Electric Conductance Converter
Print pageAll Equivalents Reference Table
| Unit | Equivalent Value |
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Electric Conductance (also known as Electrical Admittance Magnitude, Transconductance Intensity, Conductive Permeability Rate, or Inverse Resistance, symbolized by G or gm) measures the quantitative ease with which an electric current flows through a conductor, semiconductor channel, liquid electrolyte, or ionization path (G = 1 ÷ R = I ÷ V = σ · (A ÷ L), where R is resistance in ohms, I is current in amperes, V is voltage in volts, σ is electrical conductivity, A is cross-sectional area, and L is path length). Across MOSFET semiconductor transistor amplifier design (transconductance gm = ∂ID ÷ ∂VGS), municipal water purity ionic conductivity testing (TDS), power grid transformer admittance modeling, electrochemical cell analysis, and quantum 1D ballistic electron transport, electric conductance is categorized across four major engineering unit families: International System of Units (SI metric fundamental: Siemens / S, Megasiemens / MS, Kilosiemens / kS, Millisiemens / mS, Microsiemens / μS, Ampere per Volt / A/V), Traditional Engineering units (Mho, Micromho, Gemmho), CGS Electromagnetic System units (Abmho), and Fundamental Quantum Metrology Constants (Quantized Hall Conductance / G0 = 2e2/h).
Our free online Electric Conductance Converter provides instant, high-precision conversions across all SI metric, traditional engineering, CGS electromagnetic, and quantum ballistic conductance units:
- Ampere per Volt & Mho to Siemens [SI Fundamental Identity]:
1 A/V = 1 Mho = 1.0 Siemens (S)(100% mathematically identical derived SI units). - Millisiemens to Siemens & Microsiemens [Transconductance Standard]: Multiply mS by
0.001(1 mS = 0.001 S = 1,000.0 μS = 1,000.0 micromhos ⇒ 1 S = 1,000.0 mS). - Microsiemens (micromho/gemmho) to Siemens [Water Purity Standard]: Multiply μS by
0.000001(1 μS = 1 micromho = 1 gemmho = 1.0 × 10-6 S ⇒ 1 S = 1,000,000.0 μS). - Kilosiemens to Siemens [Power Grid Admittance Standard]: Multiply kS by
1,000.0(1 kS = 1,000.0 S = 1.0 × 106 mS ⇒ 1 S = 0.001 kS). - Abmho to Siemens [CGS Electromagnetic Standard]: Multiply abmho by
1,000,000,000.0(1 abmho = 1.0 × 109 S = 1.0 Gigasiemens GS ⇒ 1 S = 1.0 × 10-9 abmho). - Statmho to Siemens [CGS Electrostatic Standard]: Multiply statmho by
1.112347052 × 10-12(1 statmho = 1.11235 × 10-12 S = 1.11235 Picosiemens pS ⇒ 1 S = 8.98755 × 1011 statmhos). - Quantized Hall Conductance (G0 = 2e2/h) to Siemens [Quantum Physics Standard]: Multiply G0 by
0.00003874045(1 Quantized Hall conductance unit = 2e2/h = 3.874045 × 10-5 S = 38.74045 μS = 38.74045 micromhos ⇒ 1 S = 25,812.807 G0).
Master Electric Conductance Conversion Table
The table below displays exact mathematical conversion relationships, SI Siemens (S) multipliers, and Microsiemens (μS) equivalents relative to 1 Siemens (1 S = 1.0 A/V = 1.0 Mho = 1,000 mS = 1,000,000 μS):
| Electric Conductance Unit Name | Symbol | Exact Value in Siemens (S) | mS, μS & Mho Equivalent | Domain & Technical Application Standard |
|---|---|---|---|---|
| 1 Siemens (Base SI Unit) | S, Ω-1 |
1.0 S (Base SI Unit) |
1,000.0 mS (1,000,000.0 μS / 1.0 Mho / 25,812.81 G0) |
SI Fundamental Derived Unit of Electric Conductance & Admittance |
| 1 Ampere per Volt | A/V |
1.0 S (Identical to Siemens) |
1,000.0 mS (1.0 S / 1,000,000.0 μS / 1.0 Mho) |
Direct Current to Voltage Flow Ratio Metric |
| 1 Mho | mho, ℧ |
1.0 S (Identical to Siemens) |
1,000.0 mS (1.0 S / 1,000,000.0 μS / 1.0 Mho) |
Traditional Engineering Conductance Unit (Lord Kelvin 1883) |
| 1 Millisiemens | mS |
0.001 S (10-3 S) |
1.0 mS (1,000.0 μS / 0.001 Mho / 25.8128 G0) |
MOSFET Transistor Transconductance (gm) Standard |
| 1 Microsiemens (Micromho / Gemmho) | μS, μmho |
1.0 × 10-6 S (10-6 S) |
0.001 mS (1.0 μmho / 1.0 gemmho / 0.025813 G0) | Water Quality Ionic Conductance & Electrochemical Sensors |
| 1 Quantized Hall Conductance (G0) | G0, 2e2/h |
3.874045 × 10-5 S |
0.03874 mS (38.74045 μS / 38.74045 micromhos) | Quantum Ballistic Point Contact Conductance Quantum |
| 1 Abmho | abmho |
1,000,000,000.0 S (109 S) |
1.0 × 1012 mS (1.0 × 109 Mhos / 2.58128 × 1013 G0) | CGS Electromagnetic System Conductance Unit |
| 1 Statmho | statmho |
1.11234705 × 10-12 S |
1.11235 × 10-6 μS (1.11235 pS / 2.87108 × 10-8 G0) | CGS Electrostatic System Conductance Unit |
Step-by-Step MOSFET Transconductance & Water Purity Conductance Calculation Example
To calculate the transconductance (gm) of an RF MOSFET transistor amplifier exhibiting a drain current change of 5.0 Milliamperes per 100 Millivolts gate-source change (ΔID = 5.0 mA, ΔVGS = 100 mV = 0.10 V), and calculate the electrical conductance of a pure laboratory water sample measuring 0.055 Microsiemens per centimeter (σ = 0.055 μS/cm = 5.5 × 10-8 S/cm) into Siemens (S), Millisiemens (mS), Mhos, and Quantized Conductance Units (G0):
Step 1 (MOSFET Transconductance Calculation): gm = ΔID ÷ ΔVGS = 0.005 A ÷ 0.10 V = 0.050 Siemens (0.050 S)
Step 2 (MOSFET Unit Conversions): gm = 0.050 S = 50.0 Millisiemens (50.0 mS) = 50,000.0 μS = 0.050 Mhos
Step 3 (MOSFET Quantized Conductance Conversion): G0_units = 0.050 S ÷ 0.00003874045 = 1,290.64 Quantum Units (1,290.64 G0)
Step 4 (Water Purity Micromho Conversion): 0.055 μS/cm = 0.055 Micromhos/cm = 0.055 Gemmhos/cm = 5.5 × 10-8 A/V per cm
Thus, the RF MOSFET exhibits a transconductance of 50.0 mS (50,000 μS = 1,290.64 G0), while the ultra-pure water conducts at 0.055 μS/cm (0.055 micromhos/cm).
Real-World Semiconductor, Water Purity & Power Benchmarks
Below is a comparative reference chart showing electric conductance values (G) across water, conductors, transistors, and quantum channels:
| Physical System / Electrolyte Solution | Electric Conductance in Siemens (S) | mS, μS & Mho Equivalent | Electrical Engineering & Physics Context |
|---|---|---|---|
| Deionized Ultra-Pure Laboratory Water (at 25°C) | 5.5 × 10-8 S/cm (0.000055 mS/cm) | 0.055 μS/cm (0.055 micromhos/cm = 0.055 gemmhos/cm) | Theoretical maximum purity limit for un-ionized water |
| Municipal Potable Drinking Tap Water | 1.0 × 10-4 – 1.0 × 10-3 S/cm (0.1 – 1.0 mS/cm) | 100.0 – 1,000.0 μS/cm (100 – 1,000 micromhos/cm) | Dissolved mineral salts ionic conductivity range |
| Seawater High-Salinity Electrolyte Solution | 0.050 S/cm (5.0 S/m) | 50.0 mS/cm (50,000.0 μS/cm = 0.050 Mhos/cm) | High ionic sodium chloride marine electrolyte conductivity |
| Quantum Ballistic Conductance Quantum (G0 = 2e2/h) | 3.874045 × 10-5 S | 0.03874 mS (38.74045 μS = 1.0 G0) | Single 1D ballistic electron channel quantum conductance |
| MOSFET Small-Signal Transconductance (gm) | 0.010 – 0.100 S (10 – 100 mS) | 10.0 – 100.0 mS (10,000 – 100,000 μS) | Integrated circuit transistor amplifier voltage gain factor |
| 1,000 Feet of 12 AWG Copper Building Wire (G = 1/R) | 0.62972 S | 629.72 mS (629,720.0 μS / 0.62972 Mho) | Loop conductance of 1,000 ft copper building wire |
History & Physics: 1866 Werner von Siemens & Lord Kelvin Mho vs 1988 Quantum Ballistic Conductance
1866 Ernst Werner von Siemens & Lord Kelvin’s Mho Unit
In 1860 and 1866, German inventor and industrialist Ernst Werner von Siemens proposed the mercury unit of resistance. In 1883, Scottish physicist William Thomson (Lord Kelvin) proposed the term mho (spelling “ohm” backwards) for electrical conductance. In 1971, the 14th General Conference on Weights and Measures (CGPM) officially adopted the Siemens (S) as the SI unit of electrical conductance, rendering “mho” an informal legacy engineering unit.
1988 Quantum Conductance Quantization (G0 = 2e2 ÷ h)
In 1988, Dutch physicists Bart van Wees and Henk van Houten discovered that electron flow through a 1D quantum point contact (nanowire or carbon nanotube) is quantized in discrete steps of G0 = 2e2 ÷ h = 38.74045 μS. This fundamental constant proves that microscopic 1D electron channels cannot conduct electricity continuously, but only in integer multiples of the quantum conductance step G0.
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Frequently Asked Questions (FAQ)
Is Siemens (S) equal to Mho (mho)?
Yes! 1 Siemens (S) is 100% mathematically equal to 1 Mho (mho) and 1 Ampere per Volt (A/V). “Mho” is simply an informal traditional term created by Lord Kelvin by spelling “ohm” backwards.
How do you convert Microsiemens (μS) to Millisiemens (mS)?
To convert μS to mS, divide μS by 1,000. For example, 2,500 μS ÷ 1,000 = 2.50 Millisiemens (2.50 mS).
What is a Gemmho or Micromho?
1 Micromho and 1 Gemmho are traditional engineering units equal to exactly 1 Microsiemens (1.0 μS = 1.0 × 10-6 S), commonly used in water quality and soil salinity testing.
What is Quantized Hall Conductance (G0)?
Quantized Hall Conductance is the fundamental quantum step of conductance for a single 1D ballistic electron channel: G0 = 2e2 ÷ h = 3.874045 × 10-5 S = 38.74045 μS (the inverse of 25,812.807 Ω divided by 2).