Statmhos to Mhos Converter

How to Convert Statmhos to Mhos

To convert an electrical conductance measurement from statmhos to mhos, divide the conductance value by the conversion factor. Since one statmho is equal to 1.1123 × 10^-12 mhos, you can use this formula:

The conductance in mhos is equal to the statmhos divided by 8.99 × 10¹¹.

How Many Mhos Are in a Statmho?

There are 1.1123 × 10^-12 mhos in one statmho.

What Is a Statmho?

The statmho (symbol: st℧), also called the statsiemens, is a unit of electrical conductance in the centimetre–gram–second electrostatic system of units (CGS-ESU). It is the reciprocal of the statohm, the CGS-ESU unit of electrical resistance. One statmho is an extremely small amount of conductance. It equals approximately 1.112 × 10⁻¹² siemens (about 1.112 picosiemens). Conversely, one siemens equals approximately 8.99 × 10¹¹ statmhos. The conversion factor between statmhos and siemens involves the speed of light in vacuum (c ≈ 2.998 × 10¹⁰ cm/s), reflecting the fundamental connection between electric and magnetic quantities in the CGS system. Specifically, 1 siemens = c²/10⁹ statmhos, where c is the speed of light in CGS units. The statmho is primarily of theoretical and historical interest. It appears in older physics literature that uses Gaussian or CGS-ESU units, particularly in classical electrodynamics and theoretical physics. Modern engineering and applied physics use SI units (siemens) exclusively for conductance measurements.

One statmho is equal to:

• ≈ 1.112 × 10⁻¹² siemens (S)
• ≈ 1.112 × 10⁻⁹ millisiemens (mS)
• ≈ 1.112 × 10⁻⁶ microsiemens (μS)
• ≈ 1.112 × 10⁻¹⁵ kilosiemens (kS)
• ≈ 1.112 × 10⁻¹⁸ megasiemens (MS)
• ≈ 1.112 × 10⁻¹² mhos (℧)
• ≈ 1.112 × 10⁻⁶ micromhos (μ℧)
• ≈ 1.112 × 10⁻²¹ abmhos (ab℧)

What Is a Mho?

The mho (symbol: ℧, an inverted omega) is a unit of electrical conductance equal to the reciprocal of the ohm. The name "mho" is simply "ohm" spelled backwards, reflecting that conductance is the inverse of resistance. The mho was the standard unit of electrical conductance before the 14th General Conference on Weights and Measures (CGPM) adopted the name "siemens" in 1971. One mho is exactly equal to one siemens; only the name changed, not the value. Despite the official adoption of the siemens, the term "mho" remains in widespread use, particularly in the United States and in older technical literature. Many practicing electrical engineers, especially those educated before the 1970s, continue to use "mho" in everyday work. The inverted omega symbol (℧) is still used on some instruments and in circuit analysis textbooks. In power systems engineering, the mho relay (distance relay) is a fundamental protective device used to detect faults on transmission lines. The name comes from the relay's operating characteristic on the impedance diagram, which appears as a circle in mho (conductance) coordinates. These relays remain a critical component of power grid protection.

One mho is equal to:

• 1 siemens (S)
• 1,000 millisiemens (mS)
• 1,000,000 microsiemens (μS)
• 0.001 kilosiemens (kS)
• 0.000001 megasiemens (MS)
• 1,000,000 micromhos (μ℧)
• 10⁻⁹ abmhos (ab℧)
• ≈ 899,000,000,227 statmhos (st℧)

Understanding Electrical Conductance

Electrical conductance is a measure of how easily electric current flows through a material or component. It is the reciprocal of electrical resistance: a component with high conductance allows current to flow easily (low resistance), while one with low conductance impedes current flow (high resistance).

The SI unit of conductance is the siemens (S), defined as one ampere per volt (A/V). The siemens replaced the older unit name "mho" (ohm spelled backwards) in 1971, though both names represent the same quantity. Conductance G is related to resistance R by the simple equation: G = 1/R.

Conductance depends on the material's conductivity (σ), the cross-sectional area (A) of the conductor, and its length (L): G = σA/L. Materials with high conductivity, such as copper and silver, are used as electrical conductors, while materials with low conductivity, such as rubber and glass, are used as insulators.

Measurement Systems

Three main unit systems are used for electrical conductance:

• SI (International System): Uses the siemens and its metric prefixes (μS, mS, kS, MS). This is the modern standard used worldwide in science and engineering.
• MKS/Practical: Uses the mho and micromho, which are older names for the siemens and microsiemens. These units are still commonly encountered, especially in American engineering practice.
• CGS-EMU (Electromagnetic): Uses the abmho (= 10⁹ S), a very large unit from the electromagnetic CGS system.
• CGS-ESU (Electrostatic): Uses the statmho (≈ 1.112 × 10⁻¹² S), a very small unit from the electrostatic CGS system.

Conductance vs. Conductivity

It is important to distinguish between conductance and conductivity:

• Conductance (G): A property of a specific component or sample, measured in siemens (S). It depends on the material, geometry, and temperature.
• Conductivity (σ): An intrinsic property of a material, measured in siemens per metre (S/m). It is independent of the sample's size or shape.

For a uniform conductor, conductance is related to conductivity by: G = σ × A / L, where A is the cross-sectional area and L is the length.

Practical Applications

• Water quality testing: Conductivity in μS/cm or mS/cm indicates dissolved mineral content and water purity
• Electronics: Component conductance in siemens or millisiemens is used in circuit analysis and design
• Power systems: Admittance (complex conductance) in siemens is used for power flow analysis and fault calculations
• Materials science: Metal conductivity in MS/m characterizes how well materials conduct electricity
• Soil science: Electrical conductivity in mS/cm assesses soil salinity for agriculture
• Medical diagnostics: Bioimpedance measurements use conductance to estimate body composition

Tips for Electrical Conductance Conversions

• For SI prefix conversions (S, mS, μS, kS, MS), each step is a factor of 1,000. Moving from a larger unit to a smaller one means multiplying by 1,000 for each prefix step.
• The siemens and the mho are exactly equal (1 S = 1 ℧). Similarly, the microsiemens and micromho are exactly equal (1 μS = 1 μ℧). These are just different names for the same units.
• The abmho is an extremely large unit: 1 ab℧ = 10⁹ S = 1 gigasiemens. Most practical conductance values are a tiny fraction of an abmho.
• The statmho is an extremely small unit: 1 st℧ ≈ 1.112 × 10⁻¹² S ≈ 1.112 picosiemens. Most practical conductance values are billions of statmhos.
• CGS units (abmhos, statmhos) are rarely used in modern practice. If you encounter them in older literature, use the conversion factors: 1 ab℧ = 10⁹ S and 1 S ≈ 8.99 × 10¹¹ st℧.
• To convert conductance to resistance, take the reciprocal: R (ohms) = 1 / G (siemens). For example, 0.5 S = 1/0.5 = 2 Ω.
• Water conductivity is typically expressed in μS/cm or mS/cm. To convert between them: 1 mS/cm = 1,000 μS/cm. Pure water has about 0.055 μS/cm, while seawater has about 50,000 μS/cm (50 mS/cm).

Statmhos to Mhos Conversion Table

The following table shows conversions from statmhos to mhos.

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