Convert Millimeter to A.u. of Length
Convert millimeters to a.u. of length instantly. 1 millimeter = 1.889726e+7 a.u. of length — use the live calculator, the exact formula, a conversion table and worked examples. Also check the A.u. of Length to Millimeter converter for the reverse conversion.
Units explained
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
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 to A.u. of Length conversion formula
The relationship between millimeters and a.u. of length:
To convert millimeters to a.u. of length, multiply the value in millimeters by 1.889726e+7. To reverse, multiply a.u. of length by 5.291772e-8.
How to use this converter
Type a value into the calculator. The result in a.u. of length updates as you type. Tap a quick value, copy the result with one click, or use the swap arrow to jump straight to the A.u. of Length to Millimeter converter for the reverse direction.
Step-by-step: convert millimeters to a.u. of length
- Write down the value in millimeters (mm).
- Multiply that value by the factor 1.889726e+7.
- The product is the equivalent value in a.u. of length (a.u.).
- To reverse, multiply the a.u. of length value by 5.291772e-8.
Worked examples
Example 1 — Convert 1 mm to a.u.:
1 × 1.889726e+7 = 1.889726e+7 a.u.
Example 2 — Convert 100 mm to a.u.:
100 × 1.889726e+7 = 1.889726e+9 a.u.
Real-world example — Small-scale to atomic-scale
One millimeter equals 10 million a.u. of length — useful for physics curricula that relate everyday measurements to atomic and optical scales.
1 mm × 1.889726e+7 = 1.889726e+7 a.u.
Real-world example — Centimeter to wavelength scale
One millimeter equals 10 million a.u. of length. Physics curricula use this kind of conversion to relate everyday measurements to atomic and optical scales.
1 mm × 1.889726e+7 = 1.889726e+7 a.u.
Millimeter to A.u. of Length conversion table
Standard reference values for converting millimeters to a.u. of length:
| Millimeter [mm] | A.u. of Length [a.u.] |
|---|---|
| 0.01 | 188972.612462577 |
| 0.1 | 1889726.1246257704 |
| 1 | 1.889726e+7 |
| 2 | 3.779452e+7 |
| 3 | 5.669178e+7 |
| 4 | 7.558904e+7 |
| 5 | 9.448631e+7 |
| 10 | 1.889726e+8 |
| 20 | 3.779452e+8 |
| 30 | 5.669178e+8 |
| 40 | 7.558904e+8 |
| 50 | 9.448631e+8 |
| 100 | 1.889726e+9 |
| 500 | 9.448631e+9 |
| 1000 | 1.889726e+10 |
Frequently asked questions
How many a.u. of length is 1 millimeter?
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Popular length unit conversions
Convert Millimeter to other length units
Show all Millimeter conversions
Metric / SI (17 units)
Imperial / US Customary (27 units)
Nautical (1 units)
Astronomical (9 units)
Atomic / Physics (6 units)
Typographic (3 units)
Sources & references
Conversion factor (1 mm = 1.889726e+7 a.u.) 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.