Convert Arc Seconds (") to Radians (rad)
1 arc second equals 4.84814 × 10⁻⁶ radians.
Arc Second to Radian Converter
How to Convert Arc Second to Radian
1 arc second = 4.84814 × 10-6 radians
Radian = Arc Second × 4.84814 × 10-6
Example: 1" × 4.84814 × 10-6 = 4.84814 × 10-6 rad
Reverse Conversion
To convert radians back to arc seconds:
- Remember, 1 radian equals 206265 arc seconds.
- To convert 4.84814 × 10-6 rad to", multiply
4.84814 × 10-6 x 206265, resulting in1".
Common Arc Second to Radian Conversions
| Arc Second | Radian | Actions |
|---|---|---|
| 1 arc second | 4.84814 × 10-6 radians | |
| 5 arc seconds | 2.42407 × 10-5 radians | |
| 10 arc seconds | 4.84814 × 10-5 radians | |
| 25 arc seconds | 0.000121203 radians |
| Arc Second | Radian | Actions |
|---|---|---|
| 50 arc seconds | 0.000242407 radians | |
| 100 arc seconds | 0.000484814 radians | |
| 500 arc seconds | 0.00242407 radians | |
| 1000 arc seconds | 0.00484814 radians |
Arc seconds to radians Conversion Table
Reference table with common arc seconds to radians conversions. All values calculated with high precision.
Arc Seconds to Radians Table
100 to 500000
Arc Seconds to Radians Table
1000000 to 1 × 1011
Radians to Arc Seconds Table
0.0001 to 12
Radians to Arc Seconds Table
1 to 100000
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 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 arc second?
One arc second equals 4.84814 × 10-6 radians. To convert, multiply the arc second value by 4.84814 × 10-6. For the reverse, divide the radian value by 4.84814 × 10-6 (or multiply by 206265).
What is 100 arc seconds in radians?
100 arc seconds = 0.00048481 radians. This is one of the most commonly searched conversions for this pair.
How precise is the arc second-to-radian conversion?
The factor 4.84814 × 10-6 is accurate to 6 significant figures, derived from international measurement standards. Our calculator uses full precision internally.
Looking for the reverse? Convert Radian to Arc Second
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