Convert Centimeter to Bohr Radius
Convert centimeters to bohr radii instantly. 1 centimeter = 1.889726e+8 bohr radius — use the live calculator, the exact formula, a conversion table and worked examples. Also check the Bohr Radius to Centimeter converter for the reverse conversion.
Units explained
Centimeter
A centimeter is a metric unit of length equal to one hundredth of a meter (1/100 m). It is one of the most commonly used SI sub-units in daily life, especially for measuring small objects, body dimensions, paper sizes, and short distances.
The centimeter emerged from the French metric system established by the French Academy of Sciences in 1793. The metric system introduced decimal-based prefixes (milli-, centi-, deci-, deca-, hecto-, kilo-) to create proportional sub-units of the meter.
Centimeters are the standard unit for everyday measurement in nearly every country outside the United States. They are used for body height, clothing sizes, rainfall, paper formats (A4 is 21 × 29.7 cm), screen dimensions, and most consumer product specifications.
Developed in France during the late 18th century as part of the metric system designed by the French Academy of Sciences. Formally adopted in France in 1795 and ratified internationally through the Metre Convention signed in Paris in 1875.
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.
Centimeter to Bohr Radius conversion formula
The relationship between centimeters and bohr radii:
To convert centimeters to bohr radii, multiply the value in centimeters by 1.889726e+8. To reverse, multiply bohr radii by 5.291772e-9.
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 Centimeter converter for the reverse direction.
Step-by-step: convert centimeters to bohr radii
- Write down the value in centimeters (cm).
- Multiply that value by the factor 1.889726e+8.
- The product is the equivalent value in bohr radii (a₀).
- To reverse, multiply the bohr radius value by 5.291772e-9.
Worked examples
Example 1 — Convert 1 cm to a₀:
1 × 1.889726e+8 = 1.889726e+8 a₀
Example 2 — Convert 100 cm to a₀:
100 × 1.889726e+8 = 1.889726e+10 a₀
Real-world example — Small-scale to atomic-scale
One centimeter equals 10 million bohr radii — useful for physics curricula that relate everyday measurements to atomic and optical scales.
1 cm × 1.889726e+8 = 1.889726e+8 a₀
Real-world example — Centimeter to wavelength scale
One centimeter equals 10 million bohr radii. Physics curricula use this kind of conversion to relate everyday measurements to atomic and optical scales.
1 cm × 1.889726e+8 = 1.889726e+8 a₀
Centimeter to Bohr Radius conversion table
Standard reference values for converting centimeters to bohr radii:
| Centimeter [cm] | Bohr Radius [a₀] |
|---|---|
| 0.01 | 1889726.1246257701 |
| 0.1 | 1.889726e+7 |
| 1 | 1.889726e+8 |
| 2 | 3.779452e+8 |
| 3 | 5.669178e+8 |
| 4 | 7.558904e+8 |
| 5 | 9.448631e+8 |
| 10 | 1.889726e+9 |
| 20 | 3.779452e+9 |
| 30 | 5.669178e+9 |
| 40 | 7.558904e+9 |
| 50 | 9.448631e+9 |
| 100 | 1.889726e+10 |
| 500 | 9.448631e+10 |
| 1000 | 1.889726e+11 |
Frequently asked questions
How many bohr radii is 1 centimeter?
How do I convert centimeters to bohr radii?
How do I convert bohr radii back to centimeters?
How many bohr radii is 100 centimeters?
Popular length unit conversions
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Imperial / US Customary (27 units)
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Astronomical (9 units)
Atomic / Physics (6 units)
Typographic (3 units)
Sources & references
Conversion factor (1 cm = 1.889726e+8 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.