full circle |
| 720 ° | 4.32e+04 ′ | Two rotations |
| 1080 ° | 6.48e+04 ′ | Three rotations |
Mental Math Tricks
Degrees × 60 = arcminutes. Exact — 60 arcminutes per degree.
1° = 60′, 90° = 5,400′, 360° = 21,600′.
Arcminutes ÷ 60 = degrees.
Who Uses This Conversion?
Measures horizontal and vertical angles in degrees for land surveys and boundary marking.
Specifies roof pitches, staircase angles, and geometric building features in degrees.
Uses compass bearings and course headings expressed in degrees for maritime and aviation.
Learns sine, cosine, and tangent functions using degree inputs on a calculator.
Specifies shaft rotation, cam profiles, and gear engagement angles in degrees.
Reports wind direction in degrees from north (0°–360°) for weather forecasts.
Related Conversions
Frequently Asked Questions
About Degree and Arcminute
Degree (°)
The degree (°) divides a full circle into 360 equal parts. This system traces back to ancient Babylonian astronomy, which used a base-60 (sexagesimal) number system. The choice of 360 is practical: it is divisible by 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, and 120.
Degrees remain the dominant angle unit in everyday life, navigation, surveying, and most engineering disciplines. Compass bearings, latitude and longitude, and architectural drawings all use degrees.
Interesting fact: The Babylonians may have chosen 360 because they approximated the solar year as 360 days, making each day of travel correspond to one degree of the Sun's apparent annual motion around the sky.
Arcminute (′)
The arcminute (′) is 1/60 of a degree. The subdivision of degrees into 60 parts follows the Babylonian sexagesimal system. In astronomy, arcminutes have been used to describe angular separations since antiquity.
Arcminutes are used in astronomy (angular size of the Moon ≈ 31′), navigation (1 arcminute of latitude ≈ 1 nautical mile — the origin of the nautical mile definition), and ophthalmology (20/20 vision corresponds to resolving features 1 arcminute apart).
Interesting fact: The full Moon subtends about 31 arcminutes in the sky. Human visual acuity limit is about 1 arcminute — the basis of the 20/20 vision standard.
About Degree to Arcminute Conversion
Converting degree to arcminute is essential in mathematics, physics, engineering, and surveying. Degrees are used in everyday contexts and navigation; radians are the standard in calculus and physics; gradians are common in European surveying. Having accurate conversions ensures correct results across disciplines.
Key reference: a right angle (90°) = 5400 ′. A full circle (360°) = 2.16e+04 ′. Reverse: 1 ′ = 0.01667 °. Exact factor: 1 ° = 60 ′.
All conversions use IEEE 754 double-precision arithmetic, accurate to at least 8 significant figures.