Radian to Minute Converter
Enter the value that you want to convert radian (rad) to minute (') or minute to radian.Also written as RAD to ' conversion.
1 radian = 3437.7467020 minute
Formula: minute = radian value × 3437.7467020
RAD to ' — radian to minute
10 radian = 34377.46702 minute
Popular Degree Converters:
How Radian Relates to Minute
The Radian: History & Usage
The radian is defined as the angle subtended at the center of a circle by an arc equal in length to the radius.
Adopted as the SI unit of angular measure, the radian makes calculus and physics equations significantly simpler because it eliminates conversion constants. One full revolution equals 2π radians (≈ 6.2832 rad). Radians are essential in signal processing, robotics, computer graphics (3D rotations), oscillation analysis, and any domain where angular velocity or frequency calculations are performed.
Understanding the Minute
Minute (') is a unit of degree measurement. 1 minute is equal to 0.0002909 radian.
Why Angle Conversions Matter
Angle conversions bridge the gap between everyday measurement (degrees) and mathematical computation (radians). A mechanical engineer designing a robotic arm needs radians for inverse kinematics. A pilot reads compass headings in degrees. A surveyor might work in gradians. Game developers convert between degrees (artist-friendly) and radians (GPU shaders) hundreds of times per frame. Understanding these conversions is essential across STEM fields, navigation, and digital media production.
radian to minute metric conversion table
| 0.01 rad | = | 34.37747 ' |
| 0.1 rad | = | 343.77467 ' |
| 1 rad | = | 3437.74670 ' |
| 2 rad | = | 6875.49340 ' |
| 3 rad | = | 10313.24011 ' |
| 4 rad | = | 13750.98681 ' |
| 5 rad | = | 17188.73351 ' |
| 6 rad | = | 20626.48021 ' |
| 7 rad | = | 24064.22691 ' |
| 8 rad | = | 27501.97362 ' |
| 9 rad | = | 30939.72032 ' |
| 10 rad | = | 34377.46702 ' |
| 11 rad | = | 37815.21372 ' |
| 12 rad | = | 41252.96042 ' |
| 13 rad | = | 44690.70713 ' |
| 14 rad | = | 48128.45383 ' |
| 15 rad | = | 51566.20053 ' |
| 16 rad | = | 55003.94723 ' |
| 17 rad | = | 58441.69393 ' |
| 18 rad | = | 61879.44064 ' |
| 19 rad | = | 65317.18734 ' |
| 20 rad | = | 68754.93404 ' |
| 30 rad | = | 103132.40106 ' |
| 40 rad | = | 137509.86808 ' |
| 50 rad | = | 171887.33510 ' |
| 60 rad | = | 206264.80212 ' |
| 70 rad | = | 240642.26914 ' |
| 80 rad | = | 275019.73616 ' |
| 90 rad | = | 309397.20318 ' |
| 100 rad | = | 343774.67020 ' |
| 200 rad | = | 687549.34041 ' |
| 300 rad | = | 1031324.01061 ' |
| 400 rad | = | 1375098.68081 ' |
| 500 rad | = | 1718873.35101 ' |
| 600 rad | = | 2062648.02122 ' |
| 700 rad | = | 2406422.69142 ' |
| 800 rad | = | 2750197.36162 ' |
| 900 rad | = | 3093972.03182 ' |
| 1000 rad | = | 3437746.70203 ' |
How to Convert RAD to ' (Radian to Minute)?
We can convert radian to minute by using an example.
Example:
Convert 20 Radian to Minute?
We know 1 Radian = 3437.7467020 minute; 1 Minute = 0.0002909 radian.
20 radian = ___'
20 × 3437.7467020 = 68754.93404 ' (we know 1 radian = 3437.7467020 minute)
Answer:
20 radian = 68754.93404 minute
How to Convert Radians to Arcminutes
Since 1 radian = 180/π degrees and 1 degree = 60 arcminutes, the direct conversion is:
- Write down the angle in radians.
- Multiply by (180/π) × 60 = 10800/π ≈ 3437.75.
- Alternatively: first convert to degrees (× 180/π), then multiply by 60.
- The result is the angle in arcminutes.
Solved Examples
Question 1: Convert 0.01 radians to arcminutes.
Solution:
Arcminutes = Radians × (10800/π)
= 0.01 × 3437.75
= 34.377
Answer: 0.01 rad ≈ 34.38 arcminutes
Question 2: A telescope tracking error is 0.001 radians. How many arcminutes?
Solution:
Arcminutes = 0.001 × 3437.75
= 3.438
Answer: 0.001 rad ≈ 3.44 arcminutes
Question 3: Convert π/180 radians (1 degree) to arcminutes.
Solution:
1° = 60 arcminutes (by definition)
Verify: (π/180) × (10800/π) = 10800/180 = 60 ✓
Answer: π/180 rad = 60 arcminutes = 1°
Practice Questions
Try solving these on your own to test your understanding:
- Convert 0.1 radians to arcminutes. (Answer: ≈ 343.77′)
- A satellite drift rate is 0.0005 rad/hour. How many arcminutes/hour? (Answer: ≈ 1.72′/hr)
- Convert π/6 radians to arcminutes. (Answer: 1800′)
- A gyroscope drift is 0.015 rad. Express in arcminutes. (Answer: ≈ 51.57′)
Milliradians vs Arcminutes (MOA) in Precision Optics
Rifle and binocular optics use two competing angular systems: milliradians (mrad) and arcminutes (MOA). 1 mrad ≈ 3.438 MOA. NATO military scopes typically use milliradians, while American hunting scopes use MOA. At 100 meters: 1 mrad = 10 cm, while 1 MOA ≈ 2.91 cm. Converting between them is essential when using mixed equipment or following instructions written for the other system.
Radians to Arcminutes in Astronomy
Astronomers frequently convert small radian angles to arcminutes for expressing angular sizes. A telescope with a 1° field of view captures π/180 rad = 60 arcminutes of sky. The resolution limit due to atmospheric seeing (typically 1-2 arcseconds = 0.017-0.033 arcminutes) is often first calculated in radians using the diffraction formula θ = 1.22λ/D, then converted to arcminutes for practical use.
Key Takeaways
- Multiply radians by 10800/π (≈ 3437.75) to get arcminutes.
- 1 radian ≈ 3437.75 arcminutes ≈ 57.296°.
- 1 milliradian ≈ 3.438 MOA (minute of angle).
- Used in telescope specifications, satellite tracking, and ballistics.
- Small radian angles convert to manageable arcminute values for practical use.
Radian to Minute Conversion Formula
minute = radian × 3437.7467020
1 radian = 3437.7467020 minute
1 minute = 0.0002909 radian
Reverse: radian = minute × 0.0002909
Frequently Asked Questions
How many minute are in 1 radian?
There are 3437.7467020 minute in 1 radian. To convert radian to minute, multiply the value by 3437.7467020.
How do I convert radian to minute?
Multiply your radian value by 3437.7467020 to get the equivalent in minute. For example, 5 radian = 5 × 3437.7467020 = 17188.73351 minute.
How do I convert minute to radian?
Multiply your minute value by 0.0002909 to get the equivalent in radian. Alternatively, divide by 3437.7467020.
What is 10 radian in minute?
10 radian is equal to 34377.46702 minute.
What is 100 radian in minute?
100 radian is equal to 343774.67020 minute.