Convert A.u. of Length to Millimeter
Convert a.u. of length to millimeters instantly. 1 a.u. of length = 5.291772e-8 millimeter — use the live calculator, the exact formula, a conversion table and worked examples. Also check the Millimeter 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.
Millimeter
A millimeter is a metric unit of length equal to one thousandth of a meter (1/1000 m). It is the standard small-scale unit in the SI system and is widely used wherever sub-centimeter precision matters.
The millimeter was defined alongside the meter when France adopted the metric system in 1795, using the standard SI prefix milli- (from Latin mille, "thousand") to denote one-thousandth.
Millimeters are used in engineering drawings, machining, manufacturing, paper sizes, rainfall measurement, and any context where dimensions below one centimeter need to be specified clearly. Most rulers worldwide are marked in millimeters.
Adopted in 1795 in France as part of the original metric system; standardized internationally by the Metre Convention in 1875 and confirmed in the SI in 1960.
A.u. of Length to Millimeter conversion formula
The relationship between a.u. of length and millimeters:
To convert a.u. of length to millimeters, multiply the value in a.u. of length by 5.291772e-8. To reverse, multiply millimeters by 1.889726e+7.
How to use this converter
Type a value into the calculator. The result in millimeters updates as you type. Tap a quick value, copy the result with one click, or use the swap arrow to jump straight to the Millimeter to A.u. of Length converter for the reverse direction.
Step-by-step: convert a.u. of length to millimeters
- Write down the value in a.u. of length (a.u.).
- Multiply that value by the factor 5.291772e-8.
- The product is the equivalent value in millimeters (mm).
- To reverse, multiply the millimeter value by 1.889726e+7.
Worked examples
Example 1 — Convert 1 a.u. to mm:
1 × 5.291772e-8 = 5.291772e-8 mm
Example 2 — Convert 100 a.u. to mm:
100 × 5.291772e-8 = 5.291772e-6 mm
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 millimeters — useful when relating optical-wavelength specifications to physical mounting hardware.
1000000 a.u. × 5.291772e-8 = 0.0529177211 mm
Real-world example — Sub-micron to millimeter
500,000 a.u. of length converts to a small everyday quantity in millimeters — useful when relating optical-wavelength specifications to physical mounting hardware.
500000 a.u. × 5.291772e-8 = 0.0264588605 mm
A.u. of Length to Millimeter conversion table
Standard reference values for converting a.u. of length to millimeters:
| A.u. of Length [a.u.] | Millimeter [mm] |
|---|---|
| 0.01 | 5.291772e-10 |
| 0.1 | 5.291772e-9 |
| 1 | 5.291772e-8 |
| 2 | 1.058354e-7 |
| 3 | 1.587532e-7 |
| 4 | 2.116709e-7 |
| 5 | 2.645886e-7 |
| 10 | 5.291772e-7 |
| 20 | 1.058354e-6 |
| 30 | 1.587532e-6 |
| 40 | 2.116709e-6 |
| 50 | 2.645886e-6 |
| 100 | 5.291772e-6 |
| 500 | 2.645886e-5 |
| 1000 | 5.291772e-5 |
Frequently asked questions
How many millimeters is 1 a.u. of length?
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How many millimeters 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. = 5.291772e-8 mm) 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.