Convert A.u. of Length to Mile
Convert a.u. of length to miles instantly. 1 a.u. of length = 3.288155e-14 mile — use the live calculator, the exact formula, a conversion table and worked examples. Also check the Mile 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.
Mile
A mile (statute mile) is an Imperial and US customary unit of length equal to 5,280 feet or exactly 1,609.344 meters. It is the standard unit for road distances in the United States and the United Kingdom.
The mile derives from the Roman mille passus ("thousand paces" — about 1,480 meters). The English statute mile was fixed at 5,280 feet by the Weights and Measures Act of 1593, and exactly defined as 1,609.344 m by the 1959 International Yard and Pound Agreement.
Miles are used in the US and UK for road signs, speed limits (mph), athletic events (one-mile run), and geographic distances. Aviation also uses statute miles for some visibility measurements.
Roman origin (mille passus); English statute mile fixed at 5,280 feet in 1593; standardized to 1,609.344 m exactly by the 1959 International Yard and Pound Agreement.
A.u. of Length to Mile conversion formula
The relationship between a.u. of length and miles:
To convert a.u. of length to miles, multiply the value in a.u. of length by 3.288155e-14. To reverse, multiply miles by 3.041219e+13.
How to use this converter
Type a value into the calculator. The result in miles updates as you type. Tap a quick value, copy the result with one click, or use the swap arrow to jump straight to the Mile to A.u. of Length converter for the reverse direction.
Step-by-step: convert a.u. of length to miles
- Write down the value in a.u. of length (a.u.).
- Multiply that value by the factor 3.288155e-14.
- The product is the equivalent value in miles (mi).
- To reverse, multiply the mile value by 3.041219e+13.
Worked examples
Example 1 — Convert 1 a.u. to mi:
1 × 3.288155e-14 = 3.288155e-14 mi
Example 2 — Convert 100 a.u. to mi:
100 × 3.288155e-14 = 3.288155e-12 mi
Real-world example — Twelve orders of magnitude
A trillion a.u. of length maps to a single, recognizable distance in miles. This kind of conversion arises in cosmology and electromagnetic-spectrum exercises where atomic and astronomical scales sit side by side.
1e+12 a.u. × 3.288155e-14 = 0.0328815474 mi
Real-world example — Wavelength to road distance
A trillion a.u. of length equals one mile — the kind of conversion that appears in physics problems spanning the electromagnetic spectrum across many orders of magnitude.
1e+12 a.u. × 3.288155e-14 = 0.0328815474 mi
A.u. of Length to Mile conversion table
Standard reference values for converting a.u. of length to miles:
| A.u. of Length [a.u.] | Mile [mi] |
|---|---|
| 0.01 | 3.288155e-16 |
| 0.1 | 3.288155e-15 |
| 1 | 3.288155e-14 |
| 2 | 6.576309e-14 |
| 3 | 9.864464e-14 |
| 4 | 1.315262e-13 |
| 5 | 1.644077e-13 |
| 10 | 3.288155e-13 |
| 20 | 6.576309e-13 |
| 30 | 9.864464e-13 |
| 40 | 1.315262e-12 |
| 50 | 1.644077e-12 |
| 100 | 3.288155e-12 |
| 500 | 1.644077e-11 |
| 1000 | 3.288155e-11 |
Frequently asked questions
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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. = 3.288155e-14 mi) 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.