Convert Bohr Radius to Angstrom
Convert bohr radii to angstroms instantly. 1 bohr radius = 0.5291772109 angstrom — use the live calculator, the exact formula, a conversion table and worked examples. Also check the Angstrom 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.
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 to Angstrom conversion formula
The relationship between bohr radii and angstroms:
To convert bohr radii to angstroms, multiply the value in bohr radii by 0.5291772109. To reverse, multiply angstroms by 1.8897261246.
How to use this converter
Type a value into the calculator. The result in angstroms updates as you type. Tap a quick value, copy the result with one click, or use the swap arrow to jump straight to the Angstrom to Bohr Radius converter for the reverse direction.
Step-by-step: convert bohr radii to angstroms
- Write down the value in bohr radii (a₀).
- Multiply that value by the factor 0.5291772109.
- The product is the equivalent value in angstroms (Å).
- To reverse, multiply the angstrom value by 1.8897261246.
Worked examples
Example 1 — Convert 1 a₀ to Å:
1 × 0.5291772109 = 0.5291772109 Å
Example 2 — Convert 100 a₀ to Å:
100 × 0.5291772109 = 52.9177210903 Å
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 bohr radii can be re-expressed in angstroms for direct comparison with another instrument's calibration data sheet.
800 a₀ × 0.5291772109 = 423.3417687224 Å
Real-world example — Molecular dimensions
The diameter of small molecular structures (around 2 bohr radii) is often converted into related sub-micron units when comparing measurements across different microscopy techniques or imaging modalities.
2 a₀ × 0.5291772109 = 1.0583544218 Å
Bohr Radius to Angstrom conversion table
Standard reference values for converting bohr radii to angstroms:
| Bohr Radius [a₀] | Angstrom [Å] |
|---|---|
| 0.01 | 0.0052917721 |
| 0.1 | 0.0529177211 |
| 1 | 0.5291772109 |
| 2 | 1.0583544218 |
| 3 | 1.5875316327 |
| 4 | 2.1167088436 |
| 5 | 2.6458860545 |
| 10 | 5.291772109 |
| 20 | 10.5835442181 |
| 30 | 15.8753163271 |
| 40 | 21.1670884361 |
| 50 | 26.4588605451 |
| 100 | 52.9177210903 |
| 500 | 264.5886054515 |
| 1000 | 529.177210903 |
Frequently asked questions
How many angstroms is 1 bohr radius?
How do I convert bohr radii to angstroms?
How do I convert angstroms back to bohr radii?
How many angstroms 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 = 0.5291772109 Å) 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 Hydrographic Organization — Resolution on the Nautical Mile
International authority that standardised the nautical mile at exactly 1852 m in 1929 — the value adopted worldwide for sea and air navigation.