Estimate motor power in kW from operating frequency, rated power, and rated Hz for pump, fan, or conveyor loads with torque scaling.

Estimates motor output power when a VFD runs the motor below or above its rated frequency.

Pump and fan power scales with the cube of speed; constant-torque loads scale linearly.

Results are estimates. Field weakening above rated frequency, slip, and motor losses can reduce real-world output.

Hz To Kw Formula

The following formula estimates mechanical shaft power (kW) from electrical frequency (Hz), pole count, and shaft torque for a synchronous motor/generator operating at synchronous speed (i.e., neglecting slip and losses).

PkW = (4ฯ€ f tau) / (Pc ร— 1000)

Variables:

  • P is the power output (kW)
  • ฯ„ is the shaft torque (Nยทm)
  • f is the frequency (Hz)
  • P_c is the pole count
Hz to kW Example Table (Assumes synchronous speed, Pc = 4 poles, ฯ„ = 10 Nยทm)
Frequency (Hz) Power (kW)
50.157
100.314
150.471
200.628
300.942
401.257
501.571
601.885
752.356
902.827
1003.142
1203.770
1504.712
1805.655
2006.283
2407.540
3009.425
36011.310
40012.566
50015.708
* Rounded to 3 decimals. Formula: P(kW) = (4ฯ€ f ฯ„) / (Pc ร— 1000). Assumes torque ฯ„ = 10 Nยทm and pole count Pc = 4. 1 kW = 1000 W.

What is Hz To Kw?

Hz (hertz) is a unit of frequency (cycles per second), while kW (kilowatt) is a unit of power. There is no universal โ€œHz to kWโ€ conversion because power depends on the system. In rotating AC machines, frequency and pole count determine synchronous speed (for example, 60 Hz and 4 poles corresponds to 1800 rpm), and with a known shaft torque you can estimate mechanical power using P = ฯ„ยทฯ‰. (If you need electrical real power from voltage/current, frequency is not a multiplicative factor; for example, threeโ€‘phase real power is P(kW) = โˆš3 ยท V ยท I ยท PF / 1000.)

How to Calculate Hz To Kw?

The following steps outline how to estimate mechanical kW from frequency using the given formula:

  1. Determine the frequency (f) in hertz (Hz).
  2. Determine the pole count (Pc) of the machine (2, 4, 6, โ€ฆ).
  3. Determine the shaft torque (ฯ„) in newtonโ€‘meters (Nยทm).
  4. Calculate the synchronous angular speed: ฯ‰ = 4ฯ€f / Pc (rad/s).
  5. Calculate mechanical power in watts: P(W) = ฯ„ ยท ฯ‰.
  6. Convert watts to kilowatts: P(kW) = P(W) / 1000, which gives P(kW) = (4ฯ€ f ฯ„) / (Pc ร— 1000).

Example Problem:

Use the following variables as an example problem to test your knowledge:

frequency (f) = 60 Hz

pole count (Pc) = 4

shaft torque (ฯ„) = 10 Nยทm

power (P) = (4ฯ€ ยท 60 ยท 10) / (4 ยท 1000) = 1.88496 kW