Convert Arcseconds to Radians
Instantly convert Arcseconds (″) to Radians (rad) with our free online calculator.
Formula: ″ to rad — multiply by 4.8481e-6
Reference Table
| Arcseconds (″) | Radians (rad) |
|---|---|
| 1 | 0.00000484814 |
| 5 | 0.0000242407 |
| 10 | 0.0000484814 |
| 25 | 0.000121203 |
| 50 | 0.000242407 |
| 100 | 0.000484814 |
How to Convert Arcseconds to Radians
Formula
To convert Arcseconds (″) to Radians (rad): multiply by 4.8481e-6
Step-by-Step
- Start with your value in Arcseconds (″).
- Multiply by 4.8481e-6 to perform the conversion.
- The result is your value expressed in Radians (rad).
Conversion Factor
1 ″ = 0.00000484814 rad
Reverse Factor
1 rad = 206265 ″
Worked Example
Convert 25 Arcseconds to Radians: 25 ″ = 0.000121203 rad
About Arcsecond (″)
A unit of plane angle equal to exactly 1/3600 of a degree (= 1/60 of an arcminute = π/648,000 rad ≈ 4.848 × 10⁻⁶ rad). Arcseconds are the working unit of modern observational astronomy: stellar parallax (the parsec — fundamental astronomical distance unit — is defined as the distance at which one astronomical unit subtends one arcsecond), telescope angular resolution (Hubble Space Telescope ~0.05 arcsec; the Extremely Large Telescope under construction ~0.005 arcsec diffraction-limited; the Event Horizon Telescope reached ~20 microarcseconds to image M87* and Sgr A* black-hole shadows), and astrometric catalogs (Gaia DR3 reports positions and proper motions in microarcseconds for ~1.8 billion stars). Geodetic GPS and high-precision surveying also specify coordinate accuracy in arcseconds, where sub-arcsecond resolution corresponds to centimeter-level positioning on Earth (1 arcsec of latitude ≈ 31 m at the equator). Symbol ″ (double prime); not to be confused with the inch-symbol ″.
About Radian (rad)
The SI unit of plane angle (ISO 80000-3 §3-5, BIPM SI Brochure), defined as the plane angle subtended at the center of a circle by a circular arc equal in length to the radius. One full revolution is exactly 2π radians ≈ 6.2832 rad; one degree = π/180 radians ≈ 0.01745 rad. Radians are the native unit for calculus — derivative identities (d/dx sin x = cos x; d/dx cos x = −sin x) only hold when x is in radians, not degrees, because the small-angle limit lim x→0 sin(x)/x = 1 only equals 1 in radians — and for every physics and engineering formula involving rotational dynamics, wave-phase calculations (Fourier series, signal processing), angular frequency ω = 2πf in oscillation analysis, complex-number arguments (Argand-plane angle = radians by convention), and gyroscope output. Reference values: 30° = π/6 rad, 45° = π/4 rad, 60° = π/3 rad, 90° = π/2 rad, 180° = π rad, 360° = 2π rad. The radian is technically a dimensionless ratio (arc length / radius), but is treated as a unit by SI convention.
Quick Facts
- 1 Arcsecond equals 0.00000484814 Radians
- 1 Radian equals 206265 Arcseconds
- Arcsecond is a unit of angle
- Radian is a unit of angle
- This conversion is commonly used in surveying, navigation, trigonometry, and mechanical design
Common Arcsecond to Radian Conversions
| Arcseconds (″) | Radians (rad) |
|---|---|
| 0.01 | 4.848137e-8 |
| 0.1 | 4.848137e-7 |
| 0.25 | 0.00000121203 |
| 0.5 | 0.00000242407 |
| 1 | 0.00000484814 |
| 2 | 0.00000969627 |
| 3 | 0.0000145444 |
| 5 | 0.0000242407 |
| 10 | 0.0000484814 |
| 15 | 0.0000727221 |
| 20 | 0.0000969627 |
| 25 | 0.000121203 |
| 50 | 0.000242407 |
| 75 | 0.00036361 |
| 100 | 0.000484814 |
| 250 | 0.00121203 |
| 500 | 0.00242407 |
| 1000 | 0.00484814 |
| 5000 | 0.0242407 |
| 10000 | 0.0484814 |
Understanding Arcseconds
The Arcsecond (symbol: ″) is a unit of angle. A unit of plane angle equal to exactly 1/3600 of a degree (= 1/60 of an arcminute = π/648,000 rad ≈ 4.848 × 10⁻⁶ rad). Arcseconds are the working unit of modern observational astronomy: stellar parallax (the parsec — fundamental astronomical distance unit — is defined as the distance at which one astronomical unit subtends one arcsecond), telescope angular resolution (Hubble Space Telescope ~0.05 arcsec; the Extremely Large Telescope under construction ~0.005 arcsec diffraction-limited; the Event Horizon Telescope reached ~20 microarcseconds to image M87* and Sgr A* black-hole shadows), and astrometric catalogs (Gaia DR3 reports positions and proper motions in microarcseconds for ~1.8 billion stars). Geodetic GPS and high-precision surveying also specify coordinate accuracy in arcseconds, where sub-arcsecond resolution corresponds to centimeter-level positioning on Earth (1 arcsec of latitude ≈ 31 m at the equator). Symbol ″ (double prime); not to be confused with the inch-symbol ″.
Arcseconds are commonly used in surveying, navigation, trigonometry, and mechanical design.
Understanding Radians
The Radian (symbol: rad) is a unit of angle. The SI unit of plane angle (ISO 80000-3 §3-5, BIPM SI Brochure), defined as the plane angle subtended at the center of a circle by a circular arc equal in length to the radius. One full revolution is exactly 2π radians ≈ 6.2832 rad; one degree = π/180 radians ≈ 0.01745 rad. Radians are the native unit for calculus — derivative identities (d/dx sin x = cos x; d/dx cos x = −sin x) only hold when x is in radians, not degrees, because the small-angle limit lim x→0 sin(x)/x = 1 only equals 1 in radians — and for every physics and engineering formula involving rotational dynamics, wave-phase calculations (Fourier series, signal processing), angular frequency ω = 2πf in oscillation analysis, complex-number arguments (Argand-plane angle = radians by convention), and gyroscope output. Reference values: 30° = π/6 rad, 45° = π/4 rad, 60° = π/3 rad, 90° = π/2 rad, 180° = π rad, 360° = 2π rad. The radian is technically a dimensionless ratio (arc length / radius), but is treated as a unit by SI convention.
Radians are commonly used in surveying, navigation, trigonometry, and mechanical design.
Why Convert Arcseconds to Radians?
Converting between Arcseconds and Radians is a frequent requirement for engineers, scientists, and students working with angle values. Different industries and regions favour different unit systems, so having a dependable conversion tool saves time and prevents errors in technical calculations. Whether you are verifying a specification sheet, cross-checking simulation results, or preparing a report for an international audience, accurate angle conversion is essential.
Frequently Asked Questions
How do I convert Arcseconds to Radians?
A unit of plane angle equal to exactly 1/3600 of a degree (= 1/60 of an arcminute = π/648,000 rad ≈ 4. To convert Arcseconds to Radians, multiply by 4.8481e-6. For example, 25 ″ equals 0.000121203 rad.
How many Radians are in 1 Arcsecond?
There are 0.00000484814 Radians in 1 Arcsecond.
How many Arcseconds are in 1 Radian?
There are 206265 Arcseconds in 1 Radian.
What is the formula for Arcsecond to Radian conversion?
The formula is: multiply by 4.8481e-6. This means 1 ″ = 0.00000484814 rad.
Is a Arcsecond bigger than a Radian?
Yes. One Arcsecond is larger than one Radian because 1 ″ equals 0.00000484814 rad, which is less than 1.
When do you need to convert between Arcseconds and Radians?
The SI unit of plane angle (ISO 80000-3 §3-5, BIPM SI Brochure), defined as the plane angle subtended at the center of a circle by a circular arc equal in length to the radius. Arcsecond and Radian are both angle units, so conversion comes up whenever one source of information uses one unit and another uses the other — a classic cross-reference challenge in engineering, trade, travel, and everyday life.