Convert Abmhos to Quantized Hall Conductances
Abmho (abmho) to Quantized Hall Conductance (e²/h) electric conductance conversion — enter any value below to get an instant result, or use the table for common values.
Results from this calculator are estimates provided for general informational purposes only, based on formulas, rates, and standards commonly accepted as of 2026. Figures may differ slightly from other calculators or professional sources due to rounding methods, differing assumptions, or regional regulations, and rules may change over time. Always consult a qualified professional — such as a financial advisor, healthcare provider, or other relevant specialist — before making decisions based on these results.
Result
1 abmho = 2.58128E+13 e²/h
1 Abmho = 2.58128E+13 Quantized Hall Conductances
1 Quantized Hall Conductance = 3.87405E-14 Abmhos
1 abmho in every supported unit
Conversion chart: Abmho to Quantized Hall Conductances
Conversion table
| Abmho (abmho) | Quantized Hall Conductance (e²/h) |
|---|---|
| 0.01 abmho | 2.58128E+11 e²/h |
| 0.1 abmho | 2.58128E+12 e²/h |
| 1 abmho | 2.58128E+13 e²/h |
| 2 abmho | 5.16256E+13 e²/h |
| 3 abmho | 7.74383E+13 e²/h |
| 5 abmho | 1.29064E+14 e²/h |
| 10 abmho | 2.58128E+14 e²/h |
| 20 abmho | 5.16256E+14 e²/h |
| 50 abmho | 1.29064E+15 e²/h |
| 100 abmho | 2.58128E+15 e²/h |
| 1000 abmho | 2.58128E+16 e²/h |
Abmho (abmho)
Definition: A unit of conductance from the CGS-EMU (centimeter-gram-second, electromagnetic) system of units, equal to one billion siemens. It is the reciprocal of the abohm, the CGS-EMU unit of resistance, which is itself defined as 10⁻⁹ ohm.
History: The abmho emerged in the 19th century alongside the rest of the CGS-EMU system, which physicists used for electromagnetic calculations before the modern SI (built on the meter-kilogram-second-ampere system) became the international standard in the mid-20th century.
Current use: Rarely used today outside of historical physics literature and specialized electromagnetic theory contexts that still work natively in CGS units, since virtually all modern engineering work has standardized on the SI siemens.
Quantized Hall Conductance (e²/h)
Definition: A fundamental physical constant of conductance, equal to the square of the elementary charge divided by the Planck constant (e²/h ≈ 3.87405 × 10⁻⁵ S). It is the natural step size by which conductance jumps in the quantum Hall effect, observed in two-dimensional electron systems under strong magnetic fields at low temperature.
History: It was discovered experimentally by Klaus von Klitzing in 1980, who found that the Hall conductance of a two-dimensional electron gas increases in exact, universal integer steps of e²/h regardless of the material or sample geometry — a discovery that earned him the 1985 Nobel Prize in Physics.
Current use: Used today as a precision metrological reference: because e²/h depends only on fundamental constants, the quantum Hall effect underpins the international standard for the ohm (and by reciprocal extension, the siemens), letting national metrology labs realize electrical resistance and conductance from first principles rather than physical artifact standards.
Supported Units
| Unit | Symbol | In Siemens |
|---|---|---|
| Siemens | S | 1 S |
| Megasiemens | MS | 1000000 S |
| Kilosiemens | kS | 1000 S |
| Millisiemens | mS | 0.001 S |
| Microsiemens | µS | 1E-06 S |
| Ampere/Volt | A/V | 1 S |
| Mho | ℧ | 1 S |
| Gemmho | gemmho | 1E-06 S |
| Micromho | µmho | 1E-06 S |
| Abmho | abmho | 1E+09 S |
| Statmho | statmho | 1.11235E-12 S |
| Quantized Hall Conductance | e²/h | 3.87405E-05 S |
About These Parameters
- Value
- The conductance value you want to convert, expressed in the "From" unit. Accepts decimals, and can represent anything from a picosiemens-level insulator leakage figure to a gigasiemens-scale superconductor measurement.
- From Unit
- The unit your input value is currently measured in — a modern component datasheet's siemens (S) rating, or a legacy figure quoted in mho, abmho, or statmho.
- To Unit
- The unit you want the result converted into. Use the swap button to flip From and To instantly, which is handy when translating an older mho-based figure into the modern siemens or vice versa.
How Electric Conductance Conversion Works
The Formula
Every unit here is defined by a fixed multiplier relative to the siemens. To convert a value from one unit to another:
result = value × (factor of "From" unit ÷ factor of "To" unit)
For Abmho → Quantized Hall Conductance: multiply by 2.58128E+13. For example, 1 abmho × 2.58128E+13 = 2.58128E+13 e²/h.
Conductance Is the Reciprocal of Resistance
Conductance and resistance describe the same physical relationship between voltage and current from opposite directions: resistance (ohms) measures how strongly a component opposes current flow, while conductance (siemens) measures how readily it allows current through. Because they are exact reciprocals (G = 1/R), a very good conductor — a thick copper busbar, for example — has a tiny resistance and a correspondingly large conductance, while a good insulator has a huge resistance and a conductance so small it is usually expressed in picosiemens or smaller. This reciprocal relationship is also why conductances of components wired in parallel simply add together, while their resistances do not.
From Mho to Siemens
Before 1971, the unit of conductance had no single settled name: engineers commonly called it the "mho" — "ohm" spelled backwards, with an upside-down omega (℧) as its symbol — to emphasize that it was resistance's reciprocal. The International Electrotechnical Commission formally adopted "siemens," named for Ernst Werner von Siemens, in 1935, and the unit was folded into the International System of Units in 1971, gradually displacing "mho" in textbooks, standards, and datasheets over the following decades. The two units remain numerically identical (1 mho = 1 S), so older equipment and literature that still uses "mho" converts to the modern siemens with a factor of exactly 1.
Example
A conductance of 1 abmho equals 2.58128E+13 e²/h. For scale, a typical incandescent light bulb filament has a conductance around 0.08 siemens (roughly 12 ohms of resistance), a thick copper ground strap can exceed several thousand siemens, and a high-quality electrical insulator's leakage conductance is often measured in picosiemens or smaller.
Frequently Asked Questions
How many Quantized Hall Conductances are in 1 Abmho?
1 Abmho (abmho) equals exactly 2.58128E+13 Quantized Hall Conductances (e²/h).
What is the difference between conductance and conductivity?
Conductance (siemens) describes a specific object or component's ability to conduct current — it depends on that object's size, shape, and material. Conductivity (siemens per meter) is a material property that strips out size and shape, describing how well a material conducts current per unit length regardless of the particular sample. Use this converter for whole-component conductance; use the companion Electric Conductivity Converter for the size-independent material property.
Is mho the same as siemens?
Yes — mho and siemens are numerically identical (1 mho = 1 S). "Mho" was the informal, widely used name for the unit before the International Electrotechnical Commission standardized "siemens" in 1935, and it still appears in older equipment, textbooks, and some U.S. water-quality literature.
Why is the quantized Hall conductance such a small, oddly specific number?
The quantized Hall conductance (e²/h ≈ 3.87405 × 10⁻⁵ S) is a fundamental physical constant, not a rounded engineering unit — it's built from the elementary charge (e) and the Planck constant (h). Discovered by Klaus von Klitzing in 1980, it's the exact step size by which conductance jumps in the quantum Hall effect, and because it depends only on fundamental constants, it's used today as a precision reference for realizing the ohm and siemens in metrology labs.
What are abmho and statmho used for today?
Abmho (from the CGS-EMU system) and statmho (from the CGS-ESU system) are both 19th-century units of conductance that predate the SI. They're rarely used in modern engineering, but still appear occasionally in historical physics literature and in theoretical work that frames electromagnetic calculations natively in CGS units rather than SI.