Unit

Use the unit calculator

The embedded calculator converts between voltage (V), current (A), power (W / kW), and resistance (Ω) — the four units engineers convert between most often. Switch to the 3-phase tab for kVA / kW / kVAR conversions on three-phase systems.

Unit formulas

The per-unit system normalises every quantity in a power network — voltages, currents, impedances, powers — to a fraction of a chosen base. Transformer impedances stated in per-unit (typically 5–8 %) stay constant when referred across the transformer turns ratio; in actual ohms they would change by the square of the turns ratio. This is what makes large-network analysis tractable.

Standards: SI, IEC 60027, IEEE

Three standards govern unit usage in electrical engineering:

• SI (International System of Units) — maintained by BIPM (Bureau International des Poids et Mesures). The 2019 SI redefinition fixed seven base units to seven exact-valued natural constants: caesium hyperfine frequency for the second, speed of light for the metre, Planck constant for the kilogram, elementary charge for the ampere, Boltzmann constant for the kelvin, Avogadro constant for the mole, and luminous efficacy for the candela. Every other unit (W, V, Ω, kVA, J, Hz) derives from these.
• IEC 60027 — Letter symbols to be used in electrical technology. Defines symbol conventions: V (italic) for the variable voltage vs V (roman) for the unit volt, I for current vs A for ampere, Z for impedance vs Ω for ohm. Internationally accepted notation for engineering documents.
• IEEE Std 945 — Recommended Practice for Preferred Metric Units. Tables of preferred unit prefixes and rounding conventions for the US engineering community.

Reference: SI prefixes for electrical units

The complete set of SI prefixes used with W, V, A, Ω, J, Hz. Every prefix is a power of ten; never mix prefixes within a calculation.

SI prefix usage rules: capitalise prefix symbol if multiplier is ≥10⁶ (M, G, T) but lowercase if ≤10³ (k, m, µ, n, p). The unit symbol always keeps its case (W, A, V are roman uppercase; Ω is uppercase Greek; Hz is mixed). Do not stack prefixes (no µkW); pick one.

How to choose and convert between units, step by step

1. Identify the physical quantity. Power → watts (W). Apparent power → volt-amperes (VA / kVA). Reactive power → volt-amperes reactive (VAR / kVAR). Impedance → ohms (Ω). Voltage → volts (V). Current → amperes (A). Frequency → hertz (Hz). Energy → joules (J) or watt-hours (Wh, kWh).
2. Pick the correct SI prefix. W for sensors and small electronics. kW (10³ W) for appliances and motors. MW (10⁶ W) for industrial plants and substations. GW (10⁹ W) for utility generation. Same logic for energy: Wh, kWh, MWh, GWh, TWh.
3. Convert when crossing standards. BTU/h ↔ W (1 BTU/h ≈ 0.293 W; 12 000 BTU/h = 1 ton ≈ 3.5 kW). HP ↔ W (1 hp ≈ 745.7 W). cal ↔ J (1 cal = 4.184 J). The unit conversion is dimensional — never multiply quantities of different units.
4. For per-unit analysis, pick base values first. Pick a base power (e.g. S_base = 100 MVA) and a base voltage (V_base) at one bus. From these, base current and base impedance follow: I_base = S_base / (√3·V_base) and Z_base = V_base² / S_base. Every actual quantity divided by its base gives a per-unit value.
5. Reference values back to ratings. Transformer % impedance is a per-unit value: 5.75 % means Z_actual = 0.0575 × Z_base. Generator reactance X_d″ is per-unit on the machine's own MVA base. To use across systems, refer to a common system base.
6. Verify dimensional consistency. Both sides of every equation must have the same units. P (watts) = V (volts) × I (amperes) — units balance because 1 V × 1 A = 1 W = 1 J/s = 1 kg·m²/s³. If the units do not balance, the formula is wrong before any number can be computed.

Worked example: per-unit short-circuit calculation

A 100 MVA, 230 kV / 13.8 kV, 8 % impedance transformer feeds a bus. Choose system base S_base = 100 MVA, V_base = 13.8 kV at the secondary. Compute base values and find the secondary fault current at the bus.

Both methods give the same answer; per-unit is dramatically faster when the network has many transformers, because impedances stay numerically constant across the turns ratio. The 52 kA fault current sets the AIC requirement for downstream switchgear — every breaker on the bus must be rated for at least 65 kA AIC (next standard above 52.3).

SI vs Imperial vs CGS unit systems

Three measurement systems coexist in engineering. The SI is the international standard; imperial and CGS persist in specific industries.

Modern engineering uses SI almost exclusively, with limited holdouts: HVAC sizing in BTU/h (US), motor power in HP (US), aviation altitude in feet. Always convert imperial values to SI before mixing with formulas — every modern textbook and standard is SI.

Variants and edge cases

SI unit of frequency, heat, and charge

Common follow-up "what is the SI unit of X" questions: frequency → hertz (Hz) = 1/s. Heat (energy) → joule (J). Heat flow rate → watt (W). Electric charge → coulomb (C) = A·s. Capacitance → farad (F) = C/V. Inductance → henry (H) = Wb/A. Magnetic flux → weber (Wb). Magnetic flux density → tesla (T). All derived from the SI seven base units.

The 2019 SI redefinition

From May 2019 the seven SI base units are defined entirely from natural constants. The kilogram is now realised through the Kibble (watt) balance using a fixed Planck constant; the ampere through fixed elementary charge e = 1.602 176 634 × 10⁻¹⁹ C. No physical artefact is required. This guarantees that the units are reproducible to better than 10⁻⁸ in any laboratory worldwide.

Per-unit base changes

When combining equipment with different MVA bases, convert each impedance to the system base: Z_new = Z_old × (S_new / S_old). A generator with X_d″ = 0.20 pu on its 50 MVA rating becomes 0.20 × (100 / 50) = 0.40 pu on the 100 MVA system base. Skipping this conversion is the most common per-unit error.

Trip-unit nomenclature confusion

"AC Pro trip unit" (Eaton brand), "MicroLogic trip unit" (Schneider), "Cubicle Bus trip unit" (ABB) — all are electronic modules inside a circuit breaker that contain the protection logic. The "unit" here is a hardware sub-assembly, not a unit of measurement. Don\'t confuse trip-unit settings (multipliers on a current rating) with per-unit values (dimensionless ratios).

The 2019 SI redefinition

The International System of Units, the SI, is the system of units in which the unperturbed ground-state hyperfine transition frequency of the caesium-133 atom Δν_Cs is 9 192 631 770 Hz, the speed of light in vacuum c is 299 792 458 m/s, the Planck constant h is 6.626 070 15 × 10⁻³⁴ J·s, the elementary charge e is 1.602 176 634 × 10⁻¹⁹ C, the Boltzmann constant k is 1.380 649 × 10⁻²³ J/K, the Avogadro constant N_A is 6.022 140 76 × 10²³ mol⁻¹, and the luminous efficacy of monochromatic radiation of frequency 540 × 10¹² Hz, K_cd, is 683 lm/W.

Related concepts on this site

Frequently asked questions

What is the SI unit of frequency?

The SI unit of frequency is the hertz (Hz), defined as one cycle per second. So 60 Hz = 60 cycles per second (the North American AC line frequency); 50 Hz is the European / Australian standard. The unit is named after Heinrich Hertz, who first demonstrated electromagnetic waves in the 1880s. In SI base units, 1 Hz = 1 / s (inverse seconds). The 2019 SI redefinition fixed the second by the caesium-133 hyperfine transition at exactly 9 192 631 770 Hz, giving an absolute reference for every other frequency.

What is the W unit?

The W unit is the watt — the SI unit of power. One W = one joule per second = one volt × one ampere. Defined since 1971 in honour of James Watt. In SI base units: 1 W = 1 kg·m²/s³. Common multiples: kW (10³ W) for appliances, MW (10⁶) for power plants, GW (10⁹) for utility-scale generation. See the dedicated Watt page for full coverage.

What is a kVA unit?

kVA (kilovolt-ampere) is the SI unit of apparent power — the product of RMS voltage and RMS current in an AC circuit, regardless of the phase angle between them. 1 kVA = 1 000 VA. Apparent power equals real power (kW) only when the power factor is 1.0; for reactive loads, kVA > kW. Transformer and generator nameplates rate capacity in kVA because the alternator winding heat scales with current (kVA), not with the actual work done (kW).

What is the per unit formula?

In the per-unit system, every quantity is normalised to a chosen base value: X_pu = X_actual / X_base. With S_base in kVA and V_base in kV: I_base = S_base / (√3 · V_base) in A; Z_base = V_base² · 1000 / S_base in Ω. Per-unit voltages, currents, and impedances are then dimensionless ratios; transformer impedances stay constant across voltage levels, simplifying multi-bus power-system analysis.

How do I do a per unit calculation?

Pick a system MVA base and a voltage base at one bus. Compute Z_base on each side of every transformer (Z_base = V_LL² / MVA_base). Express every impedance in per-unit by dividing by Z_base on its own side. Solve in per-unit (impedances now add directly), then convert back: V_actual = V_pu × V_base, I_actual = I_pu × I_base. Used for short-circuit studies, power-flow, and protection coordination.

What is the impedance unit?

The impedance unit is the ohm (Ω), same as resistance. Impedance Z is the AC opposition to current flow, combining resistance R and reactance X: Z = √(R² + X²) in magnitude, ∠ arctan(X/R) in angle. For a pure resistor, Z = R + j·0. For a pure inductor, Z = j·ωL. For a pure capacitor, Z = −j/(ωC). All three measured in ohms. Per-unit impedance is dimensionless (Z / Z_base).

What is an AC Pro trip unit?

A trip unit is the electronic module inside a circuit breaker that detects overcurrent and triggers the breaker mechanism. The Eaton "AC Pro" trademark refers to a microprocessor-based trip unit family (used in Magnum, NRX, Series C breakers) with adjustable long-time, short-time, instantaneous, and ground-fault settings. The trip unit "unit" here is the physical sub-assembly inside the breaker, not a unit of measurement.

What is the SI unit of heat?

Heat is energy in transit, so the SI unit of heat is the joule (J). The full phrasing — "the SI unit of heat is the joule" — applies because heat is a form of energy and energy in SI is measured in joules. The traditional unit calorie (cal ≈ 4.184 J) and BTU (≈ 1 055 J) are still used in some contexts (food labelling, HVAC) but the SI replaces them with joules. For power flow of heat the unit is the watt (J/s) — same as electrical power.

Sources and further reading

1. BIPM. The International System of Units (SI), 9th Edition, 2019. The official SI definitions of all base and derived units.
2. NIST. NIST Special Publication 330 — The International System of Units (SI), 2019.
3. IEC. IEC 60027 — Letter Symbols to be Used in Electrical Technology, parts 1–7.
4. IEEE. IEEE Std 945 — Recommended Practice for Preferred Metric Units for Use in Electrical and Electronics Science and Technology.
5. IEEE. IEEE Std 141 — Recommended Practice for Electric Power Distribution for Industrial Plants (Red Book), 1993 (R1999). Per-unit method.
6. Stevenson, W.D. Elements of Power System Analysis, 4th Edition. McGraw-Hill, 1982. Standard reference for per-unit calculations.
7. Jeffery, K. Quanta and Constants — The 2019 SI Revision. Physics Today, May 2019.