Electrical Units

The SI units used for current, voltage, resistance, power, charge and energy, how each is built from the others, and the non-SI units such as kWh, VA and dBm that appear on bills, nameplates and datasheets.

SI electrical units

The ampere is one of the seven SI base units. Since 2019 it is defined by fixing the elementary charge at exactly e = 1.602 176 634 × 10⁻¹⁹ C, so one ampere is one coulomb of charge passing per second. The other electrical units are derived units with special names, each expressible through the ampere and the mechanical units.

SI electrical units with symbols and relations to other SI units
UnitSymbolQuantityIn other SI unitsIn base units
ampereAelectric currentC/sA (base unit)
coulombCelectric chargeA·sA·s
voltVelectric potential difference (voltage)W/Akg·m²·s⁻³·A⁻¹
ohmΩelectric resistanceV/Akg·m²·s⁻³·A⁻²
siemensSelectric conductanceA/V = 1/Ωkg⁻¹·m⁻²·s³·A²
wattWpowerJ/s = V·Akg·m²·s⁻³
jouleJenergy, workN·m = W·skg·m²·s⁻²
faradFcapacitanceC/Vkg⁻¹·m⁻²·s⁴·A²
henryHinductanceWb/A = V·s/Akg·m²·s⁻²·A⁻²
weberWbmagnetic fluxV·skg·m²·s⁻²·A⁻¹
teslaTmagnetic flux densityWb/m²kg·s⁻²·A⁻¹
hertzHzfrequency1/ss⁻¹

Sources: BIPM: The International System of Units (SI Brochure), 9th edition; NIST: SI Units

Units used alongside the SI

Several units that are not SI units with special names are standard in electrical work. The kilowatt-hour is a unit of energy equal to one kilowatt sustained for one hour. The volt-ampere is the product of RMS voltage and RMS current and is used for apparent power; the SI Brochure lists the var as a special name for the volt ampere when it expresses reactive power.

Common electrical units that are multiples, products or special names of SI units
UnitSymbolUsed forValue in SI unitsStatus
kilowattkWpower1 kW = 1000 WSI prefix + SI unit
watt-hourWhenergy1 Wh = 3600 Jnon-SI (product of W and h)
kilowatt-hourkWhenergy (utility billing)1 kWh = 3.6 × 10⁶ J = 3.6 MJnon-SI
volt-ampereVAapparent power S = V·I1 VA = 1 V × 1 Acoherent SI unit V·A
kilovolt-amperekVAapparent power (transformers, generators)1 kVA = 1000 VASI prefix + V·A
varvarreactive power Q1 var = 1 V·Aspecial name listed in the SI Brochure, Table 8
ampere-hourAhbattery charge capacity1 Ah = 3600 Cnon-SI (product of A and h)
electronvolteVenergy of particles1 eV = 1.602176634 × 10⁻¹⁹ J (exact)non-SI, listed in the SI Brochure, Table 8

Sources: BIPM: The International System of Units (SI Brochure), 9th edition

Decibels: dB, dBm and dBW

The bel and decibel express logarithmic ratios (1 dB = 0.1 B). For a power-like quantity the level is L = 10 log₁₀(P/P₀) dB, and the reference P₀ must always be stated. dBW uses P₀ = 1 W, so L = 10 log₁₀(P/1 W). dBm uses P₀ = 1 mW, so L = 10 log₁₀(P/1 mW), which makes dBm = dBW + 30.

For amplitude quantities such as voltage across the same impedance, power scales with the square of amplitude, so the level becomes 20 log₁₀(V/V₀) dB. Every 3 dB is very nearly a doubling of power and every 10 dB is exactly a factor of 10.

Power levels in dBm and dBW (computed from 10 log₁₀ of the ratio)
PowerdBmdBW
1 µW−30−60
10 µW−20−50
100 µW−10−40
1 mW0−30
10 mW+10−20
100 mW+20−10
500 mW+26.99−3.01
1 W+300
2 W+33.01+3.01
10 W+40+10
100 W+50+20
1 kW+60+30

Sources: BIPM: The International System of Units (SI Brochure), 9th edition

References

Frequently asked questions

Is the kilowatt-hour an SI unit?

No. The SI unit of energy is the joule. The kilowatt-hour is a widely used non-SI unit equal to exactly 3.6 megajoules (1000 W × 3600 s).

What is the difference between kW and kVA?

kW measures real power, the rate at which energy is actually delivered. kVA measures apparent power, RMS volts times RMS amps. They are equal only when the power factor is 1; otherwise kW = kVA × power factor.

What does 0 dBm mean?

0 dBm is a power of exactly 1 milliwatt, because 10 log₁₀(1 mW / 1 mW) = 0. Positive values are above 1 mW and negative values below it; 30 dBm is 1 W.