13 minute equals approximately 0.0382 radians.
To convert 13 minutes to radians, remember that one degree equals 60 minutes and one degree equals π/180 radians. First, convert minutes to degrees by dividing by 60, then multiply by π/180 to get radians. So, 13 minutes is (13/60) degrees, which in radians is (13/60) * (π/180).
Conversion Result and Explanation
Conversion Tool
Result in radian:
Conversion Formula
The formula to convert minutes to radians is: radians = (minutes / 60) * (π / 180). Since there are 60 minutes in a degree and π radians in 180 degrees, dividing minutes by 60 gives degrees, which then multiplied by π/180 converts to radians. For example, for 13 minutes:
- Dividing 13 by 60 gives approximately 0.2167 degrees.
- Multiplying 0.2167 by π/180 yields about 0.0038 radians.
This method works because it systematically converts minutes into degrees, then degrees into radians, following the fundamental relationships between these units.
Conversion Example
- Convert 20 minutes to radians:
- 20/60 = 0.3333 degrees.
- 0.3333 * π/180 ≈ 0.0058 radians.
- Convert 45 minutes:
- 45/60 = 0.75 degrees.
- 0.75 * π/180 ≈ 0.0131 radians.
- Convert 5 minutes:
- 5/60 ≈ 0.0833 degrees.
- 0.0833 * π/180 ≈ 0.0015 radians.
- Convert 60 minutes:
- 60/60 = 1 degree.
- 1 * π/180 ≈ 0.0175 radians.
- Convert 0 minutes:
- 0/60 = 0 degrees.
- 0 * π/180 = 0 radians.
Conversion Chart
| Minutes | Radians |
|---|---|
| -12.0 | -0.0035 |
| -11.0 | -0.0034 |
| -10.0 | -0.0029 |
| -9.0 | -0.0026 |
| -8.0 | -0.0023 |
| -7.0 | -0.0020 |
| -6.0 | -0.0017 |
| -5.0 | -0.0014 |
| -4.0 | -0.0011 |
| -3.0 | -0.0008 |
| -2.0 | -0.0006 |
| -1.0 | -0.0003 |
| 0.0 | 0.0000 |
| 1.0 | 0.0003 |
| 2.0 | 0.0006 |
| 3.0 | 0.0008 |
| 4.0 | 0.0011 |
| 5.0 | 0.0014 |
| 6.0 | 0.0017 |
| 7.0 | 0.0020 |
| 8.0 | 0.0023 |
| 9.0 | 0.0026 |
| 10.0 | 0.0029 |
| 11.0 | 0.0034 |
| 12.0 | 0.0035 |
| 13.0 | 0.0038 |
| 14.0 | 0.0041 |
| 15.0 | 0.0042 |
| 20.0 | 0.0058 |
| 30.0 | 0.0087 |
| 40.0 | 0.0116 |
| 50.0 | 0.0145 |
| 60.0 | 0.0175 |
| 70.0 | 0.0204 |
| 80.0 | 0.0233 |
| 90.0 | 0.0262 |
| 100.0 | 0.0291 |
| 110.0 | 0.0320 |
| 120.0 | 0.0350 |
| 130.0 | 0.0379 |
| 140.0 | 0.0408 |
| 150.0 | 0.0437 |
| 160.0 | 0.0466 |
| 170.0 | 0.0495 |
| 180.0 | 0.0524 |
| 190.0 | 0.0553 |
| 200.0 | 0.0582 |
| 210.0 | 0.0611 |
| 220.0 | 0.0640 |
| 230.0 | 0.0669 |
| 240.0 | 0.0698 |
| 250.0 | 0.0727 |
| 260.0 | 0.0756 |
| 270.0 | 0.0785 |
| 280.0 | 0.0814 |
| 290.0 | 0.0843 |
| 300.0 | 0.0872 |
Use this chart to quickly estimate radians for various minute values, noting the linear relationship between minutes and radians.
Related Conversion Questions
- How many radians is 13 minutes in a circle?
- What is the radian equivalent of 13 minutes of angle?
- How do I convert 13 minutes to radians for trigonometry calculations?
- What is the formula to change 13 minutes into radians?
- How many radians are in 13 minutes of arc?
- Can I convert 13 minutes directly to radians without intermediate steps?
- What is the radian measure of 13 minutes in a circle?
Conversion Definitions
A minute (‘) is a unit of angular measurement equal to 1/60 of a degree, used in navigation and astronomy to describe small angles with high precision.
A radian is an angular measurement where one radian equals the angle at the center of a circle subtended by an arc equal in length to the circle’s radius, linking linear and angular measurements mathematically.
Conversion FAQs
How many radians are in 13 minutes?
Using the conversion formula, 13 minutes equals approximately 0.0038 radians, calculated by dividing 13 by 60 to get degrees and then multiplying by π/180 to convert degrees into radians.
Why is there a π in the conversion formula?
Because π radians equal 180 degrees, the factor π/180 converts degrees into radians, maintaining the correct proportion between linear and angular measurements.
Can I convert minutes to radians without a calculator?
Yes, if you memorize common conversions like 1 degree equals π/180 radians, and know that 1 minute is 1/60 of a degree, you can perform mental math to approximate the answer.
What applications use minute to radian conversions?
This conversion is frequently used in astronomy, navigation, and engineering where precise angular measurements are necessary, especially when dealing with small angles or minute-based units.