Radians to Seconds of Arc Converter

To convert radians to seconds of arc, simply multiply the angle in radians by the conversion ratio of 206,264.806247 seconds of arc per radian.

How to Convert Radians to Seconds of Arc

1. Starting Point – Understanding the Inputs:

To begin, you’ll input the angle in radians into the calculator. Radians are a way to measure angles, much like degrees, but they’re based on the radius of a circle. So, when you input an angle in radians, you’re essentially describing how far around the edge of a circle you’ve gone.

The calculator also offers the option to swap units, which isn’t necessary for this conversion.



2. The Calculation Process:

Now, let’s understand how the calculator converts radians into seconds of arc. It uses a fixed conversion ratio: 206,264.806247 seconds of arc per radian. This means for every radian you input, the calculator multiplies it by this fixed value to get the equivalent in seconds of arc.



3. Understanding the Formula:

The formula used by the calculator is straightforward: seconds of arc = radians × 206,264.806247. Here, “seconds of arc” is what we’re trying to find, and “radians” is the angle in radians we’ve input.

For example, if you input 5 radians into the calculator, the formula becomes:

seconds of arc = (5 rad × 206,264.806247) = 1,031,324.031235



4. Understanding the Units:

Radians and seconds of arc are both units used to measure angles, but they’re different. Radians are based on the radius of a circle, while seconds of arc are based on dividing a circle into 360 degrees, then each degree into 60 minutes, and each minute into 60 seconds. So, seconds of arc are a smaller unit of measurement than radians.

The conversion table provided gives various radian measurements converted into seconds of arc for reference.



5. Final Outcome:

The calculator then displays the result in seconds of arc, showing you the equivalent angle measurement in this unit.

Radians to Seconds of Arc Converter (Frequently Used Values)

Radians (rad)	Seconds of Arc (”)
0.00	0.00
0.05	10.95
0.10	21.91
0.15	32.86
0.20	43.82
0.25	54.77
0.30	65.73
0.35	76.68
0.40	87.64
0.45	98.59
0.50	109.55
0.55	120.50
0.60	131.46
0.65	142.41
0.70	153.37
0.75	164.32
0.80	175.28
0.85	186.23
0.90	197.19
0.95	208.14
1.00	219.10
1.05	230.05
1.10	241.01
1.15	251.96
1.20	262.92
1.25	273.87
1.30	284.83
1.35	295.78
1.40	306.74
1.45	317.69
1.50	328.65
1.55	339.60
1.60	350.56
1.65	361.51
1.70	372.47
1.75	383.42
1.80	394.38
1.85	405.33
1.90	416.29
1.95	427.24
2.00	438.20
2.05	449.15
2.10	460.11
2.15	471.06
2.20	482.02
2.25	492.97
2.30	503.93
2.35	514.88
2.40	525.84

Related posts:

1. Radian Conversion Calculator
2. Angle Converter
3. Radians to Milliradians Converter
4. Radians to Degrees Converter