Electrical Units Demystified:

Volts, Ohms, Watts, and Their SI Relationships

Article By Global Instruments

Why Electrical Units Feel Different From Other SI Units

Most people encounter the units of length, mass, and time early in life and build an intuitive feel for them. A meter is roughly a stride. A kilogram is roughly a bag of sugar. A second is roughly a heartbeat.

Electrical units offer no such intuitive anchor. Nobody has ever directly felt a volt, held an ohm, or seen a coulomb, and this absence of everyday sensory reference is a major reason electrical units remain confusing well past the point where students have mastered mechanics.

Yet electrical units are among the most rigorously and elegantly defined quantities in the entire SI system. Since the 2019 redefinition of the SI base units, the ampere — the base unit of electric current — is now defined by fixing the exact numerical value of the elementary charge, tying electrical measurement directly to a fundamental constant of nature rather than to a physical artifact or a fixed macroscopic experiment. Everything else in electrical science — volts, ohms, watts, farads, henries — is built from this single base unit in combination with the mechanical base units of mass, length, and time.

This article works through the core electrical units, how they relate to one another through Ohm's Law and the definitions of electrical power and energy, and where the practical confusion tends to arise for students, technicians, and working engineers.

The Ampere: Where Electrical Units Begin

The ampere (A) is the SI base unit of electric current, and it is the only base unit among the seven that is specifically electrical. Before 2019, the ampere was defined through a somewhat impractical thought experiment involving the force between two infinitely long, infinitely thin parallel wires carrying current one meter apart. Since the 2019 redefinition, the ampere is defined by fixing the elementary charge e at exactly 1.602176634 × 10⁻¹⁹ coulombs, which makes current traceable directly to a count of moving charge rather than to a mechanical force experiment.

Practically, one ampere represents a flow of roughly 6.242 × 10¹⁸ elementary charges per second past a given point in a circuit. This is an enormous number, which is part of why current feels abstract — a single ampere, a very ordinary household-scale current, represents an almost unimaginable number of individual charge carriers in motion.

The Volt: Electrical Potential Difference

The volt (V) measures electric potential difference, or what is colloquially called "voltage" — the energy available to move a unit of charge between two points in a circuit. Formally, one volt is defined as the potential difference that will impart one joule of energy to one coulomb of charge:

1 V = 1 J/C

Because the coulomb itself is defined as the amount of charge transported by one ampere of current flowing for one second (1 C = 1 A·s), the volt can also be expressed in base SI units as:

1 V = 1 kg·m²/(A·s³)

This expression looks intimidating, but it simply reflects the fact that voltage is fundamentally a statement about energy per unit charge, and energy itself decomposes into mass, length, and time through the definition of the joule.

A useful mental model, borrowed from hydraulics, treats voltage as analogous to water pressure in a pipe — it represents the "push" available to drive charge through a circuit, independent of how much charge is actually flowing.

The Ohm: Electrical Resistance

The ohm (Ω), named after Georg Simon Ohm, measures electrical resistance — the opposition a material or component presents to the flow of current. The ohm is defined through Ohm's Law itself, one of the most widely used relationships in all of applied science:

V = I × R, therefore 1 Ω = 1 V/A

Ohm's Law states that the voltage across a resistive element equals the current flowing through it multiplied by its resistance. Rearranged, this single equation allows any one of voltage, current, or resistance to be calculated if the other two are known, and it forms the foundation of nearly all basic circuit analysis.

In base SI units, the ohm expands to:

1 Ω = 1 kg·m²/(A²·s³)

Resistance is a property of materials and geometry — a longer, thinner wire has more resistance than a short, thick one of the same material, and different materials (copper versus nichrome, for instance) have intrinsically different resistivities. This distinction between resistance (a property of a specific object) and resistivity (an intrinsic material property, measured in ohm-meters) is a common point of confusion for students moving from introductory circuits into materials science.

The Watt: Electrical Power

The watt (W) is the SI unit of power — the rate at which energy is transferred or converted — and it applies equally to mechanical, thermal, and electrical systems. In an electrical context, power is calculated as the product of voltage and current:

P = V × I, therefore 1 W = 1 V × 1 A

Combining this with Ohm's Law produces two additional, equally useful power formulas that electrical engineers use constantly depending on which two quantities are known:

P = I²R (power in terms of current and resistance) P = V²/R (power in terms of voltage and resistance)

In base SI units, the watt expands to:

1 W = 1 kg·m²/s³

This is identical to the mechanical definition of the watt (one joule per second), which is precisely the point of SI coherence — electrical power and mechanical power are the same physical quantity, measured in the same unit, regardless of which domain produced them. A 100-watt light bulb and a 100-watt mechanical motor are drawing on the identical underlying physical concept of energy transfer rate.

The Coulomb, the Farad, and the Henry: Supporting Cast

Three additional electrical units round out the core vocabulary needed for circuit analysis.

The coulomb (C) is the SI unit of electric charge, defined as the charge transported by a current of one ampere flowing for one second (1 C = 1 A·s). It is a large unit in practical terms — a typical AA battery might deliver only a few thousand coulombs over its entire lifetime, and static electricity discharges typically involve only a tiny fraction of a coulomb.

The farad (F) measures capacitance, the ability of a component to store electrical charge per unit of voltage: 1 F = 1 C/V. A farad is an enormous unit for most practical electronic components, which is why capacitors are usually rated in microfarads (µF), nanofarads (nF), or picofarads (pF).

The henry (H) measures inductance, the property of a coil or circuit that opposes changes in current flow: 1 H = 1 V·s/A. Like the farad, the henry is often too large for everyday electronic components, which are commonly rated in millihenries (mH) or microhenries (µH).

Electrical Energy: Joules and Kilowatt-Hours

While the watt measures the rate of energy transfer, actual electrical energy consumption is measured in joules when working within pure SI, or, far more commonly in commercial and household contexts, in kilowatt-hours (kWh). A kilowatt-hour represents the energy consumed by a one-kilowatt load operating continuously for one hour:

1 kWh = 1000 W × 3600 s = 3,600,000 J (3.6 MJ)

This is the unit that appears on virtually every household electricity bill worldwide, precisely because the joule is inconveniently small for describing household-scale energy consumption over meaningful time periods — a typical household might use tens of kilowatt-hours per day, which would translate to tens of millions of joules, an unwieldy number for a monthly bill.

Relationship Table: The Core Electrical Units

Quantity	Symbol	SI Unit	Defining Relationship	Base SI Units
Current	I	Ampere (A)	Base unit (fixed via elementary charge)	A
Charge	Q	Coulomb (C)	Q = I × t	A·s
Voltage	V	Volt (V)	V = W/Q (energy per charge)	kg·m²/(A·s³)
Resistance	R	Ohm (Ω)	R = V/I	kg·m²/(A²·s³)
Power	P	Watt (W)	P = V × I	kg·m²/s³
Capacitance	C	Farad (F)	C = Q/V	A²·s⁴/(kg·m²)
Inductance	L	Henry (H)	L = V·s/A	kg·m²/(A²·s²)
Energy	E	Joule (J)	E = P × t	kg·m²/s²

Common Sources of Practical Confusion

A handful of recurring misunderstandings account for most of the practical confusion around electrical units.

The first is confusing power (watts) with energy (joules or kilowatt-hours). Power is an instantaneous rate; energy is the accumulated total over time. A device rated at 1000 watts does not "use 1000 watts" over the course of a day — it uses 1000 watts of power whenever it is switched on, and the total energy consumed depends on how long it runs.

The second is confusing AC and DC voltage and current values, particularly the distinction between peak voltage and root-mean-square (RMS) voltage in alternating current systems. Household AC voltage figures — 230 V in most of the world, 120 V in North America — refer to RMS values, not peak values, and the actual peak voltage of an AC waveform is higher by a factor of √2.

The third is the casual conflation of resistance and impedance. Resistance, measured in ohms, applies straightforwardly to direct current and purely resistive components. Impedance, also measured in ohms but properly represented as a complex quantity with both magnitude and phase, is needed to correctly describe how alternating current interacts with capacitors and inductors, which introduce frequency-dependent and phase-shifting behavior that simple resistance cannot capture.

Conclusion

Electrical units form one of the most internally consistent and mathematically elegant corners of the SI system, built from a single base unit — the ampere — combined systematically with the mechanical units of mass, length, and time. The volt, ohm, and watt are bound together by Ohm's Law and the definition of power in a way that makes any two of the three quantities sufficient to calculate the third. Despite lacking the intuitive, everyday reference points of mechanical units, electrical quantities reward the effort of careful study: once the underlying relationships between charge, potential difference, resistance, and power are internalized, the entire vocabulary of electrical engineering — from household wiring to microelectronics — becomes a matter of applying a small number of consistent, well-defined rules.

Units of Force, Energy, and Pressure: