Single-Phase kW Calculator
Calculate single-phase real power in kW from voltage, current and power factor. Works for 120 V and 240 V residential circuits.
Common conversions
| Input | Result |
|---|---|
| 15 A @ 120 V (PF 1.0) lighting circuit | 1.80 kW |
| 20 A @ 120 V (PF 0.95) countertop appliance | 2.28 kW |
| 24 A @ 240 V (PF 0.99) electric dryer | 5.70 kW |
| 30 A @ 240 V (PF 1.0) range element | 7.20 kW |
| 40 A @ 240 V (PF 1.0) water heater | 9.60 kW |
| 50 A @ 240 V (PF 0.9) central AC condenser | 10.80 kW |
| 12 A @ 230 V (PF 0.85) EU appliance | 2.35 kW |
| 16 A @ 100 V (PF 1.0) Japan appliance | 1.60 kW |
The math behind it
- kW = (V × A × PF) / 1000
- kW = (240 × 24 × 0.99) / 1000
- kW = 5,702 / 1000
Everything you need to know
How split-phase 120/240 V service is wired
Most North American homes run on split-phase service, not true two-phase or three-phase power. The utility transformer has a single secondary winding with a center tap. That center tap is grounded and becomes the system neutral, while the two ends of the winding become hot legs L1 and L2, each 120 V from neutral but 180° out of phase with each other. Because the two legs are opposite halves of the same winding, the voltage between them adds up to 240 V rather than canceling out. A single-pole breaker taps one hot leg plus the neutral to feed 120 V branch circuits (lighting, receptacles). A double-pole breaker ties both hot legs together to feed a 240 V circuit (dryer, range, water heater, central AC) with no neutral needed for a purely 240 V load. This is why the panel schedule shows some breakers as single slots and others as two slots tied with a handle.
Outside North America, single-phase service is usually simpler: one hot conductor and one neutral straight from a wye-connected distribution transformer, at 230 V (most of Europe, Asia, and Africa) or 100 V (Japan). There's no split winding and no 240 V line-to-line option, just one voltage for everything on that service. Either way, the math is identical: real power equals voltage times current times power factor, with no √3 term anywhere.
Deriving the single-phase power formula
Instantaneous power is voltage times current at each moment: p(t) = v(t) × i(t). For a sinusoidal AC circuit with voltage and current out of phase by angle φ, averaging p(t) over a full cycle collapses to P = Vrms × Irms × cos(φ). That cos(φ) term is the power factor, and Vrms × Irms alone is the apparent power in kVA. Real power (kW) is always less than or equal to apparent power (kVA); they're equal only when the load is purely resistive and φ = 0, so PF = 1. This is the same reasoning used on the power factor page, just applied here to a single line and neutral instead of three lines.
Applying it to real household and shop equipment
A 240 V, 24 A dryer heating element with PF 0.99 (nearly pure resistance) draws about 5.70 kW, close to the 5.6 to 5.8 kW nameplate rating printed on most electric dryers. A 120 V window air conditioner rated at 12 A with PF 0.9 (compressor motor, not pure resistance) draws about 1.30 kW, noticeably less than the naive 120 × 12 / 1000 = 1.44 kVA a shopper might expect from the amp rating alone. RV and marine shore power pedestals rated "50 A" are actually split-phase, delivering two separate 120 V, 50 A legs rather than one 240 V, 50 A leg; total connected capacity is 120 × 50 × 2 / 1000 = 12 kW, not the 24 kW someone gets by plugging 240 V straight into the formula. Reading the pedestal's actual configuration, not just the amp number stamped on it, is the difference between a correct load calculation and one that's off by a factor of two.
Common applications
120 V receptacles and lighting, plus 240 V dryer, range, and water heater circuits, are all single-phase. Multiply V × A × PF / 1000 to estimate load and check it against NEC 80% continuous-load rules.
Most small offices and retail spaces receive single-phase 240/120 V service. Use this calculator to estimate HVAC and equipment kW before requesting a utility service upgrade.
30 A pedestals are true single-leg 120 V; 50 A pedestals are split-phase with two 120 V legs. Knowing the real kW per leg prevents tripping the pedestal breaker when running AC and a water heater together.
Consumer portable generators are single-phase, typically 120/240 V split output. Adding up the kW of intended loads at their actual PF avoids overloading a generator rated only in surge watts.
Common mistakes
North American 240 V is single-phase math from a calculation standpoint, just V × A × PF. Never apply the √3 factor, that's reserved for true three-phase systems.
Motors and compressors run PF 0.7 to 0.9. Using PF = 1 for these loads overstates real kW and misrepresents the current the breaker actually sees.
A 208 V circuit tapped off a three-phase wye panel is single-phase in wiring but delivers 13% less voltage than a true 240 V split-phase circuit at the same current, so a 240 V-rated heater underperforms on 208 V.
A '50 A' RV pedestal is two 120 V, 50 A legs, not one 240 V, 50 A leg. Plugging 240 V and 50 A into the formula overstates capacity by 2x.
Frequently asked questions
Do I need power factor for resistive loads?+
No, resistive loads like a dryer element or a water heater have PF at or near 1.0, so the term drops out of the formula entirely.
Is North American 240 V single-phase or two-phase?+
Single-phase. It's two 120 V hot legs from a center-tapped transformer winding, 180° apart, which is called split-phase, not true two-phase power.
How many amps does a 5.7 kW electric dryer draw at 240 V?+
About 24 A at PF 0.99, which is why dryer circuits are typically wired for a 30 A double-pole breaker with 10 AWG copper.
What's the difference between line-to-line and line-to-neutral in single-phase math?+
In split-phase service, line-to-line (240 V, both hots) and line-to-neutral (120 V, one hot plus neutral) both use the same V × A × PF formula, just with a different voltage plugged in. There's no √3 factor in either case.
Can a single-phase circuit have a power factor below 1?+
Yes, any inductive load such as a motor, compressor, or older fluorescent ballast on a single-phase circuit has PF below 1.0, typically 0.8 to 0.95.
How many kW can a 50 A RV shore power pedestal deliver?+
About 12 kW total. A 50 A RV pedestal supplies two separate 120 V, 50 A legs, not a single 240 V, 50 A leg, so the total is 120 × 50 × 2 / 1000, not 240 × 50 / 1000.
Should I size a breaker to the exact kW-derived amps?+
No, apply a 125% continuous-load multiplier for circuits expected to run 3 hours or more, per NEC 210.19, before picking the breaker and wire size.
How many amps does a 1.3 kW, 120 V window air conditioner draw?+
About 12.0 A at PF 0.9, calculated as A = (1,300) / (120 × 0.9).
Is single-phase voltage the same in every country?+
No, it ranges from 100 V in Japan to 120 V in North America to 230 V across most of Europe, Asia, and Africa. Always use the local nameplate voltage, not an assumed default.
Does the single-phase kW formula work for DC circuits?+
No, DC has no power factor because there's no phase angle between voltage and current. Use kW = (V × A) / 1000 for DC, dropping the PF term entirely.