--- title: "HP to Amps Calculator" description: "Motor full load current from horsepower at 415 V or 230 V, with efficiency and power factor applied — the two terms a plain HP to kW conversion omits." standard: "I = HP × 746 / (√3 × V × PF × η)" source: "https://energycalchq.com/tools/hp-to-amps" --- Getting from horsepower to amps needs two numbers that a straight unit conversion does not use — efficiency and power factor. Leave either out and the current comes back low, which is how cables get undersized. ## The formula ``` Three phase: I = HP × 746 / (√3 × V × PF × η) Single phase: I = HP × 746 / (V × PF × η) ``` Where `η` is motor efficiency and `PF` is the power factor at the load the motor is actually running. Three terms in the denominator, and only one of them appears in a unit conversion. That is why "5 HP is 3.73 kW, so divide by 415 and √3" gives an answer roughly a quarter too low. ## Why both terms are needed **Efficiency** accounts for the losses between the supply and the shaft. The horsepower on the plate is what comes out; the supply has to deliver that plus the copper, iron, friction and windage losses. At 88 % efficiency, 5 HP of shaft power needs 4.24 kW of electrical input. **Power factor** accounts for the magnetising current. An induction motor draws current to establish its rotating field whether or not it is doing work, and that current is out of phase with the voltage. It does no work, but it flows in the cable and it heats it exactly as any other current does. Together they are the difference between a plausible number and a correct one: ``` 5 HP, 415 V three-phase, PF 0.85, η 88 % Shaft power = 5 × 0.7457 = 3.73 kW Electrical input = 3.73 / 0.88 = 4.24 kW Full load current = 4240 / (1.732 × 415 × 0.85) = 6.9 A ``` Ignore both terms and the same motor appears to draw 5.2 A. That is 25 % low, before any derating is applied. ## Power factor falls when the motor is lightly loaded This is the part that surprises people. An induction motor's power factor is worst at no load and improves as it is loaded up — a motor running at a quarter of its rating can sit near 0.4 rather than the 0.85 on its plate. The magnetising current is roughly constant, so as the working current falls the ratio between them worsens. Which means an oversized motor is a double penalty: it costs more, and it draws more current per unit of useful work than a correctly sized one would. The nameplate power factor applies at full load. If the machine habitually runs at half load, use a lower figure. ## Starting current is a different question The calculator also reports around **six times full load current**, which is what a direct-on-line induction motor draws until it reaches speed. That figure sizes the **protection**, not the cable. A cable can carry a several-hundred-percent overload for a couple of seconds without harm, because heating takes time — so cables are sized on full load current, and the starting transient is handled by choosing a breaker curve that does not trip on it. The [motor starter calculator](/tools/motor-starter) covers the protection side, and [cable sizing](/tools/cable-size) the conductor. If the starting current is the problem rather than the protection — lights dimming, a generator stumbling, an inverter tripping — the answer is a different starting method. Star-delta, a soft starter or a VFD each reduce it, and [choosing between them](/blog/choosing-a-motor-starter) depends on the load rather than the motor. ## Typical full load currents at 415 V, three phase At 0.85 power factor and 88 % efficiency: | HP | kW shaft | Full load A | DOL start A | |---|---|---|---| | 1 | 0.75 | 1.4 | 8 | | 2 | 1.49 | 2.8 | 17 | | 3 | 2.24 | 4.2 | 25 | | 5 | 3.73 | 6.9 | 42 | | 7.5 | 5.59 | 10.4 | 62 | | 10 | 7.46 | 13.9 | 83 | | 15 | 11.19 | 20.8 | 125 | | 20 | 14.91 | 27.7 | 166 | | 25 | 18.64 | 34.7 | 208 | Use these to sanity-check a measurement, not to design from. Efficiency and power factor both vary with size, speed and load, and the nameplate figures for the actual machine are always better than a table. ## The current the cable sees is not the current on the plate Nameplate current is stated at rated voltage, rated frequency and full load. A motor in service rarely meets all three at once, and the direction of the error is usually the unhelpful one. Voltage is the main offender. A motor driving a fixed mechanical load delivers the same shaft power regardless of supply voltage, so when the voltage falls the current rises to compensate. A 10 per cent low supply — well within what Indian distribution routinely delivers at the end of a rural feeder — pushes full load current up by roughly the same proportion, and the winding heats as the square of it. Unbalance compounds it. A few per cent of voltage unbalance between phases produces a much larger current unbalance, so one winding carries considerably more than the calculation predicts while the other two carry less. The average looks correct and the hottest phase is what fails. This is why the overload relay is set from the measured running current where that is available, and why a clamp meter reading on all three phases at normal load is the single most useful record to take at commissioning. ## Sizing the contactor, which is a different question The cable and the overload relay follow the full load current. The contactor does not — it is selected by utilisation category, because what wears a contactor out is the current it has to make and break rather than the current it carries. AC-3 is the category for squirrel-cage motors switched normally: making at starting current, breaking at running current. That is the everyday case, and a contactor rated AC-3 at the motor kW is the correct choice for a direct-on-line starter. AC-4 covers inching, plugging and reverse operation, where the contactor has to break full starting current repeatedly. The same physical contactor carries a substantially lower AC-4 rating than its AC-3 one, often by a factor of three or more. Selecting an AC-3 rating for a load that is actually AC-4 duty gives a starter that works perfectly on test and welds its contacts within months. If the application reverses under power, jogs for positioning, or starts far more often than a few times an hour, size against the AC-4 figure in the manufacturer's table and not against the motor rating alone.