Skip to content
OverCalculator
  1. Home
  2. Conversion
  3. Degrees to Minutes Converter
Conversion

Degrees to Minutes Converter

Convert degrees to arcminutes and arcminutes to degrees with the exact 60 arcminutes per degree relationship, examples, and DMS context.

Published

Converted angle
Arcminutes
150 ′
Degrees
2.5 °
Arcminutes
150 ′
Arcseconds
9,000 ″

2.5 ° equals 150 ′.

Conversion direction
°

Results update as you type.

Degrees to Minutes Converter

Degrees and arcminutes are two levels of the same angular system. A degree divides a circle into 360 equal parts. An arcminute divides one degree into 60 smaller parts. This converter moves between those two levels and also shows the equivalent arcseconds so the relationship to full DMS notation is clear.

The calculator is useful for angle work in surveying notes, GPS coordinate cleanup, astronomical fields of view, optical alignment, map labels, and CAD drawings that need smaller-than-degree precision. It can also help when reading older references that use minutes of arc rather than decimal degrees. It is not a time converter: a minute of arc measures an angle, while a minute on a clock measures duration. If you need clock units, use the time converter. If you need radians, gradians, or turns, use the angle converter. For complete DMS notation, use the degrees minutes seconds calculator.

What the calculation does

The converter has two modes. In Degrees to arcminutes mode, the active input is the angle in degrees. The calculation checks that this value is finite. It then sets degrees equal to the input, multiplies by 60 to get arcminutes, and multiplies the arcminutes by 60 to get arcseconds.

In Arcminutes to degrees mode, the active input is the angle in arcminutes. The calculation again checks only that the value is finite. It sets arcminutes equal to the input, divides by 60 to get degrees, and multiplies arcminutes by 60 to get arcseconds. There is no restriction that the value must be positive or that it must fit inside one full rotation. A signed or very large angle is converted exactly according to the same ratio.

The primary result label changes with the mode. When starting from degrees, the primary output is Arcminutes. When starting from arcminutes, the primary output is Degrees. The item list always includes degrees, arcminutes, and arcseconds. Degree and arcminute values display with up to six decimal places; arcseconds display with up to three decimal places.

Formula

The forward conversion is:

arcminutes=degrees×60\text{arcminutes} = \text{degrees} \times 60

The reverse conversion is:

degrees=arcminutes60\text{degrees} = \frac{\text{arcminutes}}{60}

The related arcsecond total is:

arcseconds=arcminutes×60=degrees×3600\text{arcseconds} = \text{arcminutes} \times 60 = \text{degrees} \times 3600

A worked conversion

The default degree input is 2.5°. In the calculator’s default mode, the calculation sets degrees to 2.5, then multiplies by 60:

arcminutes=2.5×60=150\text{arcminutes} = 2.5 \times 60 = 150

It then multiplies the arcminute total by 60:

arcseconds=150×60=9000\text{arcseconds} = 150 \times 60 = 9000

The primary result is therefore 150′. The item list shows 2.5°, 150′, and 9000″. The note says that 2.5° equals 150′, matching the exact values returned by the calculation.

If you switch to arcminutes-to-degrees and leave the default 150′, the reverse path divides 150 by 60. The primary result becomes 2.5°, while the item list still shows 150′ and 9000″.

Reference table

DegreesArcminutesArcsecondsTypical interpretation
0.0166667°1′60″One arcminute
0.25°15′900″Quarter degree
0.5°30′1,800″Half degree
1°60′3,600″One degree
2.5°150′9,000″Default example
180°10,800′648,000″Straight angle

Where arcminutes are used

In surveying, a bearing may be refined beyond whole degrees by adding minutes and seconds. In GPS and navigation, latitude and longitude can be published as decimal degrees, DMS, or degrees and decimal minutes. Astronomy uses arcminutes for angular sizes that are too small for whole degrees but too large to make arcseconds convenient. Optics and camera work may use minutes of angle to describe field of view or pointing precision. CAD and machining contexts may use decimal degrees for calculation, then minutes for readable drawings or tolerance notes.

The geographic context deserves special care. A latitude of 40° 30′ N is 40.5 decimal degrees north. A longitude of 73° 30′ W is -73.5 decimal degrees if your software uses signed east-positive longitude. This converter can calculate the 30′ to 0.5° relationship, but it does not attach N, S, E, or W. Use the coordinates converter for a latitude-longitude pair and the lat long to UTM converter when you need a projected coordinate in meters.

Common pitfalls

  • Reading arcminutes as minutes of time. They share a base-60 structure, but they measure different quantities.
  • Writing 12° 30′ as 12.30°. The correct decimal value is 12.5°.
  • Forgetting that negative values remain negative through the conversion.
  • Confusing the prime mark for arcminutes with the double-prime mark for arcseconds.
  • Assuming arcminute conversion applies a map projection. It does not; it is only angular unit conversion.

Sources

Frequently asked questions

How many arcminutes are in one degree?
There are exactly 60 arcminutes in one degree. The relationship comes from the sexagesimal angle system used by DMS notation. Because an arcminute is smaller than a degree, converting degrees to arcminutes multiplies the number by 60, while converting arcminutes back to degrees divides by 60.
What does the prime symbol mean in an angle?
The prime symbol, written as ′, usually marks arcminutes when it appears after an angle. For example, 30′ means thirty minutes of arc, or one half of a degree. It should not be read as feet, time minutes, or a plain apostrophe without considering the surrounding notation.
Does this converter accept negative values?
Yes. The calculator only checks that the active input is a finite number. Negative degrees become negative arcminutes, and negative arcminutes become negative degrees. That can be appropriate for signed angles or signed coordinate components, but coordinate hemispheres still need careful interpretation.
Why does the calculator also show arcseconds?
Arcseconds are the next subdivision in the same DMS system. After computing degrees and arcminutes, the form multiplies arcminutes by 60 to report the equivalent arcseconds. This helps when you are deciding whether a job needs minute precision or a more detailed second-level notation.
Are arcminutes used in astronomy?
Yes. Astronomy often describes angular diameters, separations, and telescope fields of view in arcminutes or arcseconds. The same units also appear in surveying and navigation. The unit still measures angle, not time, even when the observation itself is tied to a clock or celestial event.

Related calculators

Degrees Minutes Seconds CalculatorConvert between decimal degrees and degrees minutes seconds with exact DMS formulas, signed results, coordinate notes, and arcminute and arcsecond totals.Degrees to Seconds ConverterConvert degrees to arcseconds and arcseconds to degrees using 3600 arcseconds per degree, with formulas, exact examples, and DMS context.Minute ConverterConvert minutes to seconds, hours, and days with exact formulas, a worked example, and guidance for schedules and logs.Seconds to Minutes ConverterConvert stopwatch seconds to minutes, or minutes back to seconds, for workouts, cooking, media clips, timers, and short measured intervals.Hour ConverterConvert hours to minutes, seconds, days, weeks, and 365-day years with formulas, a worked example, and scheduling guidance.Hours to Minutes ConverterConvert hours to minutes for schedules, billable work, time cards, service blocks, and decimal-hour entries, with seconds and day context.

Degrees to Minutes Converter updated at