--- title: "kW to Amps Calculator" description: "Convert kW to amps for single-phase and three-phase supplies, with power factor and motor efficiency handled properly. Formula and a 415 V chart." standard: "I = P × 1000 / (√3 × V × PF)" source: "https://energycalchq.com/tools/kw-to-amps" --- Kilowatts describe how much work a load does. Amps describe what the cable and the breaker have to survive. Converting between them takes voltage and power factor — and on a motor, one more term that most calculators quietly leave out. ## The formula For a balanced three-phase supply: ``` I = (P × 1000) / (√3 × V × PF) ``` And for single-phase: ``` I = (P × 1000) / (V × PF) ``` Where `P` is real power in kW, `V` is voltage in volts, `PF` is power factor, and `I` is the resulting current in amps. The `× 1000` converts kilowatts to watts. The `√3` — 1.732 — appears only on three-phase, and it is the ratio between line and phase voltage in a star connected system, a consequence of the three phases sitting 120° apart rather than of anything to do with there being three of them. Which voltage you enter matters. For a three-phase supply it is the **line-to-line** voltage: 415 V in India, 400 V across most of Europe, 480 V in North American industrial supplies. For single-phase it is **line-to-neutral**: 230 V in India, 120 V in North America. ## A worked example A 45 kW motor on a 415 V three-phase supply at 0.86 power factor: ``` I = (45 × 1000) / (1.732 × 415 × 0.86) I = 45,000 / 618.1 I = 72.8 A ``` So the cable and the starter have to carry about 73 A continuously. The calculator above loads with exactly these figures, so you can change one value at a time and watch which way the answer moves. ## The efficiency term everyone forgets Here is the mistake that costs money on real jobs. A motor nameplate states **output** power at the shaft. Current flows on the **input** side. The difference between the two is the motor's efficiency, and it is not small. That 45 kW motor at 92 % efficiency draws current corresponding to: ``` Input power = 45 / 0.92 = 48.9 kW I = (48.9 × 1000) / (1.732 × 415 × 0.86) = 79.1 A ``` That is 79 A, not 73 A — an 8.6 % difference, which on a cable schedule is frequently one full size, and on a breaker selection is the difference between a device that holds and one that nuisance-trips on a hot afternoon. The rule is simple. If your kW figure came off a **motor nameplate**, it is output power: divide by efficiency before converting. If it came from a **meter, a clamp, or a heater or lighting rating**, it is already input power: use it as it is. ## Power factor, and what to use when you don't know it Power factor is the fraction of the current that is doing work. At 0.86, the supply carries about 16 % more current than the real power alone would suggest, because the magnetising current in the motor windings flows whether it does anything useful or not. | Load | Typical PF | | --- | --- | | Resistive heater, filament lamp | 1.0 | | Induction motor at full load | 0.85 – 0.90 | | Induction motor at half load | 0.70 – 0.80 | | Induction motor unloaded | 0.20 – 0.40 | | LED lighting with driver | 0.90 – 0.95 | | Welding set | 0.50 – 0.70 | | Distribution transformer, mixed load | 0.85 – 0.95 | | VFD with front-end rectifier | 0.95 – 0.98 displacement | Two of these deserve a warning. A **lightly loaded motor** has a far worse power factor than its nameplate — a motor running at 30 % load can sit near 0.5, and its current does not fall anything like as fast as its output does. And a **VFD** shows a good displacement power factor but a poor total power factor once harmonic current is counted; sizing its supply cable on 0.95 alone understates the heating in the conductor. If you genuinely have no figure, 0.8 is the conservative assumption for a mixed industrial load. It overstates the current slightly, which is the direction you want to be wrong in. ## kW to amps at 415 V, three-phase Line current at 415 V three-phase, at three common power factors: | kW | PF 0.8 | PF 0.85 | PF 0.9 | | --- | --- | --- | --- | | 0.75 | 1.3 A | 1.2 A | 1.2 A | | 1.5 | 2.6 A | 2.5 A | 2.3 A | | 2.2 | 3.8 A | 3.6 A | 3.4 A | | 3.7 | 6.4 A | 6.1 A | 5.7 A | | 5.5 | 9.6 A | 9.0 A | 8.5 A | | 7.5 | 13.0 A | 12.3 A | 11.6 A | | 11 | 19.1 A | 18.0 A | 17.0 A | | 15 | 26.1 A | 24.6 A | 23.2 A | | 22 | 38.3 A | 36.0 A | 34.0 A | | 30 | 52.2 A | 49.1 A | 46.4 A | | 45 | 78.3 A | 73.7 A | 69.6 A | | 55 | 95.7 A | 90.0 A | 85.1 A | | 75 | 130.4 A | 122.8 A | 116.0 A | | 90 | 156.5 A | 147.3 A | 139.1 A | | 110 | 191.3 A | 180.0 A | 170.1 A | | 132 | 229.5 A | 216.0 A | 204.1 A | | 160 | 278.2 A | 261.9 A | 247.4 A | These are **input** currents for the stated kW. For motors, apply efficiency as described above, or use the [motor full load current chart](/blog/motor-full-load-current-chart-415v), which has the efficiency already built into the figures. ## Why single-phase current is so much higher The same load on single-phase draws considerably more current than on three-phase, and it catches people out constantly. A 5 kW load at 0.9 PF: - Three-phase at 415 V: `5000 / (1.732 × 415 × 0.9)` = **7.7 A** - Single-phase at 230 V: `5000 / (230 × 0.9)` = **24.2 A** Three times the current, for the same work. Two reasons combine: the single-phase voltage is lower (230 V against 415 V), and there is no √3 sharing the load across three conductors. This is why a 5 kW single-phase water heater needs 4 mm² cable while the same duty on three-phase runs happily on 1.5 mm². ## What to do with the answer The current out of this calculation is the **design current**, usually written `Ib`. It is the start of the sizing sequence, not the end of it: 1. **Ib** — the current the load draws. This calculator. 2. **In** — the protective device rating, which must be at least `Ib`. See [MCB and MCCB sizing](/tools/breaker-sizing). 3. **Iz** — the cable's current carrying capacity *after* derating for ambient temperature, grouping and installation method, which must be at least `In`. See [cable sizing](/tools/cable-size). The relationship `Ib ≤ In ≤ Iz` is the whole of circuit protection in one line. And separately, the volt drop over the run has to stay inside 3 % for lighting or 5 % for power — on a long run that, not the current, is usually what sets the cable size. The [voltage drop calculator](/tools/voltage-drop) covers that side. ## Common mistakes **Using 230 V for a three-phase calculation.** The phase voltage of a 415 V system is 240 V, and it is tempting to use it. Don't — the formula with √3 expects the line-to-line value. **Converting kVA as though it were kW.** A 100 kVA generator is not a 100 kW generator; at 0.8 PF it is an 80 kW machine. Use the [kVA to amps calculator](/tools/kva-to-amps) for apparent power. **Applying power factor twice.** If you have already converted kW to kVA, the power factor is spent. Divide kVA by `√3 × V` and stop. **Sizing on running current alone.** A direct-on-line motor draws six to eight times its full load current for the first few seconds. The cable is sized on running current, but the protection has to ride through the start — which is what the trip curve, not the rating, decides.