Convert Bohr Radius to Millimeter
Convert bohr radii to millimeters instantly. 1 bohr radius = 5.291772e-8 millimeter — use the live calculator, the exact formula, a conversion table and worked examples. Also check the Millimeter to Bohr Radius converter for the reverse conversion.
Units explained
Bohr Radius
The Bohr radius is approximately 5.292×10⁻¹¹ meters — the most probable distance between the proton and electron in a hydrogen atom in its ground state.
Defined by Niels Bohr in his 1913 model of the hydrogen atom. The current CODATA 2018 value of 5.29177210903×10⁻¹¹ m is derived from the elementary charge, electron mass, and Planck's constant.
The Bohr radius is used throughout atomic physics, quantum chemistry, and computational chemistry as the natural length scale for electronic-structure calculations. The atomic unit (a.u.) of length equals the Bohr radius.
Defined by Bohr in 1913; current value via CODATA 2018.
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.
Bohr Radius to Millimeter conversion formula
The relationship between bohr radii and millimeters:
To convert bohr radii to millimeters, multiply the value in bohr radii 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 Bohr Radius converter for the reverse direction.
Step-by-step: convert bohr radii to millimeters
- Write down the value in bohr radii (a₀).
- 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 a₀ to mm:
1 × 5.291772e-8 = 5.291772e-8 mm
Example 2 — Convert 100 a₀ to mm:
100 × 5.291772e-8 = 5.291772e-6 mm
Real-world example — Sub-micron to millimeter
500,000 bohr radii converts to a small everyday quantity in millimeters — useful when relating optical-wavelength specifications to physical mounting hardware.
500000 a₀ × 5.291772e-8 = 0.0264588605 mm
Real-world example — From wavelengths to millimeter-scale objects
A value of one million bohr radii 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 a₀ × 5.291772e-8 = 0.0529177211 mm
Bohr Radius to Millimeter conversion table
Standard reference values for converting bohr radii to millimeters:
| Bohr Radius [a₀] | 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 bohr radius?
How do I convert bohr radii to millimeters?
How do I convert millimeters back to bohr radii?
How many millimeters is 100 bohr radii?
Popular length unit conversions
Convert Bohr Radius to other length units
Show all Bohr Radius conversions
Metric / SI (4 units)
Imperial / US Customary (4 units)
Sources & references
Conversion factor (1 a₀ = 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.