Convert Ell to Microinch
Convert ells to microinches instantly. 1 ell = 4.5e+7 microinch — use the live calculator, the exact formula, a conversion table and worked examples. Also check the Microinch to Ell converter for the reverse conversion.
Units explained
Ell
An ell is an Imperial unit of length equal to 45 inches (1.143 m), historically used as the standard measure of cloth in English commerce.
The ell derives from old English elna (forearm) and was standardised in medieval English trade as the cloth-measuring yard equivalent. The English ell is 45 inches; other regional ells differed.
Ells appear in historical English commerce records (especially cloth and tapestry trade). Used in legal documents through the 19th century; rare in modern commerce but referenced in literary and historical contexts.
Medieval English cloth-trade origin; standardised at 45 inches; became exact via the 1959 International Yard and Pound Agreement.
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.
Ell to Microinch conversion formula
The relationship between ells and microinches:
To convert ells to microinches, multiply the value in ells by 4.5e+7. To reverse, multiply microinches by 2.222222e-8.
How to use this converter
Type a value into the calculator. The result in microinches updates as you type. Tap a quick value, copy the result with one click, or use the swap arrow to jump straight to the Microinch to Ell converter for the reverse direction.
Step-by-step: convert ells to microinches
- Write down the value in ells (ell).
- Multiply that value by the factor 4.5e+7.
- The product is the equivalent value in microinches (µin).
- To reverse, multiply the microinch value by 2.222222e-8.
Worked examples
Example 1 — Convert 1 ell to µin:
1 × 4.5e+7 = 4.5e+7 µin
Example 2 — Convert 100 ell to µin:
100 × 4.5e+7 = 4.5e+9 µin
Real-world example — Human-scale to atomic dimensions
One ell equals one billion microinches — the canonical metric conversion bridging everyday objects and atomic-scale features in physics, chemistry, and electronics.
1 ell × 4.5e+7 = 4.5e+7 µin
Real-world example — Meter to nanoscale
One ell equals one billion microinches. Physics curricula use this conversion to teach orders of magnitude when introducing the electromagnetic spectrum.
1 ell × 4.5e+7 = 4.5e+7 µin
Ell to Microinch conversion table
Standard reference values for converting ells to microinches:
| Ell [ell] | Microinch [µin] |
|---|---|
| 0.01 | 450000 |
| 0.1 | 4500000 |
| 1 | 4.5e+7 |
| 2 | 9e+7 |
| 3 | 1.35e+8 |
| 4 | 1.8e+8 |
| 5 | 2.25e+8 |
| 10 | 4.5e+8 |
| 20 | 9e+8 |
| 30 | 1.35e+9 |
| 40 | 1.8e+9 |
| 50 | 2.25e+9 |
| 100 | 4.5e+9 |
| 500 | 2.25e+10 |
| 1000 | 4.5e+10 |
Frequently asked questions
How many microinches is 1 ell?
How do I convert ells to microinches?
How do I convert microinches back to ells?
How many microinches is 100 ells?
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Metric / SI (4 units)
Imperial / US Customary (26 units)
Sources & references
Conversion factor (1 ell = 4.5e+7 µin) 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.