Convert Microinch to Fathom
Convert microinches to fathoms instantly. 1 microinch = 1.388889e-8 fathom — use the live calculator, the exact formula, a conversion table and worked examples. Also check the Fathom to Microinch converter for the reverse conversion.
Units explained
Microinch
A microinch is an Imperial unit of length equal to one millionth of an inch (2.54×10⁻⁸ m). It is used almost exclusively in surface-finish specifications for precision machining and optical components.
The microinch is derived from the inch using the SI-style prefix micro- to denote one millionth. Standardised through the 1959 International Yard and Pound Agreement, which fixed the inch at exactly 25.4 mm.
Microinches express surface roughness (Ra values) in US-based precision manufacturing — typical machined surfaces are 16–125 µin. Optical components and bearing races are often specified to 1–4 µin Ra.
Used in US precision-manufacturing literature throughout the 20th century; value became exact in 1959 when the inch was fixed at 25.4 mm via the International Yard and Pound Agreement.
Fathom
A fathom is an Imperial unit of length equal to 6 feet or exactly 1.8288 meters. It is used almost exclusively for measuring water depth in maritime contexts.
The fathom derives from the Old English word fæthm, meaning "the embracing arms" — the distance between the fingertips of a person's outstretched arms. Standardized at 6 feet in English maritime tradition.
Fathoms are used in nautical depth charts, scuba diving, oceanography, and maritime literature. Despite metrication efforts, fathoms remain common in English-language nautical charts and recreational diving.
Old English origin (predating 1066); standardized at 6 feet by English maritime tradition; fixed at 1.8288 m exactly via the 1959 International Yard and Pound Agreement.
Microinch to Fathom conversion formula
The relationship between microinches and fathoms:
To convert microinches to fathoms, multiply the value in microinches by 1.388889e-8. To reverse, multiply fathoms by 7.2e+7.
How to use this converter
Type a value into the calculator. The result in fathoms updates as you type. Tap a quick value, copy the result with one click, or use the swap arrow to jump straight to the Fathom to Microinch converter for the reverse direction.
Step-by-step: convert microinches to fathoms
- Write down the value in microinches (µin).
- Multiply that value by the factor 1.388889e-8.
- The product is the equivalent value in fathoms (ftm).
- To reverse, multiply the fathom value by 7.2e+7.
Worked examples
Example 1 — Convert 1 µin to ftm:
1 × 1.388889e-8 = 1.388889e-8 ftm
Example 2 — Convert 100 µin to ftm:
100 × 1.388889e-8 = 1.388889e-6 ftm
Real-world example — From sub-micron to human scale
One billion microinches equals one fathom — the conversion that drives home the gulf between atomic-scale features and everyday objects in physics curricula.
1e+9 µin × 1.388889e-8 = 13.8888888889 ftm
Real-world example — Bridging nine orders of magnitude
500 million microinches equals a value comfortably in the human-scale fathoms range. Physics problems that span this gap are common when comparing the wavelength of light to the path length of an experiment.
5e+8 µin × 1.388889e-8 = 6.9444444444 ftm
Microinch to Fathom conversion table
Standard reference values for converting microinches to fathoms:
| Microinch [µin] | Fathom [ftm] |
|---|---|
| 0.01 | 1.388889e-10 |
| 0.1 | 1.388889e-9 |
| 1 | 1.388889e-8 |
| 2 | 2.777778e-8 |
| 3 | 4.166667e-8 |
| 4 | 5.555556e-8 |
| 5 | 6.944444e-8 |
| 10 | 1.388889e-7 |
| 20 | 2.777778e-7 |
| 30 | 4.166667e-7 |
| 40 | 5.555556e-7 |
| 50 | 6.944444e-7 |
| 100 | 1.388889e-6 |
| 500 | 6.944444e-6 |
| 1000 | 1.388889e-5 |
Frequently asked questions
How many fathoms is 1 microinch?
How do I convert microinches to fathoms?
How do I convert fathoms back to microinches?
How many fathoms is 100 microinches?
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Sources & references
Conversion factor (1 µin = 1.388889e-8 ftm) 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.