1,800
RPM
188.5
rad/s
1,800
RPM
188.5
rad/s
The Motor Speed Calculator determines the synchronous speed of an AC induction motor based on the supply frequency and the number of magnetic poles. Understanding motor speed is fundamental to electric motor selection, drive system design, and industrial automation engineering.
AC induction motors rotate at a speed governed by the relationship between supply frequency and pole count. The synchronous speed — the theoretical maximum speed of the rotating magnetic field — is given by the formula Ns = 120f / P, where f is the supply frequency in hertz and P is the total number of magnetic poles in the stator winding.
In practice, induction motors always run slightly below synchronous speed due to slip — the difference between the rotating field speed and actual rotor speed. Synchronous motors, however, lock onto the field and run at exactly the synchronous speed. This calculator computes the synchronous speed, which serves as the baseline for all motor speed calculations.
The number of poles is always even (2, 4, 6, 8, etc.) because magnetic poles always come in north-south pairs. A 2-pole motor runs fastest, while higher pole counts yield slower, higher-torque operation. Standard industrial motors in 60 Hz systems run at 3600 RPM (2-pole), 1800 RPM (4-pole), 1200 RPM (6-pole), 900 RPM (8-pole), and so on.
In 50 Hz countries (Europe, Asia, Africa, Australia), these values drop proportionally: 3000, 1500, 1000, and 750 RPM respectively. Variable frequency drives (VFDs) allow engineers to adjust motor speed by varying the supply frequency, making this formula indispensable for drive system commissioning.
Angular velocity in radians per second (rad/s) is the SI unit for rotational speed, used in torque-power calculations where power P = Tω. Converting RPM to rad/s uses the factor 2π/60. This calculator provides both units for convenience in mechanical and electrical design workflows.
Motor speed selection affects conveyor belt velocity, pump flow rates, compressor throughput, and fan airflow. Selecting the wrong pole count for a given frequency results in either insufficient speed or excessive speed, leading to mechanical damage or process inefficiency. Always verify nameplate data against calculated synchronous speed when troubleshooting motor performance issues.
The synchronous speed formula derives from the physics of rotating magnetic fields. When a three-phase AC supply energizes the stator windings, it creates a magnetic field that rotates at a rate determined by the frequency and pole arrangement. For a 2-pole motor, the field completes one full revolution per electrical cycle, so at 60 Hz it rotates 60 times per second = 3600 RPM. For a 4-pole motor, one full mechanical revolution requires two electrical cycles, halving the speed to 1800 RPM. The general formula is Ns = 120f/P, where the factor 120 = 2 × 60 (converting Hz to RPM by multiplying by 60 seconds/minute, then dividing the cycle-to-revolution factor of 2 into the pole-pair count).
The synchronous speed result is the no-load theoretical maximum. Actual rotor speed will be 2-5% less for induction motors (due to slip). For a 4-pole, 60 Hz motor: synchronous = 1800 RPM, actual ≈ 1740-1760 RPM. Angular velocity in rad/s is used directly in the torque equation P = Tω when SI units are required.
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Standard US industrial motor — synchronous speed 1800 RPM, actual rotor speed approximately 1750-1775 RPM under load.
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Results
Common in European pumps and fans. Lower speed means higher torque for same power output.
Magnetic poles always exist in north-south pairs. A single north pole cannot exist without a corresponding south pole. Therefore, all motors have 2, 4, 6, 8... poles — never an odd number.
Synchronous speed is the speed of the rotating magnetic field. Actual rotor speed in an induction motor is slightly less — this difference is called slip. Slip is typically 2-5% at full load. Synchronous motors run at exactly synchronous speed by locking to the field.
A Variable Frequency Drive (VFD) changes the output frequency of the power supply to the motor. By reducing frequency below 60 Hz, the synchronous speed decreases proportionally. Most VFDs also vary voltage proportionally (V/Hz control) to maintain constant flux and torque.
Yes, but the motor will run at 5/6 of its rated speed (83.3%). A 4-pole motor designed for 1800 RPM at 60 Hz will run at 1500 RPM on 50 Hz. Torque remains similar but power output drops because P = Tω and ω is lower. Cooling may also be reduced for self-ventilated motors.
A pole pair is one north pole plus one south pole. A 4-pole motor has 2 pole pairs. The number of pole pairs (p) is P/2. Some textbooks write the speed formula as N = 60f/p using pole pairs instead of total poles.
Multiply RPM by 2π/60 ≈ 0.10472. So 1800 RPM × 0.10472 = 188.5 rad/s. This conversion is needed when calculating mechanical power from torque: P (watts) = Torque (N·m) × ω (rad/s).
4-pole motors (1800 RPM at 60 Hz, 1500 RPM at 50 Hz) are the most common in industrial applications. They offer a good balance of speed, torque, size, and efficiency. 2-pole motors are used for high-speed applications; 6- and 8-pole for lower-speed, higher-torque loads.
Roboculator Team
The Roboculator Team explains calculations, planning tools, and practical formulas in clear language for real-life situations.
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