Convert A.u. of Length to Inch
Convert a.u. of length to inches instantly. 1 a.u. of length = 2.083375e-9 inch — use the live calculator, the exact formula, a conversion table and worked examples. Also check the Inch 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.
Inch
An inch is an Imperial and US customary unit of length defined since 1959 as exactly 25.4 millimeters (0.0254 meters). It is still the standard small unit of length in the United States, the United Kingdom (informally), and a few other countries.
The inch derives from the Roman uncia (one-twelfth of a foot) and survived through Anglo-Saxon and medieval English measurement systems. Various definitions persisted regionally until the 1959 International Yard and Pound Agreement standardized the inch globally as exactly 25.4 mm.
Inches are used in the US and UK for body height, screen sizes (TVs, monitors, phones), tire sizes, plumbing, lumber, paper sizes (US Letter is 8.5 × 11 in), and most consumer product specifications in the United States.
Anglo-Saxon origin (predating 1066); standardized to 25.4 mm exactly by the International Yard and Pound Agreement of 1959, signed by the US, UK, Canada, Australia, New Zealand, and South Africa.
A.u. of Length to Inch conversion formula
The relationship between a.u. of length and inches:
To convert a.u. of length to inches, multiply the value in a.u. of length by 2.083375e-9. To reverse, multiply inches by 4.799904e+8.
How to use this converter
Type a value into the calculator. The result in inches updates as you type. Tap a quick value, copy the result with one click, or use the swap arrow to jump straight to the Inch to A.u. of Length converter for the reverse direction.
Step-by-step: convert a.u. of length to inches
- Write down the value in a.u. of length (a.u.).
- Multiply that value by the factor 2.083375e-9.
- The product is the equivalent value in inches (in).
- To reverse, multiply the inch value by 4.799904e+8.
Worked examples
Example 1 — Convert 1 a.u. to in:
1 × 2.083375e-9 = 2.083375e-9 in
Example 2 — Convert 100 a.u. to in:
100 × 2.083375e-9 = 2.083375e-7 in
Real-world example — Sub-micron to millimeter
500,000 a.u. of length converts to a small everyday quantity in inches — useful when relating optical-wavelength specifications to physical mounting hardware.
500000 a.u. × 2.083375e-9 = 0.0010416874 in
Real-world example — From wavelengths to millimeter-scale objects
A value of one million a.u. of length sounds vast at the atomic scale but converts to a small everyday quantity in inches — useful when relating optical-wavelength specifications to physical mounting hardware.
1000000 a.u. × 2.083375e-9 = 0.0020833748 in
A.u. of Length to Inch conversion table
Standard reference values for converting a.u. of length to inches:
| A.u. of Length [a.u.] | Inch [in] |
|---|---|
| 0.01 | 2.083375e-11 |
| 0.1 | 2.083375e-10 |
| 1 | 2.083375e-9 |
| 2 | 4.16675e-9 |
| 3 | 6.250125e-9 |
| 4 | 8.333499e-9 |
| 5 | 1.041687e-8 |
| 10 | 2.083375e-8 |
| 20 | 4.16675e-8 |
| 30 | 6.250125e-8 |
| 40 | 8.333499e-8 |
| 50 | 1.041687e-7 |
| 100 | 2.083375e-7 |
| 500 | 1.041687e-6 |
| 1000 | 2.083375e-6 |
Frequently asked questions
How many inches is 1 a.u. of length?
How do I convert a.u. of length to inches?
How do I convert inches back to a.u. of length?
How many inches is 100 a.u. of length?
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. = 2.083375e-9 in) 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.