Convert Minutes (') to Radians (rad)
1 minute equals 0.000290888 radians.
Minute to Radian Converter
How to Convert Minute to Radian
1 minute = 0.000290888 radians
Radian = Minute × 0.000290888
Example: 1' × 0.000290888 = 0.000290888 rad
Reverse Conversion
To convert radians back to minutes:
- Remember, 1 radian equals 3437.75 minutes.
- To convert 0.000290888 rad to', multiply
0.000290888 x 3437.75, resulting in1'.
Common Minute to Radian Conversions
| Minute | Radian | Actions |
|---|---|---|
| 1 minute | 0.000290888 radians | |
| 5 minutes | 0.00145444 radians | |
| 10 minutes | 0.00290888 radians | |
| 25 minutes | 0.00727221 radians |
| Minute | Radian | Actions |
|---|---|---|
| 50 minutes | 0.0145444 radians | |
| 100 minutes | 0.0290888 radians | |
| 500 minutes | 0.145444 radians | |
| 1000 minutes | 0.290888 radians |
Minutes to radians Conversion Table
Reference table with common minutes to radians conversions. All values calculated with high precision.
Minutes to Radians Table
10000 to 1 × 109
Radians to Minutes Table
1 to 100000
Definition of Minute
- Definition
An arcminute (minute of arc) is 1/60 of a degree.
It is used in astronomy, optics, navigation, geodesy, and surveying for small angular measurements.
- Exact factor
- 1′ = 1/60° = π/10,800 rad (exact)
- Examples
- 60′ = 1°
- 30′ = 0.5°
Definition of Radian
- Definition
The radian (rad) is the SI derived unit of plane angle. It is defined as the angle subtended at the center of a circle by an arc equal in length to the radius.
Although mathematically dimensionless, the radian is retained as a named unit in the SI to preserve clarity in scientific, engineering, physics, trigonometry, and calculus contexts.
- Exact factor
- Base unit: 1 rad = 1 rad; full circle: 2π rad = 360°
- Examples
- π rad = 180°
- 1 rad ≈ 57.2958°
- 2π rad = 1 turn
About the Minute
Facts & Uses
- 1 arcminute (′) = 1/60 of a degree = π/10800 rad ≈ 0.000291 rad. NOT to be confused with the time minute.
- Standard for geographic latitude/longitude (1 nautical mile = 1 arcminute of latitude, the original definition).
- Used in astronomy for angular sizes of celestial objects (the full Moon ≈ 31′, Jupiter ≈ 30-50″ depending on opposition).
- Common in marksmanship as MOA (Minutes of Angle) for scope adjustment: 1 MOA ≈ 1 inch at 100 yards (actually 1.047″).
Curiosities
- The arcminute symbol ′ (prime, U+2032) is distinct from the apostrophe ('); using the wrong character is a common typesetting error in scientific writing.
- Human visual acuity: a person with 20/20 vision can distinguish two points separated by about 1 arcminute — the basis of the Snellen eye chart design.
- Geographic coordinates: 40°45′ N reads as "forty degrees, forty-five minutes north" — a precision of about 1.85 km in latitude.
- Approximate equivalents: 1 arcminute = 1/60° = 60 arcseconds ≈ 0.000291 rad.
Sources
About the Radian
Facts & Uses
- SI coherent unit of plane angle: 1 rad = the angle subtended at a circle's center by an arc equal in length to the radius. 1 full circle = 2π rad ≈ 6.283 rad.
- Universal in mathematics, physics, engineering, and computer graphics — wherever calculus or trigonometric derivatives are involved.
- Standard for angular velocity (rad/s), angular acceleration (rad/s²), and phase angles in electrical engineering and signal processing.
- Common reference: π/6 rad = 30°, π/4 = 45°, π/3 = 60°, π/2 = 90°, π = 180°, 2π = 360°.
Curiosities
- The radian was first proposed by Roger Cotes in 1714, but the name "radian" wasn't coined until 1873 by James Thomson (brother of Lord Kelvin).
- Programming functions like Math.sin() and Math.cos() in JavaScript, Python, C, and most languages take radians as input — a frequent source of bugs for developers expecting degrees.
- The reason calculus prefers radians: the derivative of sin(x) is cos(x) only when x is in radians. With degrees, you'd need a π/180 factor everywhere.
- Approximate equivalents: 1 rad ≈ 57.2958° ≈ 63.66 grad ≈ 3437.75 arcminutes.
Sources
Frequently Asked Questions
How many radians are in one minute?
One minute equals 0.000290888 radians. To convert, multiply the minute value by 0.000290888. For the reverse, divide the radian value by 0.000290888 (or multiply by 3437.75).
What is 231.3 minutes in radians?
231.3 minutes = 0.067282 radians. This is one of the most commonly searched conversions for this pair.
How precise is the minute-to-radian conversion?
The factor 0.000290888 is accurate to 6 significant figures, derived from international measurement standards. Our calculator uses full precision internally.
Looking for the reverse? Convert Radian to Minute
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