Units
Units in electrical engineering have two meanings: SI units of measurement (W for power, Ω for impedance, kVA for apparent power, kWh for energy) and utility-billing "units" (informal slang for kilowatt-hours on the bill). This page covers both — with worked conversions for kVA → units, the impedance units used in power-system analysis, and the photovoltaic kWp / kWh distinction.
Use the unit calculator
The embedded calculator converts between voltage, current, power, and resistance — and across single-phase and three-phase systems. Useful for converting kVA nameplates into kWh consumed (units) and for sanity-checking utility-bill calculations.
Pure DC: P = V · I. Resistance shown is V/I (Ohm's law equivalent).
- Apparent power S
- — kVA
- Reactive power Q
- — kVAR
- Power factor used
- —
- Mechanical equivalent
- — HP
- Heat output
- — BTU/hr
P = V · I = ... Unit conversion formulas
- E_kWh
- energy consumed (units), kWh
- S_kVA
- apparent power, kVA
- t
- time at that load, h
- cos φ
- power factor, —
The single most-used conversion in utility billing. For pure resistive loads (PF = 1), kVA × hours = kWh directly. For motors / industrial loads (PF 0.7–0.9), the kWh figure is lower than the kVA × hours product. Smart meters log kWh and kVAh independently.
- R, X
- resistance and reactance components, Ω
- Z
- complex impedance, Ω
- P_kWp
- PV array DC peak power at STC, kWp
- H
- annual irradiation per kWp installed, kWh/kWp/year
- PR
- performance ratio (0.75–0.85 typical), —
Standards: SI and utility billing
BIPM SI 9th Edition (2019) defines the seven base units and all derived units (W, Ω, V, A, kVA, J, kWh, Hz). The SI is based on units of length (metre), mass (kilogram), time (second), electric current (ampere), thermodynamic temperature (kelvin), amount of substance (mole), and luminous intensity (candela) — every other electrical unit is derived from this set. IEC 60027 defines letter symbols for electrical technology. IEEE Std 945 recommends SI prefix usage in US engineering documents. Utility billing is national: UK Ofgem sets unit (kWh) reporting standards; India CEA regulates kWh meter accuracy; US FERC + state PUCs control billing units and demand-charge structure. Every modern bill itemises units consumed, demand peak, and PF penalty (if any).
Reference: typical "units" usage
| Application | Typical units / day (kWh) | Notes |
|---|---|---|
| UK 1-bedroom flat (no electric heat) | 5–8 | Lighting + appliances |
| UK 3-bedroom house (gas heat) | 8–12 | Ofgem typical-domestic average |
| UK house with heat pump | 15–25 | Winter: 30+ |
| EV (full BEV, 10 000 km/year) | + 5–8 | ~ 1 800 kWh/year additional |
| US average household (mixed climate) | 28–32 | 10 500 kWh/year EIA average |
| US household with electric heat + AC | 40–60 | Texas / Arizona summer peak |
| India urban household | 5–10 | Higher in summer (AC) up to 25 |
| Small office (200 m²) | 50–100 | HVAC + lighting + IT |
| Restaurant / café | 100–300 | Cooking + refrigeration dominant |
| Small datacenter (50 kW IT) | ~ 1 800 | 50 kW × 24 × PUE 1.5 |
| Hyperscale datacenter (100 MW) | ~ 3 600 000 | 3.6 GWh/day; small-city scale |
How to read units on the bill, step by step
- Read the energy charge in units (kWh) on your bill. Utility bills list electrical energy in units, which is informal billing slang for the kilowatt-hour (kWh). Common in South Asia, the UK, and parts of Africa: "350 units this month" means 350 kWh consumed.
- Compute kVA → units (kWh) for billed time. Apparent power × time × power factor = energy. A 25 kVA load running 8 hours/day at PF 0.85 → 25 × 8 × 0.85 = 170 kWh = 170 units per day. Many utilities bill commercial sites by both energy (kWh) AND demand (peak kW or kVA) — check your tariff schedule.
- For PV / solar, sum daily kWh production. A 5 kWp PV system in a 4 kWh/kWp/day climate produces 5 × 4 = 20 kWh = 20 units per day, ≈ 7 300 kWh/year. The "p" in kWp means peak — DC power at standard test conditions; actual AC output is 80–85 % of nameplate after derating.
- Convert impedance units when crossing standards. Impedance unit is the ohm (Ω) — same in SI, imperial, and CGS. Per-unit impedance (dimensionless) = Z_actual / Z_base, where Z_base = V² / S. Always confirm whether nameplate %Z is on machine base or system base before adding impedances.
- Apply correct SI prefixes. k (kilo, 10³), M (mega, 10⁶), G (giga, 10⁹). 1 MW = 1 000 kW = 1 000 000 W. Capitalisation matters: M (mega) ≠ m (milli, 10⁻³). Mixing case in calculations is the most common engineering-units error.
- Verify on the meter. Modern smart meters log kWh and kVARh independently. Compare the energy reading to your manual sum (Σ load × hours). Discrepancy > 5 % suggests metering error, sub-meter mismatch, or unmetered theft. Utility energy auditors check this monthly.
Worked example: factory monthly bill
Small factory: average load 50 kVA, PF 0.80, runs 10 hours/day, 25 days/month. Compute monthly units (kWh), kVA peak demand, and approximate UK-rate bill.
| Step | Calculation | Result |
|---|---|---|
| Monthly hours running | 10 × 25 | 250 h |
| kWh = kVA × h × PF | 50 × 250 × 0.80 | 10 000 units (kWh) |
| Energy charge @ £0.27/kWh | 10 000 × 0.27 | £2 700 |
| Demand charge (UK industrial, ~ £8/kVA·month) | 50 × 8 | £400 |
| PF penalty if PF < 0.95 | ~ 5 % of kVA charge | £20 |
| Total monthly bill | 2 700 + 400 + 20 | £3 120 |
| Correct PF to 0.95 (Q_corr ≈ 22 kVAR) | kVA drops 50 → 42 | −£60/month savings |
Power vs energy vs demand units
Three concepts often confused on bills.
| Concept | SI unit | What it measures | Bill component |
|---|---|---|---|
| Power | W, kW, MW | Instantaneous rate of energy use | Not billed directly |
| Energy | Wh, kWh (units), MWh | Power × time | Energy charge — main item on bill |
| Apparent power | VA, kVA, MVA | RMS V × RMS I (sets alternator size) | Demand charge in industrial tariffs |
| Demand | kW or kVA peak | Highest 15-min average in the period | Demand charge — separate from energy |
| Power factor | — | kW / kVA ratio | PF penalty if PF < 0.85–0.95 |
Edge cases: kVA-only billing and net metering
kVA-only tariffs (some industrial accounts) bill purely on apparent power × time, regardless of PF — the utility does not let you avoid charges by improving PF. Used in some French and Italian industrial schedules. Verify before installing PFC capacitors.
Net metering for solar: residential PV exports excess production back to the grid. Net units = grid-supplied units − exported units. Most US states (and California / Australia) credit at retail rate; UK SEG pays a separate per-kWh export rate. Always confirm tariff structure before sizing the PV system.
Demand reset: if your monthly bill has an unexpected spike, check for a single 15-minute peak that set the demand charge. A welder fired up once for 10 minutes can cost more in demand charge than its energy use justifies.
The kilowatt-hour as a billing unit
Energy used is measured in units of kilowatt-hours (kWh). One kWh is the energy used by a 1 kilowatt appliance running for one hour, or a 100 watt appliance running for ten hours. Your bill multiplies the units used by your unit rate (price per kWh) to produce the energy charge.
Related concepts on this site
Frequently asked questions
- What are W units?
- In SI, the W unit is the watt — the unit of power equal to one joule per second. Multiples include kW, MW, GW. In utility-billing parlance, "units" usually means kilowatt-hours (kWh) — the unit of energy. Both are derived units of the SI; the watt is power (rate), the watt-hour is energy (cumulative).
- How do I convert kVA to units?
- Apparent power × time × power factor = real energy in kWh (= units). 1 kVA running for 1 hour at PF 1.0 = 1 kWh = 1 unit. At PF 0.85, the same kVA gives 0.85 units per hour. A 100 kVA factory bus at 0.80 PF, 12 hours/day, 25 days/month = 100 × 12 × 25 × 0.80 = 24 000 units per month.
- What is a "unit of electricity"?
- In most utility billing (UK, India, Pakistan, parts of Africa), "1 unit of electricity = 1 kWh". A 100 W bulb running 10 hours uses 1 kWh = 1 unit. A 1.5 kW heater for 4 hours uses 6 units. Modern bills sometimes also charge by kVA peak demand (separately from kWh) for industrial customers.
- What are impedance units?
- The SI impedance unit is the ohm (Ω), same as resistance. For per-unit system analysis: dimensionless ratio (Z_actual / Z_base). For very low impedances (cable, busbar): milli-ohm (mΩ) and micro-ohm (µΩ) are common. Resistivity is in Ω·m; conductance in siemens (S = 1/Ω); admittance in S; reactance in Ω.
- What are PV units (kWp, kWh)?
- kWp (kilowatt-peak) rates a solar panel's maximum DC output at standard test conditions (1 000 W/m² irradiance, 25 °C cell). kWh (kilowatt-hour) is actual energy produced. A 5 kWp system in a 4 kWh/kWp/day climate produces ~ 20 kWh/day = 20 units/day, after AC inverter derating (~ 85 % of nameplate). Annual: 5 × 365 × 4 × 0.85 ≈ 6 200 kWh/year.
- What is the SI based on?
- The SI is based on seven base units: metre (length), kilogram (mass), second (time), ampere (electric current), kelvin (temperature), mole (amount of substance), candela (luminous intensity). Since the 2019 redefinition, all seven are tied to fixed values of natural constants — no physical artefact is required. Every other unit (W, V, Ω, kVA, J, Hz, …) is derived from these seven.
- How many units (kWh) does a typical home use?
- Region-dependent. UK average household: 8–12 units/day (3 000–4 000 kWh/year). US average: ~ 30 units/day (~ 11 000 kWh/year — much higher because of electric heat / AC). India average urban: 8–10 units/day. EVs add ~ 10 units/day on average (1 hour fast-charge); heat pumps roughly double a UK household winter usage.
- What's the difference between kVA, kW, and kVAR units?
- kVA = apparent power (the alternator must supply this current). kW = real power (the work actually done). kVAR = reactive power (circulates between source and load). Related by the right-triangle: kVA² = kW² + kVAR². Power factor = kW / kVA. Industrial sites with low PF carry more kVA than they need in kW.
Sources and further reading
- BIPM. The International System of Units (SI), 9th Edition, 2019.
- IEC. IEC 60027 — Letter Symbols to be Used in Electrical Technology.
- IEC. IEC 61724 — Photovoltaic system performance monitoring.
- UK Ofgem. Guide to Your Electricity Bill, latest issue.
- US EIA. Annual Energy Outlook 2024 — Residential Energy Consumption Survey.
- India CEA. Electricity Rules 2005 — Annexure II metering accuracy and units.
- IEEE. IEEE Std 945 — Recommended Practice for Preferred Metric Units.