Arc Minute To Degrees Conversion
45 arcminutes is 0.75 degrees, because it takes 60 arcminutes to make one degree.
Quick answer: Divide the arcminutes by 60. For example, 45 arcmin is 0.75 deg, 90 arcmin is 1.5 deg and 22.5 arcmin is 0.375 deg.
The arcminutes to degrees formula
Degrees equal arcminutes divided by 60.
The factor 1 divided by 60 is about 0.016667.
Take 45 arcmin. 45 × 0.01666667 gives 0.75 deg.
Take 90 arcmin. 90 × 0.01666667 gives 1.5 deg.
Sixty to a degree
One degree is made of 60 arcminutes, and one arcminute is made of 60 arcseconds (Wikipedia: Minute and second of arc).
So you divide arcminutes by 60 to get degrees. The arcminute is written with a single prime mark.
How to convert arcminutes to degrees step by step
- Read the angle in arcminutes.
- Divide it by 60.
- Write the answer in degrees.
- For arcseconds, multiply the arcminutes by 60.
Example 1: 45 arcmin
- Start with 45 arcmin.
- 45 × 0.01666667 = 0.75.
- The angle is 0.75 deg.
45 arcmin = 0.75 deg
Example 2: 90 arcmin
- Start with 90 arcmin.
- 90 × 0.01666667 = 1.5.
- The angle is 1.5 deg.
90 arcmin = 1.5 deg
Example 3: 22.5 arcmin
- Start with 22.5 arcmin.
- 22.5 × 0.01666667 = 0.375.
- The angle is 0.375 deg.
22.5 arcmin = 0.375 deg
Example 4: 225 arcmin
- Start with 225 arcmin.
- 225 × 0.01666667 = 3.75.
- The angle is 3.75 deg.
225 arcmin = 3.75 deg
Example 5: 450 arcmin
- Start with 450 arcmin.
- 450 × 0.01666667 = 7.5.
- The angle is 7.5 deg.
450 arcmin = 7.5 deg
Example 6: 4.5 arcmin
- Start with 4.5 arcmin.
- 4.5 × 0.01666667 = 0.075.
- The angle is 0.075 deg.
4.5 arcmin = 0.075 deg
Round only at the end. Rounding in the middle of a sum adds small errors that grow.
arcminutes to degrees conversion table
| Arcminutes (arcmin) | Degrees (deg) | Arcseconds (arcsec) |
|---|---|---|
| 0.45 arcmin | 0.0075 deg | 27 arcsec |
| 4.5 arcmin | 0.075 deg | 270 arcsec |
| 22.5 arcmin | 0.375 deg | 1,350 arcsec |
| 45 arcmin | 0.75 deg | 2,700 arcsec |
| 90 arcmin | 1.5 deg | 5,400 arcsec |
| 225 arcmin | 3.75 deg | 13,500 arcsec |
| 450 arcmin | 7.5 deg | 27,000 arcsec |
| 1,125 arcmin | 18.75 deg | 67,500 arcsec |
| 4,500 arcmin | 75 deg | 270,000 arcsec |
The highlighted row is the default of the calculator. The last column gives Arcseconds (arcsec).
A quick mental shortcut for arcminutes to degrees
Think of minutes in an hour. 30 arcminutes is half a degree, and 15 arcminutes is a quarter.
So 45 arcminutes is three quarters of a degree.
Maps and sky
Map coordinates and star charts use degrees and arcminutes. A position of 40 degrees 30 arcminutes is the same as 40.5 degrees.
Turn the minutes into a decimal to add them to the degrees.
Adding to whole degrees
If you have 12 degrees and 45 arcminutes, divide 45 by 60 to get 0.75. Then add it to 12 to get 12.75 degrees.
Do the same for arcseconds, with 3,600 in place of 60.
Quick conversion answers
| Conversion | Result |
|---|---|
| 4.5 arcmin | 0.075 deg |
| 45 arcmin | 0.75 deg |
| 450 arcmin | 7.5 deg |
| 4,500 arcmin | 75 deg |
Where this conversion is used
Navigators and surveyors turn minutes into decimal degrees.
Astronomers compare small angles in degrees.
Common mistakes to avoid
- Multiplying by 60. Going to degrees means dividing.
- Using 100. There are 60 arcminutes in a degree, not 100.
- Mixing arcminutes and arcseconds. An arcsecond is 1/60 of an arcminute.
- Mixing minutes of time. Arcminutes are angles, not time.
Related converters
More values at a glance
0.9 arcmin is 0.015 deg. 9 arcmin is 0.15 deg. 13.5 arcmin is 0.225 deg.
33.75 arcmin is 0.5625 deg. 67.5 arcmin is 1.125 deg. 135 arcmin is 2.25 deg.
180 arcmin is 3 deg. 900 arcmin is 15 deg. 2,250 arcmin is 37.5 deg.
Checking the answer
Multiply the degrees by 60. You should get the arcminutes you started with.
For 0.75 degrees, that is 0.75 × 60 = 45 arcminutes.
If the check fails, look for a slipped decimal point.
Landmarks to remember
15 arcminutes is 0.25 degrees, 30 arcminutes is 0.5 degrees, 45 arcminutes is 0.75 degrees and 60 arcminutes is 1 degree.
More worked values
1 arcmin is 0.016667 deg. 2 arcmin is 0.033333 deg. 4 arcmin is 0.066667 deg.
8 arcmin is 0.133333 deg. 15 arcmin is 0.25 deg. 25 arcmin is 0.416667 deg.
40 arcmin is 0.666667 deg. 75 arcmin is 1.25 deg. 100 arcmin is 1.666667 deg.
Going the other way
To turn deg back into arcmin, do the opposite step.
1 deg is 60 arcmin. 5 deg is 300 arcmin. 10 deg is 600 arcmin.
20 deg is 1,200 arcmin. 50 deg is 3,000 arcmin. 100 deg is 6,000 arcmin.
250 deg is 15,000 arcmin. 500 deg is 30,000 arcmin.
A full worked example
Take 7.5 arcmin. Multiply by 0.016667 to get 0.125 deg.
Now check it. Turn 0.125 deg back into arcmin and you should land on 7.5 again.
If you do not, look for a slipped decimal point or a swapped unit.
Rounding the answer
Most work uses two to four decimals. For example, 1.2345 arcmin is 0.020575 deg, which rounds to 0.02 deg.
Round only at the end. Rounding early can add a small error to the final number.
Small and large values
0.1 arcmin is 0.001667 deg. 0.25 arcmin is 0.004167 deg. 0.5 arcmin is 0.008333 deg.
3 arcmin is 0.05 deg. 6 arcmin is 0.1 deg. 12 arcmin is 0.2 deg.
30 arcmin is 0.5 deg. 60 arcmin is 1 deg. 150 arcmin is 2.5 deg.
200 arcmin is 3.333333 deg. 300 arcmin is 5 deg. 400 arcmin is 6.666667 deg.
More values in the reverse direction
2 deg is 120 arcmin. 3 deg is 180 arcmin. 25 deg is 1,500 arcmin.
30 deg is 1,800 arcmin. 40 deg is 2,400 arcmin. 60 deg is 3,600 arcmin.
75 deg is 4,500 arcmin. 200 deg is 12,000 arcmin. 400 deg is 24,000 arcmin.
1,000 deg is 60,000 arcmin.
Frequently asked questions
How many Degrees (deg) is 1 arcmin?
1 arcmin is 0.01666667 deg.
How many Degrees (deg) is 90 arcmin?
90 arcmin is 1.5 deg.
How many Arcminutes (arcmin) is 1 deg?
1 deg is 60 arcmin.
How many degrees is 1 arcminute?
About 0.016667 degrees.
How many degrees is 30 arcminutes?
0.5 degrees.
How do I go from degrees to arcminutes?
Multiply by 60.
Sources
- Wikipedia: Minute and second of arc (en.wikipedia.org)
