Convert A.u. of Length to Sun's Radius
Convert a.u. of length to sun's radii instantly. 1 a.u. of length = 7.606399e-20 sun's radius — use the live calculator, the exact formula, a conversion table and worked examples. Also check the Sun's Radius to A.u. of Length converter for the reverse conversion.
Units explained
A.u. of Length
The atomic unit of length (a.u.) is equal to the Bohr radius — approximately 5.292×10⁻¹¹ m. Despite the abbreviation matching 'astronomical unit', this is a different unit used in atomic and molecular physics.
The atomic unit system was developed in the 1950s for quantum-chemistry calculations. The a.u. of length is defined as the Bohr radius (a₀), the most probable distance between the proton and electron in a hydrogen atom in its ground state.
The atomic unit of length is used throughout quantum chemistry, electronic-structure theory, and computational physics. Most quantum-mechanical equations simplify when expressed in atomic units rather than SI units.
Atomic unit system developed by Hartree in the 1920s; value fixed via CODATA 2018 determination of fundamental physical constants.
Sun's Radius
The Sun's radius is approximately 695,700 km (6.957×10⁸ m), defined as the IAU 2015 nominal solar radius for use in stellar physics and exoplanet research.
The IAU (International Astronomical Union) Resolution B3 in 2015 defined a nominal solar radius of exactly 6.957×10⁸ m to serve as a stable reference, independent of actual measurement-uncertainty variations in the real Sun.
Solar radii are used in stellar physics, exoplanet characterisation, and any context where a star's size is expressed relative to the Sun. Most stellar radius measurements are quoted in solar-radius units rather than meters.
Defined exactly at 6.957×10⁸ m by IAU Resolution B3 in 2015.
A.u. of Length to Sun's Radius conversion formula
The relationship between a.u. of length and sun's radii:
To convert a.u. of length to sun's radii, multiply the value in a.u. of length by 7.606399e-20. To reverse, multiply sun's radii by 1.314682e+19.
How to use this converter
Type a value into the calculator. The result in sun's radii updates as you type. Tap a quick value, copy the result with one click, or use the swap arrow to jump straight to the Sun's Radius to A.u. of Length converter for the reverse direction.
Step-by-step: convert a.u. of length to sun's radii
- Write down the value in a.u. of length (a.u.).
- Multiply that value by the factor 7.606399e-20.
- The product is the equivalent value in sun's radii (R☉).
- To reverse, multiply the sun's radius value by 1.314682e+19.
Worked examples
Example 1 — Convert 1 a.u. to R☉:
1 × 7.606399e-20 = 7.606399e-20 R☉
Example 2 — Convert 100 a.u. to R☉:
100 × 7.606399e-20 = 7.606399e-18 R☉
Real-world example — Molecular dimensions
The diameter of small molecular structures (around 2 a.u. of length) is often converted into related sub-micron units when comparing measurements across different microscopy techniques or imaging modalities.
2 a.u. × 7.606399e-20 = 1.52128e-19 R☉
Real-world example — Wavelengths across the spectrum
Optical and atomic-scale phenomena are routinely cross-converted between sub-micron units. A photon of wavelength 800 a.u. of length can be re-expressed in sun's radii for direct comparison with another instrument's calibration data sheet.
800 a.u. × 7.606399e-20 = 6.08512e-17 R☉
A.u. of Length to Sun's Radius conversion table
Standard reference values for converting a.u. of length to sun's radii:
| A.u. of Length [a.u.] | Sun's Radius [R☉] |
|---|---|
| 0.01 | 7.606399e-22 |
| 0.1 | 7.606399e-21 |
| 1 | 7.606399e-20 |
| 2 | 1.52128e-19 |
| 3 | 2.28192e-19 |
| 4 | 3.04256e-19 |
| 5 | 3.8032e-19 |
| 10 | 7.606399e-19 |
| 20 | 1.52128e-18 |
| 30 | 2.28192e-18 |
| 40 | 3.04256e-18 |
| 50 | 3.8032e-18 |
| 100 | 7.606399e-18 |
| 500 | 3.8032e-17 |
| 1000 | 7.606399e-17 |
Frequently asked questions
How many sun's radii is 1 a.u. of length?
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How do I convert sun's radii back to a.u. of length?
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Popular length unit conversions
Convert A.u. of Length to other length units
Show all A.u. of Length conversions
Metric / SI (4 units)
Imperial / US Customary (4 units)
Astronomical (8 units)
Sources & references
Conversion factor (1 a.u. = 7.606399e-20 R☉) verified against the following authoritative sources:
- BIPM — The International System of Units (SI Brochure 9th ed.)
Official BIPM publication defining the seven SI base units (including the meter) and the rules for their use. The global authority on units of measurement.
- NIST — Guide to the SI
US National Institute of Standards and Technology reference covering the SI base and derived units with definitions and usage rules for US technical practice.
- NIST Special Publication 811 — Guide for the Use of the International System of Units
Detailed NIST guide covering exact conversion factors between SI and US customary units along with formatting and rounding conventions.
- NIST — Refinement of values for the yard and pound (Federal Register 1959)
The treaty (signed by US
- International Astronomical Union — System of Astronomical Constants
The IAU defines astronomical units including the AU (149597870700 m exactly) light-year and parsec used in astronomy and astrophysics.