Generator Frequency Calculator (Poles & RPM, f = PN/120)

Generator Frequency Calculator (Poles & RPM, f = PN/120): formula and free online calculator

A synchronous generator's output frequency is fixed by how fast its rotor turns and how many magnetic poles it has. This generator frequency calculator applies f = P × N ÷ 120 to find the frequency from the speed, or the speed a prime mover must run at for 50 Hz or 60 Hz — see how an alternator works.

rpm
1,500 rpm
calculated
calculated
Type in any field to change it. Press × on a value to calculate that field instead.

How to use the generator frequency calculator

Enter the number of poles and the rotor speed in rpm to get the output frequency. To find the speed for a target frequency, enter the frequency and clear the speed field; to find the pole count for a turbine speed, clear the poles field.

Generator frequency formula

f = P × N ÷ 120  ·  N = 120 f ÷ P

Example

A 4-pole diesel generator set running at 1,500 rpm:

  • f = 4 × 1500 ÷ 120 = 50 Hz
  • At 1,800 rpm the same machine gives 4 × 1800 ÷ 120 = 60 Hz

Synchronous speed by number of poles

Poles Pole pairs Speed for 50 Hz Speed for 60 Hz Typical machines
2 1 3,000 rpm 3,600 rpm Steam / gas turbine generators
4 2 1,500 rpm 1,800 rpm Diesel gensets, turbo sets
6 3 1,000 rpm 1,200 rpm Medium-speed diesel
8 4 750 rpm 900 rpm Medium-speed diesel, small hydro
12 6 500 rpm 600 rpm Gas engines, hydro
16 8 375 rpm 450 rpm Low-speed engines, hydro
24 12 250 rpm 300 rpm Hydro
48 24 125 rpm 150 rpm Low-head hydro
96 48 62.5 rpm 75 rpm Very low-head hydro

Notes

  • The governor holds speed — and therefore frequency — constant as load changes; a 2% droop governor lets a 50 Hz set fall to 49 Hz at full load.
  • Induction motors run slightly slower than synchronous speed; see the induction motor slip calculator.
  • Before paralleling with the grid, a generator must match its frequency, voltage and phase angle.

Frequently asked questions

How do you calculate generator frequency?

f = P × N ÷ 120, with P the number of poles and N the speed in rpm. A 4-pole alternator at 1,500 rpm gives 50 Hz; at 1,800 rpm it gives 60 Hz.

Why is the formula divided by 120?

Each pole pair produces one electrical cycle per revolution, so f = (P ÷ 2) × (N ÷ 60) = P N ÷ 120.

What speed does a 2-pole generator run at?

3,000 rpm for 50 Hz and 3,600 rpm for 60 Hz — the usual speed of steam- and gas-turbine generators.

Why do hydro generators have so many poles?

Water turbines turn slowly (often 100–500 rpm), so the generator needs many poles to reach 50 or 60 Hz. A 48-pole machine runs at 125 rpm for 50 Hz.

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