Motor power calculation: HP and kW the simple way
Whether you are sizing a conveyor drive, checking a pump motor, or converting a nameplate from kW to HP, motor power comes down to two formulas: power from torque and speed, and electrical input from voltage and current. Here is each one, a full worked example, and the efficiency and power-factor details that separate a right-sized motor from a wasteful one.
The two formulas you actually need
Almost every motor question is one of these:
- Mechanical (shaft) power from torque and speed: P(kW) = T × N / 9550, where T is torque in Nm and N is speed in rpm.
- Electrical input power for a three-phase motor: P(kW) = √3 × V × I × PF / 1000, where V is line voltage, I is line current and PF is power factor.
The constant 9550 bundles the unit conversions (it is 60,000 / 2π). Memorise it — it turns Nm and rpm straight into kW.
Power from torque and speed
When you know the load torque and the running speed, mechanical power is direct. Say a mixer needs 120 Nm at 1450 rpm:
If your speed is in rad/s rather than rpm, use the cleaner form P(W) = T(Nm) × ω(rad/s). The 9550 version simply saves you converting rpm every time.
Electrical input power and current
The nameplate kW is shaft output. The motor draws more than that from the supply because of losses, so:
Input power = output power / efficiency. A 18.5 kW motor at 91% efficiency draws 18.5 / 0.91 = 20.3 kW electrical input.
To find the running current, rearrange the three-phase formula:
Worked example: a conveyor drive
A belt conveyor needs to move 8000 kg/h up a 4 m rise at 0.5 m/s. Work it through:
| Step | Calculation | Result |
|---|---|---|
| Lifting power | m·g·h per second = (8000/3600) × 9.81 × 4 | 87 W vertical |
| Friction + belt load (allow ~3×) | realistic conveyor demand | ~2.6 kW |
| Drive efficiency (gearbox 95%) | 2.6 / 0.95 | 2.74 kW |
| Service factor (1.25) | 2.74 × 1.25 | 3.42 kW |
| Next standard frame | round up | 3.7 kW (5 HP) |
The takeaway: the raw lifting power was tiny, but friction, efficiency and a sensible margin set the real motor at 3.7 kW. Skipping those steps is how plants end up with motors that trip on start-up.
kW to HP conversion table
To convert, multiply kW by 1.341 for imperial HP (or 1.3596 for metric HP). Common ratings:
| kW | HP (approx) | Typical use |
|---|---|---|
| 0.75 | 1.0 | Small pump, fan |
| 2.2 | 3.0 | Conveyor, blower |
| 3.7 | 5.0 | Compressor, hydraulic pack |
| 7.5 | 10 | Machine tool main drive |
| 15 | 20 | Large pump, mixer |
| 37 | 50 | Process fan, big compressor |
Sizing a motor without over-spending
In 14 years on the plant floor, the most common waste I saw was oversized motors. A motor running at 40% load sits at a poor power factor and lower efficiency, so it quietly burns energy for years. To size well:
- Calculate the true load power (torque × speed, or pump/fan duty).
- Divide by drive efficiency and motor efficiency.
- Add a service factor of 15–25% — not 100%.
- Pick the next standard frame up, then check it runs near 75–100% load.
A motor loaded to 75–95% of rating is in its efficiency and power-factor sweet spot. For pump and fan drives, remember the affinity laws — power rises with the cube of speed, so a small speed increase is a big power increase. If energy cost is the target, our OEE guide and cycle time guide help connect motor loading to real output.
Common motor calculation mistakes
- Confusing input and output. Nameplate kW is shaft output; supply draw is higher by the efficiency loss.
- Forgetting √3. The 1.732 factor is mandatory for three-phase — leaving it out understates power by 42%.
- Ignoring drive losses. Gearboxes, belts and couplings each take a few percent.
- Sizing on running power only. Starting torque for high-inertia or loaded starts can need a larger frame.
If your work also involves preparing inspection drawings for machined motor or pump components, CadNexa's auto-ballooning tool turns a PDF drawing into a numbered inspection sheet in minutes — handy when the same parts need an FAI. Browse more shop-floor calculators on the MetricMech templates page.