Electrical Conductance Unit Converter

How to use this calculator

Two ways to use it.

Convert a conductance value directly — Enter a number in the conductance field, pick From and To units, hit Calculate. 1 S converts to 1,000 mS. 500 µS converts to 0.5 mS. Standard unit conversion.

Convert from resistance — Enter a resistance in ohms in the optional field and leave the conductance field blank. The calculator computes G = 1/R and shows the result in all conductance units. A 100 Ω resistor has 10 mS of conductance. A 4.7 kΩ resistor (4,700 Ω) has 0.213 mS or 212.8 µS.

The output panel always shows three values: siemens, millisiemens, and equivalent resistance in ohms. So whatever you enter, you get the resistance cross-reference without an extra step.

The conversion formula

Conductance unit conversion is the same as every metric electrical unit: powers of 1,000.

1 siemens = 1,000 millisiemens 1 millisiemens = 1,000 microsiemens 1 siemens = 1,000,000 microsiemens

And the resistance relationship:

Or flipped: R = 1/G. A 2 mS conductance is 1/0.002 = 500 Ω.

The mho (℧) is exactly equal to the siemens. 1 mho = 1 S, no conversion factor needed. It’s an older unit (it’s “ohm” spelled backwards, which tells you something about how electrical engineers named things in the 19th century), and it still shows up in older textbooks and some US-published reference materials. Modern standards use siemens. The converter includes mho because you’ll encounter it when reading older datasheets and academic papers.

Full unit reference table

The equivalent resistance column is worth reading carefully. 1 µS corresponds to 1 MΩ. That’s the conductance of a good insulator, not a conductor. Water purity is measured in microsiemens per centimeter: ultrapure water is about 0.055 µS/cm, tap water is typically 50–500 µS/cm, and seawater is around 50,000 µS/cm (50 mS/cm).

Common conversions at a glance

And the resistance-to-conductance conversions that come up most in practice:

This table is more useful than the unit conversion table for most electronics work. If you know the resistance, you can read the conductance directly without computing 1/R.

The conductance vs resistance relationship

The tool’s subtitle says it: “high conductance = low resistance.” That’s the whole inverse relationship in one sentence.

But the shape of that relationship is nonlinear, and it matters.

Going from 10 Ω to 100 Ω (a factor of 10 increase in resistance) drops conductance from 100 mS to 10 mS, also a factor of 10. That part is linear in log space.

But going from 10 Ω to 20 Ω (doubling resistance) cuts conductance from 100 mS to 50 mS, exactly half. And going from 1,000 Ω to 2,000 Ω (also doubling) cuts conductance from 1 mS to 0.5 mS, also exactly half.

The percentage change in conductance always mirrors the percentage change in resistance, just inverted. This is worth knowing when you’re thinking about parallel resistor networks, where conductances add directly.

Why conductance exists as a unit at all

If you can always just use resistance, why does conductance need its own unit?

Two reasons.

Parallel circuits. Resistances in parallel combine as: 1/Rtotal = 1/R1 + 1/R2 + 1/R3… Conductances in parallel just add: Gtotal = G1 + G2 + G3. Two 1 mS conductances in parallel give 2 mS total. Much cleaner. Network analysis of complex circuits with many parallel branches is significantly easier in admittance (conductance + susceptance) than in impedance (resistance + reactance).

Transistor specifications. Transconductance (gm) is one of the most important transistor parameters. It describes how much the output current changes per unit change in input voltage: gm = ΔId / ΔVgs. The unit is siemens (or amps per volt, which is dimensionally identical to siemens). A MOSFET with gm = 50 mS changes its drain current by 50 mA for every 1V change in gate voltage. This parameter lives naturally in siemens because it’s a conductance, not a resistance.

Trying to express transistor transconductance in ohms would be awkward. The siemens unit fits the physics.

Real-world examples

Transistor transconductance

A 2N7002 N-channel MOSFET has a typical transconductance of about 100 mS at 100 mA drain current.

Water conductivity measurement

A water quality sensor reports conductivity in µS/cm. Tap water in a typical city measures around 200 µS/cm. The lab needs the value in mS/cm for a datasheet comparison.

Insulation resistance expressed as conductance

A cable test gives insulation resistance of 500 MΩ. Some test equipment also reports this as conductance. What’s the conductance?

Parallel resistor network

A circuit has three resistors in parallel: 1 kΩ, 2.2 kΩ, and 4.7 kΩ. What’s the total resistance?

Using resistance: 1/Rtotal = 1/1000 + 1/2200 + 1/4700 = 0.001 + 0.000455 + 0.000213 = 0.001668… Rtotal = 1/0.001668 = 599.5 Ω.

Using conductance:

Op-amp feedback network

An inverting op-amp configuration uses a 10 kΩ input resistor (R1) and a 100 kΩ feedback resistor (Rf). Gain = -Rf/R1 = -10.

The input impedance the source sees is approximately R1 = 10 kΩ. The conductance the source drives is:

Admittance: conductance’s AC equivalent

Conductance is the DC (or resistive) component of admittance. Admittance (Y) is to impedance (Z) what conductance is to resistance: the reciprocal.

Y = 1/Z

And just as impedance has a real part (resistance) and an imaginary part (reactance), admittance has:

• Conductance (G): the real part, in siemens
• Susceptance (B): the imaginary part, also in siemens

Susceptance comes from capacitors (positive susceptance) and inductors (negative susceptance). A capacitor with susceptance Bc = ωC, where ω = 2πf. An inductor with susceptance BL = -1/(ωL).

For parallel circuits, admittances add directly: Ytotal = Y1 + Y2 + Y3. This is the same reason conductances add in parallel (it’s the same principle, extended to AC).

The siemens unit covers all of admittance, not just conductance. When an RF engineer specifies a network element in mS or µS without saying whether it’s conductance or susceptance, context usually makes it clear, but the unit is the same regardless.

Where conductance units appear in datasheets

Most electronics datasheets don’t use “conductance” as a column header. The unit siemens (or mS or µS) shows up under different parameter names depending on the component type.

The transconductance and output conductance rows are the ones you’ll see most often in MOSFET datasheets. gm in mS is the amplification potential of the device. gds in µS tells you how close the output is to an ideal current source (lower gds = better current source = higher intrinsic voltage gain).

A MOSFET with gm = 200 mS and gds = 200 µS has an intrinsic gain of gm/gds = 200/0.2 = 1,000 (or about 60 dB). Getting to that number requires converting gds from µS to mS first: 200 µS = 0.2 mS. Then the ratio is clean.

The mho: same unit, different name

The mho (℧) is 1 siemens. The name came first, coined by Lord Kelvin in the 1880s. The siemens was adopted as the official SI unit in 1971, named after Werner von Siemens. Many US textbooks and standards documents published before the 1980s use mho. Some published after that still do.

You’ll see mho in:

• Pre-1980 electronics textbooks (Millman, Halkias, Terman)
• Some IEEE and ANSI standards (particularly older ones)
• Ham radio literature
• Certain US military and government specifications

The converter includes mho for exactly this reason: if you’re reading a 1960s transistor circuit analysis and the transconductance is given in “millimhos,” that’s millisiemens. 20 millimhos = 20 mS = 0.02 S.

One source of confusion: “millimho” looks like it might be a weird compound unit, but it’s just milli + mho = 10⁻³ mho = 10⁻³ S = 1 mS.

Common mistakes

Confusing transconductance with conductance. Transconductance (gm) is in siemens, but it relates two different quantities (output current to input voltage). Conductance (G) is 1/R and relates voltage to current in the same branch. Both use siemens; they’re not the same thing.

Forgetting to invert when switching between resistance and conductance. A 10 kΩ resistor is 0.1 mS. A 100 kΩ resistor is 0.01 mS. Going from 10 kΩ to 100 kΩ (10× larger resistance) gives 10× smaller conductance (0.1 mS to 0.01 mS). The relationship is inverse, so the direction of “larger” flips. Getting this wrong means your parallel network calculation comes out backwards.

Using conductance when the circuit is series, not parallel. Conductances add for parallel circuits. For series circuits, resistances add: Rtotal = R1 + R2 + R3. If you accidentally add conductances for a series circuit, you get a result that’s too low (higher conductance = lower resistance = smaller total resistance than the individual resistors, which is wrong for series).

Treating mho as a different unit magnitude. 1 mho = 1 siemens, exactly. There’s no conversion factor. A 1950s paper quoting “0.5 mho” means the same thing as a modern datasheet quoting “0.5 S.” The only conversion needed is if prefixes are involved: “500 millimhos” = 500 mS = 0.5 S.

The bottom line

Conductance unit conversions are powers of 1,000, same as resistance, voltage, and inductance. S to mS: multiply by 1,000. mS to µS: multiply by 1,000. Going the other direction, divide.

The extra layer conductance has: G = 1/R. Enter a resistance and the calculator finds conductance for you. Enter conductance and it gives you equivalent resistance. The output panel shows both so you’re not mentally computing 1/R while staring at a number in siemens.

The places where siemens actually matters rather than ohms: parallel circuit analysis (conductances add), MOSFET datasheets (transconductance and output conductance), water quality measurement, and anything old enough to use the word “mho.”