Convert Seconds (") to Radians (rad)
1 second equals 4.84814 × 10⁻⁶ radians.
Second to Radian Converter
How to Convert Second to Radian
1 second = 4.84814 × 10-6 radians
Radian = Second × 4.84814 × 10-6
Example: 1" × 4.84814 × 10-6 = 4.84814 × 10-6 rad
Reverse Conversion
To convert radians back to seconds:
- Remember, 1 radian equals 206265 seconds.
- To convert 4.84814 × 10-6 rad to", multiply
4.84814 × 10-6 x 206265, resulting in1".
Common Second to Radian Conversions
| Second | Radian | Actions |
|---|---|---|
| 1 second | 4.84814 × 10-6 radians | |
| 5 seconds | 2.42407 × 10-5 radians | |
| 10 seconds | 4.84814 × 10-5 radians | |
| 25 seconds | 0.000121203 radians |
| Second | Radian | Actions |
|---|---|---|
| 50 seconds | 0.000242407 radians | |
| 100 seconds | 0.000484814 radians | |
| 500 seconds | 0.00242407 radians | |
| 1000 seconds | 0.00484814 radians |
Seconds to radians Conversion Table
Reference table with common seconds to radians conversions. All values calculated with high precision.
Seconds to Radians Table
100 to 500000
Seconds to Radians Table
1000000 to 1 × 1011
Radians to Seconds Table
1 to 100000
Definition of Second
- Definition
An arcsecond (second of arc) is 1/60 of an arcminute.
It is common in astronomy, surveying, astrometry, and precision optics for high-precision angles.
- Exact factor
- 1″ = 1/3600° = π/648,000 rad (exact)
- Examples
- 60″ = 1′
- 3600″ = 1°
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 Second
Facts & Uses
- 1 arcsecond (″) = 1/60 of an arcminute = 1/3600 of a degree. NOT to be confused with the time second.
- Standard for high-precision astronomy: stellar parallax, planetary positions, telescope angular resolution.
- Used in geodesy (GPS positioning, plate tectonics measurement), gravitational lensing, and VLBI radio astronomy.
- The parsec (a key astronomical distance unit) is defined as the distance at which 1 AU subtends 1 arcsecond of parallax — about 3.26 light-years.
Curiosities
- The arcsecond symbol ″ (double prime, U+2033) is distinct from the quotation mark ("); proper Unicode usage is important in scientific publishing.
- The Hubble Space Telescope has angular resolution of about 0.05 arcsec; JWST reaches ~0.07 arcsec at infrared wavelengths but with a 6.5 m mirror vs Hubble's 2.4 m.
- Continental drift: tectonic plates move ~2-10 cm per year, which corresponds to angular displacements of tens of milliarcseconds per year — measurable by VLBI.
- Approximate equivalents: 1 arcsecond = 1/3600° ≈ 4.848 × 10⁻⁶ rad ≈ 4.848 microradians.
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 second?
One second equals 4.84814 × 10-6 radians. To convert, multiply the 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 105174 seconds in radians?
105174 seconds = 0.5099 radians. This is one of the most commonly searched conversions for this pair.
How precise is the 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 Second
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