Convert Angstrom to Bohr Radius
Convert angstroms to bohr radii instantly. 1 angstrom = 1.8897261246 bohr radius — use the live calculator, the exact formula, a conversion table and worked examples. Also check the Bohr Radius to Angstrom converter for the reverse conversion.
Units explained
Angstrom
An angstrom is a unit of length equal to exactly 10⁻¹⁰ meters (0.1 nm). Named after Swedish physicist Anders Jonas Ångström, it is the traditional unit for atomic and molecular dimensions in chemistry and crystallography.
Defined in 1907 as exactly 10⁻¹⁰ m. Although officially deprecated by the BIPM in favor of the nanometer in 1978, the angstrom remains in widespread use in chemistry and crystallography.
Angstroms express bond lengths (typical covalent bond is 1–2 Å), atomic radii, crystal lattice parameters, and X-ray wavelengths. Standard in chemistry textbooks and crystallographic data tables.
Named after Anders Jonas Ångström; defined at 10⁻¹⁰ m in 1907; deprecated as SI by BIPM in 1978 but retained universally in chemistry practice.
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.
Angstrom to Bohr Radius conversion formula
The relationship between angstroms and bohr radii:
To convert angstroms to bohr radii, multiply the value in angstroms by 1.8897261246. To reverse, multiply bohr radii by 0.5291772109.
How to use this converter
Type a value into the calculator. The result in bohr radii updates as you type. Tap a quick value, copy the result with one click, or use the swap arrow to jump straight to the Bohr Radius to Angstrom converter for the reverse direction.
Step-by-step: convert angstroms to bohr radii
- Write down the value in angstroms (Å).
- Multiply that value by the factor 1.8897261246.
- The product is the equivalent value in bohr radii (a₀).
- To reverse, multiply the bohr radius value by 0.5291772109.
Worked examples
Example 1 — Convert 1 Å to a₀:
1 × 1.8897261246 = 1.8897261246 a₀
Example 2 — Convert 100 Å to a₀:
100 × 1.8897261246 = 188.9726124626 a₀
Real-world example — Molecular dimensions
The diameter of small molecular structures (around 2 angstroms) is often converted into related sub-micron units when comparing measurements across different microscopy techniques or imaging modalities.
2 Å × 1.8897261246 = 3.7794522493 a₀
Real-world example — Wavelengths across the spectrum
Optical and atomic-scale phenomena are routinely cross-converted between sub-micron units. A photon of wavelength 800 angstroms can be re-expressed in bohr radii for direct comparison with another instrument's calibration data sheet.
800 Å × 1.8897261246 = 1511.7808997006 a₀
Angstrom to Bohr Radius conversion table
Standard reference values for converting angstroms to bohr radii:
| Angstrom [Å] | Bohr Radius [a₀] |
|---|---|
| 0.01 | 0.0188972612 |
| 0.1 | 0.1889726125 |
| 1 | 1.8897261246 |
| 2 | 3.7794522493 |
| 3 | 5.6691783739 |
| 4 | 7.5589044985 |
| 5 | 9.4486306231 |
| 10 | 18.8972612463 |
| 20 | 37.7945224925 |
| 30 | 56.6917837388 |
| 40 | 75.589044985 |
| 50 | 94.4863062313 |
| 100 | 188.9726124626 |
| 500 | 944.8630623129 |
| 1000 | 1889.7261246258 |
Frequently asked questions
How many bohr radii is 1 angstrom?
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Imperial / US Customary (4 units)
Sources & references
Conversion factor (1 Å = 1.8897261246 a₀) 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.