Motor Torque, Power & Speed Calculator

About the Motor Torque, Power & Speed Calculator

Torque, power and speed are tied together by one equation: P = T × ω, where ω is the shaft speed in radians per second. Enter any two of them — shaft power in kW, W, hp or PS, torque in N·m, lbf·ft, kgf·m and four other units, speed in rpm, rad/s or rev/s — and the calculator gives the third, converts it into every unit and shows the working.

For AC induction motors it also finds the synchronous speed from the poles and supply frequency, the slip and the rotor frequency. It estimates the full-load current from the voltage, efficiency and power factor, and the starting current for direct-on-line, star–delta and autotransformer starts. These are planning estimates: take the current for cables and protection from the motor nameplate.

The formulas

• Power, torque and speed: P = T × ω with ω = 2π × n ÷ 60 (P in W, T in N·m, n in rpm)
• SI shortcut: T [N·m] = 9549.3 × P [kW] ÷ n [rpm]; 9549.3 is 60,000 ÷ 2π
• US shortcut: T [lbf·ft] = 5252.1 × P [hp] ÷ n [rpm]; 5252.1 is 33,000 ÷ 2π, because 1 hp is 33,000 ft·lbf per minute
• Synchronous speed: n_s = 120 × f ÷ p (f in Hz, p the number of poles)
• Slip: s = (n_s − n) ÷ n_s; rotor frequency f_r = s × f
• Full-load current: I = P_out ÷ (η × √3 × V × PF) three-phase, P_out ÷ (η × V × PF) single-phase, P_out ÷ (η × V) DC
• Gearbox: n_out = n ÷ i and T_out = T × i × η_g

Units

Horsepower here is mechanical horsepower, 550 ft·lbf/s = 745.7 W; PS (metric horsepower, also CV) is 75 kgf·m/s = 735.5 W. For torque, 1 lbf·ft = 1.3558 N·m, 1 lbf·in = 0.11298 N·m, 1 kgf·m = 9.80665 N·m, 1 kgf·cm = 0.0980665 N·m and 1 ozf·in = 0.0070616 N·m — kgf·cm and ozf·in are common on small DC, servo and stepper motors. All factors follow from the exact foot (0.3048 m), pound-force (4.448 221 615 260 5 N) and standard gravity (9.806 65 m/s²).

Induction motor speed and slip

The rotor of an induction motor turns a little slower than the magnetic field. The field turns at the synchronous speed n_s = 120 × f ÷ p: 3,000, 1,500, 1,000 and 750 rpm for 2, 4, 6 and 8 poles on 50 Hz, and 3,600, 1,800, 1,200 and 900 rpm on 60 Hz. The difference is the slip, a few percent at full load for standard motors and more for small ones — so a 4-pole motor is rated around 1,450 rpm on 50 Hz or 1,750 rpm on 60 Hz. With Auto, the calculator picks the most poles whose synchronous speed is still above the speed you entered.

Starting current and starting methods

Started direct on line (DOL), an induction motor draws its locked-rotor current until it speeds up. IEC motor datasheets give it as a multiple of the rated current (I_A/I_N or I_s/I_n), often between 5 and 8; NEMA motors carry a code letter for the locked-rotor kVA per horsepower (NEMA MG 1; the same ranges are in NEC Table 430.7(B)).

• Star–delta: the windings start in star, so the line current and the starting torque are one third of DOL. The motor needs all six winding ends and a delta rating at the supply voltage
• Autotransformer at tap x: line current and torque are both x² of DOL — 42% at a 65% tap
• Soft starters and drives limit the current to a setting; see their manuals

Sources

• IEC 60034-1:2022, Rotating electrical machines — Part 1: Rating and performance
• NEMA MG 1, Motors and Generators — locked-rotor code letters
• NFPA 70, National Electrical Code: Table 430.7(B) (code letters), 430.6(A)(1) (table currents for conductors and short-circuit protection) and 430.6(A)(2) (nameplate current for overload protection)
• NIST Special Publication 811 (2008), Appendix B — conversion factors for horsepower, pound-force and kilogram-force

Limitations

• Full-load current is estimated from the efficiency and power factor you enter; the real current depends on the motor and how hard it is loaded. Set protection from the nameplate current.
• Starting currents assume a stiff supply: a weak supply lowers both the current and the voltage at the motor. The autotransformer figures ignore its magnetising current.
• Synchronous speed and slip apply to induction (asynchronous) motors. Synchronous, permanent-magnet, brushless DC and DC motors set their speed in other ways.
• Gearbox efficiency varies with load, speed and type (worm gears especially) — use the value from the gearbox datasheet.

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