Convert A.u. of Length to Earth's Polar Radius
Convert a.u. of length to earth's polar radii instantly. 1 a.u. of length = 8.324648e-18 earth's polar radius — use the live calculator, the exact formula, a conversion table and worked examples. Also check the Earth's Polar 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 Polar Radius
Earth's polar radius is the distance from the planet's center to either pole, approximately 6,356,752 meters under the WGS84 geodetic reference system. The polar radius is about 21 km shorter than the equatorial radius due to Earth's oblate spheroid shape.
Derived from WGS84's flattening parameter (f ≈ 1/298.257); the difference from the equatorial radius is the geometric signature of Earth's rotational oblateness.
Earth's polar radius is used in geodesy, satellite-orbit calculations, and global cartography. Together with the equatorial radius it defines Earth's reference ellipsoid in WGS84.
Derived from the WGS84 reference ellipsoid adopted in 1984; the value is computed from the equatorial radius minus the oblateness.
A.u. of Length to Earth's Polar Radius conversion formula
The relationship between a.u. of length and earth's polar radii:
To convert a.u. of length to earth's polar radii, multiply the value in a.u. of length by 8.324648e-18. To reverse, multiply earth's polar radii by 1.201252e+17.
How to use this converter
Type a value into the calculator. The result in earth's polar 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 Polar Radius to A.u. of Length converter for the reverse direction.
Step-by-step: convert a.u. of length to earth's polar radii
- Write down the value in a.u. of length (a.u.).
- Multiply that value by the factor 8.324648e-18.
- The product is the equivalent value in earth's polar radii (R⊕,p).
- To reverse, multiply the earth's polar radius value by 1.201252e+17.
Worked examples
Example 1 — Convert 1 a.u. to R⊕,p:
1 × 8.324648e-18 = 8.324648e-18 R⊕,p
Example 2 — Convert 100 a.u. to R⊕,p:
100 × 8.324648e-18 = 8.324648e-16 R⊕,p
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. × 8.324648e-18 = 1.66493e-17 R⊕,p
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 polar radii for direct comparison with another instrument's calibration data sheet.
800 a.u. × 8.324648e-18 = 6.659718e-15 R⊕,p
A.u. of Length to Earth's Polar Radius conversion table
Standard reference values for converting a.u. of length to earth's polar radii:
| A.u. of Length [a.u.] | Earth's Polar Radius [R⊕,p] |
|---|---|
| 0.01 | 8.324648e-20 |
| 0.1 | 8.324648e-19 |
| 1 | 8.324648e-18 |
| 2 | 1.66493e-17 |
| 3 | 2.497394e-17 |
| 4 | 3.329859e-17 |
| 5 | 4.162324e-17 |
| 10 | 8.324648e-17 |
| 20 | 1.66493e-16 |
| 30 | 2.497394e-16 |
| 40 | 3.329859e-16 |
| 50 | 4.162324e-16 |
| 100 | 8.324648e-16 |
| 500 | 4.162324e-15 |
| 1000 | 8.324648e-15 |
Frequently asked questions
How many earth's polar radii is 1 a.u. of length?
How do I convert a.u. of length to earth's polar radii?
How do I convert earth's polar radii back to a.u. of length?
How many earth's polar radii is 100 a.u. of length?
Popular length unit conversions
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Imperial / US Customary (4 units)
Astronomical (8 units)
Sources & references
Conversion factor (1 a.u. = 8.324648e-18 R⊕,p) 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.