The Complete kW Formula Reference
Every kilowatt formula in one place: DC, AC single and three-phase, horsepower, kWh, BTU, tons, kVA, kVAR, power factor, and Ohm's Law, with a live calculator.
Common conversions
| Input | Result |
|---|---|
| 10 kW → HP (mechanical) | 13.41 HP |
| 10 HP → kW (mechanical) | 7.46 kW |
| 10 kW for 2 hours → kWh | 20 kWh |
| 10 kW → BTU/hr | 34,121 BTU/hr |
| 10 kW → refrigeration tons | 2.84 tons |
| 10 kW → kVA @ PF 0.9 | 11.11 kVA |
| 10 kVA → kW @ PF 0.9 | 9.00 kW |
| 10 kW → amps @ 240 V DC | 41.67 A |
| 10 kW → amps @ 400 V 3φ, PF 0.9 | 16.04 A |
The math behind it
- kW = (√3 × V × A × PF) / 1000 = (1.732 × 400 × 45 × 0.87) / 1000
- kW = 27,132 / 1000 ≈ 27.13 kW
- kVA = kW / PF = 27.13 / 0.87 ≈ 31.18 kVA
- HP = kW / 0.7457 ≈ 36.39 HP
Everything you need to know
This page collects every formula the rest of the site uses so you can look one up without hunting through a specific converter. Each formula below uses the same variables: V for RMS voltage, A for RMS current, PF for power factor, and kW for real power in kilowatts.
Electrical power: DC, single-phase, and three-phase
Direct current has no phase angle, so power is a plain product: kW = (V × A) / 1000. AC single-phase adds the power factor term because voltage and current can shift out of step in reactive loads: kW = (V × A × PF) / 1000. Three-phase AC splits into two cases depending on how you measured voltage. With line-to-line voltage (the usual nameplate spec, 208V, 400V, 480V), use kW = (√3 × V × A × PF) / 1000, where √3 ≈ 1.732 accounts for the 120-degree spacing between the three current waveforms. With line-to-neutral voltage instead, swap √3 for a plain 3: kW = (3 × V × A × PF) / 1000. A 400 V, 45 A three-phase motor at PF 0.87 works out to about 27.13 kW using the line-to-line version, a number that would be wrong by a factor of √3 if you used the line-to-neutral formula on line-to-line voltage by mistake.
Motors, HVAC, and energy: HP, BTU, tons, and kWh
Horsepower has three slightly different conversion constants depending on the standard: mechanical (imperial) horsepower equals 0.7457 kW, electrical horsepower equals 0.746 kW, and metric horsepower (PS, common on European nameplates) equals 0.7355 kW. A 20 HP mechanical rating converts to 14.91 kW, while the same number of metric PS units converts to only 14.71 kW, a 1.4% gap that matters when comparing US and European motor catalogs. On the thermal side, HVAC engineers convert kW to BTU/hr by multiplying by 3412.14, and to refrigeration tons by dividing by 3.517, since one ton equals 12,000 BTU/hr, the rate needed to melt one short ton of ice in 24 hours. Energy is simpler than any of these: kWh = kW × hours. A 3.5 kW electric oven run for 45 minutes (0.75 hours) uses 3.5 × 0.75 = 2.625 kWh, and multiplying that by your utility rate gives the cost of that one bake.
Apparent power, reactive power, and the constants underneath it all
Apparent power (kVA) is what a generator or transformer must be rated to supply, while kW is the fraction of that which does useful work: kVA = kW / PF. The gap between the two is reactive power, measured in kVAR and found from kVAR = √(kVA² − kW²), the power that inductive loads store and release each cycle without being consumed. Every one of these formulas ultimately rests on Ohm's Law (V = I × R) and its power form, sometimes called Watt's Law (P = V × I = I²R = V²/R). Change any one of voltage, current, or resistance and every downstream kW, kVA, and amperage figure on this page shifts with it, which is why the Ohm's Law calculator is worth bookmarking alongside this one.
Common applications
Estimators pull the amps, HP, and kVA formulas from this page to size service entrances and price out conductor and breaker quantities before a job starts.
The BTU/hr and refrigeration-ton conversions let HVAC technicians move between a compressor's electrical kW rating and its cooling capacity on a spec sheet without a separate lookup table.
Backup power sizing depends on both the kW (real load) and kVA (apparent load) formulas, since generators and UPS units are rated in kVA but the connected loads are rated in kW.
Checking a motor nameplate against the three-phase and horsepower formulas catches mislabeled equipment or unit-conversion errors (metric PS vs mechanical HP) before installation.
Common mistakes
kW is real power and kVA is apparent power; they are only equal at PF 1.0. Sizing a generator in kW when the spec sheet lists kVA can undersize it by 10-25% for a typical PF 0.8-0.9 load.
Mixing mechanical HP (0.7457) with metric PS (0.7355) introduces a 1.4% error, small on one motor but significant across a facility with dozens of European and North American nameplates.
Skipping √3 (about 1.732) understates three-phase real power by 42%, one of the most common errors when adapting a single-phase spreadsheet to a three-phase job.
Forgetting to divide watts by 1000, or plugging minutes into a formula that expects hours, throws every downstream kWh and cost calculation off by a factor of 1000 or 60.
Frequently asked questions
Do all the AC formulas on this page use RMS voltage?+
Yes, every AC formula here uses RMS (root-mean-square) voltage and current, the values a standard multimeter or nameplate reports, not the peak values, which run about 41% higher for a clean sine wave.
What is the difference between mechanical, electrical, and metric horsepower?+
Mechanical (imperial) horsepower equals 745.7 W, electrical horsepower equals 746 W, and metric horsepower (PS) equals 735.5 W. A 20 HP mechanical motor is 14.91 kW, while 20 PS is only 14.71 kW.
Is kVA always larger than kW?+
Yes, apparent power (kVA) is always equal to or greater than real power (kW) because kVA = kW / PF and PF never exceeds 1.0. They are equal only when PF is exactly 1.0, meaning a purely resistive load.
How do I find reactive power if I already have kW and kVA?+
Use kVAR = √(kVA² − kW²). A load pulling 10 kVA at 8 kW real power has kVAR = √(100 − 64) = √36 = 6 kVAR of reactive power.
Which formula converts kW directly to BTU per hour?+
Multiply kW by 3412.14: BTU/hr = kW × 3412.14. A 3.5 kW space heater puts out about 11,942 BTU/hr.
Do I need power factor to convert kW to refrigeration tons?+
No, the tons formula (Tons = kW / 3.517) only converts a thermal output already expressed in kW; power factor only enters earlier, when converting the compressor's electrical input from volts and amps.
What is Watt's Law and how does it relate to Ohm's Law?+
Watt's Law is the power form of Ohm's Law: P = V × I, which combines with V = I × R to give P = I²R and P = V²/R. Every electrical kW formula on this page is a variation of Watt's Law with extra terms for AC phase and power factor.
Can I use the single-phase formula on a three-phase circuit?+
No, applying the single-phase formula to three-phase voltage and current understates real power by a factor of √3 (about 1.732) for line-to-line systems, or by a factor of 3 for line-to-neutral systems.
Why do some formulas divide by 1000 and others don't?+
The 1000 converts watts to kilowatts. Formulas that start with volts and amps (which produce watts) divide by 1000, while formulas that already start in kW, like kWh = kW × hours, skip that step.