Convert A.u. of Length to Earth's Equatorial Radius
Convert a.u. of length to earth's equatorial radii instantly. 1 a.u. of length = 8.296736e-18 earth's equatorial radius — use the live calculator, the exact formula, a conversion table and worked examples. Also check the Earth's Equatorial 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.
Earth's Equatorial Radius
Earth's equatorial radius is the distance from the planet's center to its surface at the equator, defined as exactly 6,378,137 meters by the WGS84 geodetic reference system.
The WGS84 (World Geodetic System 1984) defines Earth's reference ellipsoid for use in GPS and global cartography. The 6,378,137 m equatorial value was determined through satellite and ground geodetic measurements consolidated in 1984.
WGS84's equatorial radius is the standard reference for GPS, satellite imagery, geographic information systems, and aviation navigation. It defines the 'a' parameter of Earth's reference ellipsoid in coordinate transformations.
WGS84 reference ellipsoid adopted in 1984 by the US Department of Defense; subsequently adopted globally for GPS and civilian geodesy.
A.u. of Length to Earth's Equatorial Radius conversion formula
The relationship between a.u. of length and earth's equatorial radii:
To convert a.u. of length to earth's equatorial radii, multiply the value in a.u. of length by 8.296736e-18. To reverse, multiply earth's equatorial radii by 1.205293e+17.
How to use this converter
Type a value into the calculator. The result in earth's equatorial 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 Earth's Equatorial Radius to A.u. of Length converter for the reverse direction.
Step-by-step: convert a.u. of length to earth's equatorial radii
- Write down the value in a.u. of length (a.u.).
- Multiply that value by the factor 8.296736e-18.
- The product is the equivalent value in earth's equatorial radii (R⊕,eq).
- To reverse, multiply the earth's equatorial radius value by 1.205293e+17.
Worked examples
Example 1 — Convert 1 a.u. to R⊕,eq:
1 × 8.296736e-18 = 8.296736e-18 R⊕,eq
Example 2 — Convert 100 a.u. to R⊕,eq:
100 × 8.296736e-18 = 8.296736e-16 R⊕,eq
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 earth's equatorial radii for direct comparison with another instrument's calibration data sheet.
800 a.u. × 8.296736e-18 = 6.637389e-15 R⊕,eq
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. × 8.296736e-18 = 1.659347e-17 R⊕,eq
A.u. of Length to Earth's Equatorial Radius conversion table
Standard reference values for converting a.u. of length to earth's equatorial radii:
| A.u. of Length [a.u.] | Earth's Equatorial Radius [R⊕,eq] |
|---|---|
| 0.01 | 8.296736e-20 |
| 0.1 | 8.296736e-19 |
| 1 | 8.296736e-18 |
| 2 | 1.659347e-17 |
| 3 | 2.489021e-17 |
| 4 | 3.318695e-17 |
| 5 | 4.148368e-17 |
| 10 | 8.296736e-17 |
| 20 | 1.659347e-16 |
| 30 | 2.489021e-16 |
| 40 | 3.318695e-16 |
| 50 | 4.148368e-16 |
| 100 | 8.296736e-16 |
| 500 | 4.148368e-15 |
| 1000 | 8.296736e-15 |
Frequently asked questions
How many earth's equatorial radii is 1 a.u. of length?
How do I convert a.u. of length to earth's equatorial radii?
How do I convert earth's equatorial radii back to a.u. of length?
How many earth's equatorial radii is 100 a.u. of length?
Popular length unit conversions
Convert A.u. of Length to other length units
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Metric / SI (4 units)
Imperial / US Customary (4 units)
Astronomical (8 units)
Sources & references
Conversion factor (1 a.u. = 8.296736e-18 R⊕,eq) 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.