Torque from power and speed
T = P x 60000 / (2 x pi x n) = 9549.3 x P / n: 75 kW at 1500 1/min is 9549.3 x 75 / 1500 = 477.5 N·m. Power in kW, speed in 1/min, torque in N·m; 9549.3 = 60000 / (2 x pi).
Reference tool — arithmetic, not a shaft or coupling selection
Shaft torque calculator.
Torque · power · speed · gear output
Power, torque, speed.
Type a line (75 kW 1500 1/min; 477 N·m 1500 r/min; 250 kW 3200 N·m; 75 kW 1500 1/min ratio 4.5 efficiency 97 %) or fill in the fields: the line and the fields stay in step.
Examples:
All 130 engineering tools
Enter any two of the shaft power, the torque and the speed, and the calculator works out the third: T = 9549.3 x P / n, with P in kW, n in 1/min and T in N·m. Where the shaft drives through a gear or belt drive, add the ratio and the efficiency from the maker data, and it gives the torque, speed and power at the output. The working is shown with your numbers, and the result is a line you can copy or add to a request.
Arithmetic only: the calculator works out the steady torque that carries a stated power at a stated speed. It does not check the strength of a shaft, size a key or a coupling, or give typical torques, speeds, efficiencies or shaft sizes; the data of the coupling, key and gear unit makers and the class rules govern.
How it is worked out
Power, torque, speed.
Power or speed
P = T x n / 9549.3: 477 N·m at 1500 1/min is 74.93 kW. n = 9549.3 x P / T: 250 kW with 3200 N·m is 746 1/min. Any two give the third; three entered values are checked against each other.
Gear or belt output
n_out = n / i, T_out = T x i x efficiency, P_out = P x efficiency: 75 kW at 1500 1/min through 4.5:1 at 97 % is 333.3 1/min, 2084 N·m and 72.75 kW. You enter the efficiency; without it the output torque is shown without losses.
| Unit | Equals | Basis |
|---|---|---|
| 9549.3 | 60000 / (2 x pi) = 9549.2966 | P [kW] = T [N·m] x n [1/min] / 9549.3 |
| 1 kgf·m | 9.80665 N·m | standard gravity, 9.80665 m/s2, exact |
| 1 lbf·ft | 1.3558179483 N·m | 0.45359237 kg x 9.80665 m/s2 x 0.3048 m, exact |
| 1 lbf·in | 0.112984829 N·m | 1/12 of the lbf·ft |
| 1 hp | 745.69987 W | mechanical horsepower, 550 ft·lbf/s |
| 1 PS | 735.49875 W | metric horsepower, 75 kgf·m/s, exact |
| 1 rad/s | 9.5493 1/min | 60 / (2 x pi) |
| 1 Hz | 60 1/min | one revolution of the shaft a second, not the supply frequency |
1/min, r/min and min-1 are the same unit. hp and PS differ: hp is the mechanical horsepower, PS the metric one.
Sources
The relation of power, torque and speed, P = T x 2 x pi x n / 60, agrees in the Engineering ToolBox reference (torque and the power transmitted) and in the Wikipedia article Torque (power and torque with the speed in revolutions a minute; the US form with the divisor 5252 also checks the lbf·ft factor). For a gear, the output speed n / i, the output torque T x i x efficiency and the output power P x efficiency agree in the Engineering ToolBox gear reducing formulas and in the Firgelli Automations transmission calculator; without losses the torque ratio equals the speed ratio (Wikipedia, Gear train). The torque form also follows from the definitions: the output power is the input power times the efficiency, the output speed is n / i, and torque is power over angular speed, so T_out = T x i x efficiency. 1 kgf·m = 9.80665 N·m, 1 lbf·ft = 1.3558179483314004 N·m, 1 lbf·in = 0.1129848290276167 N·m, 1 hp = 745.69987158 W, 1 PS = 735.49875 W and 1 r/min = 2 x pi / 60 rad/s follow appendix B of NIST SP 811 and the Wikipedia articles on the kilogram-force, the pound-foot, horsepower and revolutions per minute. The data of the coupling, key and gear unit makers and the class rules always come first.
Before you work it out
Questions about shaft torque
How is the torque worked out from the power and the speed?
The torque is T = P x 60000 / (2 x pi x n) = 9549.3 x P / n, with the power P in kW, the speed n in 1/min (also written r/min or min-1) and the torque T in N·m; 9549.3 is 60000 / (2 x pi). A shaft carrying 75 kW at 1500 1/min: 9549.3 x 75 / 1500 = 477.5 N·m. It is the same relation as power = torque x angular speed: 1500 1/min is 157.08 rad/s, and 477.46 N·m x 157.08 rad/s = 75000 W.
How do I find the power from the torque and the speed, or the speed from the power and the torque?
Turn the formula round: P = T x n / 9549.3 and n = 9549.3 x P / T. 477 N·m at 1500 1/min is 477 x 1500 / 9549.3 = 74.93 kW; 250 kW carried with 3200 N·m means 9549.3 x 250 / 3200 = 746 1/min. Any two of the three give the third. When all three are entered, the calculator checks that they agree within 1 %, and otherwise says which values do not fit together.
What happens to the torque through a gear or belt drive?
With the ratio i, the input speed over the output speed, the output speed is n_out = n_in / i, the output torque is T_out = T_in x i x efficiency, and the output power is P_in x efficiency. 75 kW at 1500 1/min through a 4.5:1 reduction at an efficiency of 97 %: 1500 / 4.5 = 333.3 1/min, 477.46 x 4.5 x 0.97 = 2084 N·m and 75 x 0.97 = 72.75 kW. The efficiency is yours to enter from the maker data of the gear unit or belt drive: the calculator gives no typical efficiencies, and without one it shows the output torque without losses.
Which units does the calculator take?
Power in kW, W, hp or PS. Torque in N·m, kN·m, kgf·m (9.80665 N·m exactly), lbf·ft (1.3558179483 N·m) or lbf·in (0.1129848290 N·m). Speed in 1/min, also written r/min or min-1, in rad/s (1 rad/s = 60 / (2 x pi) = 9.5493 1/min) or in Hz, revolutions a second (1 Hz = 60 1/min). The ratio as a number (ratio 4.5) or as 4.5:1, the efficiency in per cent.
Is hp the same as PS?
No. The mechanical horsepower (hp) is 550 ft·lbf/s = 745.69987 W; the metric horsepower (PS, also CV, and the Russian l. s.) is 75 kgf·m/s = 735.49875 W, about 1.4 % less. 100 hp is 74.57 kW and 100 PS is 73.55 kW. The calculator reads hp as the mechanical horsepower; write PS for the metric one.
Does the calculator size the shaft, the key or the coupling?
No. It works out the steady torque that carries a stated power at a stated speed, nothing more. It does not check the strength of a shaft, size a key or a coupling, or give typical torques, speeds or shaft sizes; starting, peak and alternating torques are higher than the steady figure. The data of the coupling, key and gear unit makers and the class rules govern; the torque line is a starting point for a request.
A coupling, a gear unit part or a shaft seal?
Send the line and the machine plate.
The calculator works out power, torque and speed only. When a coupling, its elastic elements, gear unit parts or a shaft seal are needed, send the line from the calculator with a photograph of the motor, gear unit or coupling plate, and Vessel Core checks the details before an offer goes back.
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