Convert A.u. of Length to Foot
Convert a.u. of length to feet instantly. 1 a.u. of length = 1.736146e-10 foot — use the live calculator, the exact formula, a conversion table and worked examples. Also check the Foot to A.u. of Length converter for the reverse conversion.
Units explained
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.
Foot
A foot is an Imperial and US customary unit of length equal to 12 inches or exactly 0.3048 meters. It is the most commonly used unit of length in everyday measurement in the United States.
The foot's origin is literally the length of a human foot, used as a measurement standard since antiquity. The English foot was standardized at various points in history; the modern international foot (0.3048 m exactly) was fixed by the 1959 International Yard and Pound Agreement.
Feet are used in the US for body height, building dimensions, room sizes, road sign clearances, aviation altitude (feet above sea level), and most everyday distance estimation. The UK uses feet informally for height despite officially being metric.
Used since antiquity; standardized to 0.3048 m exactly by the International Yard and Pound Agreement of 1959. Aviation worldwide uses feet for altitude despite metric adoption elsewhere.
A.u. of Length to Foot conversion formula
The relationship between a.u. of length and feet:
To convert a.u. of length to feet, multiply the value in a.u. of length by 1.736146e-10. To reverse, multiply feet by 5.759885e+9.
How to use this converter
Type a value into the calculator. The result in feet updates as you type. Tap a quick value, copy the result with one click, or use the swap arrow to jump straight to the Foot to A.u. of Length converter for the reverse direction.
Step-by-step: convert a.u. of length to feet
- Write down the value in a.u. of length (a.u.).
- Multiply that value by the factor 1.736146e-10.
- The product is the equivalent value in feet (ft).
- To reverse, multiply the foot value by 5.759885e+9.
Worked examples
Example 1 — Convert 1 a.u. to ft:
1 × 1.736146e-10 = 1.736146e-10 ft
Example 2 — Convert 100 a.u. to ft:
100 × 1.736146e-10 = 1.736146e-8 ft
Real-world example — From sub-micron to human scale
One billion a.u. of length equals one foot — the conversion that drives home the gulf between atomic-scale features and everyday objects in physics curricula.
1e+9 a.u. × 1.736146e-10 = 0.1736145705 ft
Real-world example — Bridging nine orders of magnitude
500 million a.u. of length equals a value comfortably in the human-scale feet range. Physics problems that span this gap are common when comparing the wavelength of light to the path length of an experiment.
5e+8 a.u. × 1.736146e-10 = 0.0868072853 ft
A.u. of Length to Foot conversion table
Standard reference values for converting a.u. of length to feet:
| A.u. of Length [a.u.] | Foot [ft] |
|---|---|
| 0.01 | 1.736146e-12 |
| 0.1 | 1.736146e-11 |
| 1 | 1.736146e-10 |
| 2 | 3.472291e-10 |
| 3 | 5.208437e-10 |
| 4 | 6.944583e-10 |
| 5 | 8.680729e-10 |
| 10 | 1.736146e-9 |
| 20 | 3.472291e-9 |
| 30 | 5.208437e-9 |
| 40 | 6.944583e-9 |
| 50 | 8.680729e-9 |
| 100 | 1.736146e-8 |
| 500 | 8.680729e-8 |
| 1000 | 1.736146e-7 |
Frequently asked questions
How many feet is 1 a.u. of length?
How do I convert a.u. of length to feet?
How do I convert feet back to a.u. of length?
How many feet is 100 a.u. of length?
Popular length unit conversions
Convert A.u. of Length to other length units
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Metric / SI (4 units)
Imperial / US Customary (4 units)
Astronomical (8 units)
Sources & references
Conversion factor (1 a.u. = 1.736146e-10 ft) 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.