Horsepower and Torque Calculator
Convert torque and rpm to horsepower and back in lb-ft, N·m, hp, kW and PS, with gearbox and electric motor tabs and the 5,252 rule explained. Fill in any two of power, torque and speed, and the third comes back in every unit, so a motor, reducer or pump drive can be checked on the spot.
Enter any two of power, torque and speed
Fill in two boxes and leave the third empty. Pick hp, kW or PS for power and lb-ft, lb-in or N·m for torque.
Result
Power
33.32 hp
24.85 kW · 33.78 PS
Torque
100 lb-ft
1,200 lb-in · 135.58 N·m
Speed (rpm)
1,750 rpm
Entered
Formula: P (kW) = T (N·m) × rpm ÷ 9,549 · hp = T (lb-ft) × rpm ÷ 5,252
At 5,252 rpm the hp and lb-ft numbers are equal. In kW and N·m they meet at 9,549 rpm.
Gearbox: speed and torque out
10 for a 10:1 reducer. Below 1 for a speed increaser.
95% is a placeholder; use the catalogue figure. Worm gears can be much lower, especially at high ratios.
Result
Output speed
175 rpm
Output torque
285 lb-ft
3,420 lb-in · 386.41 N·m
Input power
10 hp
7.45 kW · 10.13 PS
Output power
9.5 hp
Lost as heat: 0.5 hp
Electric motor: shaft power from volts and amps
Example values; read volts, full-load amps, power factor and efficiency off the motor nameplate.
From the nameplate. About 0.8 to 0.9 is common for induction motors at full load.
Nameplate efficiency (NEMA NOM. EFF. or IE class figure). 90% is a placeholder.
Nameplate full-load speed, to get the shaft torque.
Result
Shaft power
10.23 hp
7.63 kW · 10.38 PS
Shaft torque
30.5 lb-ft
366.51 lb-in · 41.41 N·m
Electrical input
8.48 kW
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How the horsepower calculator works
A turning shaft delivers power equal to torque times angular speed. One horsepower is 550 ft·lbf per second, or 33,000 ft·lbf per minute, and one revolution is 2π radians. Put together: hp = torque (lb-ft) × rpm ÷ 5,252. In metric units the same rule is kW = torque (N·m) × rpm ÷ 9,549.
Enter any two of power, torque and speed and leave the third empty. The calculator works in watts and newton metres inside, so you can mix units: type kW and get lb-ft, or type lb-in and get hp.
Worked examples
A shaft turning at 1,750 rpm with 100 lb-ft of torque: 100 × 1,750 ÷ 5,252 = 33.32 hp, which is 24.85 kW.
A 10 hp motor at a full-load speed of 1,750 rpm gives 10 × 5,252 ÷ 1,750 = 30.01 lb-ft (40.69 N·m) at the shaft. A 15 kW motor at 1,460 rpm gives 9,549 × 15 ÷ 1,460 = 98.11 N·m. That is the figure to check against a coupling or reducer's torque rating.
Why horsepower and torque cross at 5,252 rpm
Because hp = lb-ft × rpm ÷ 5,252, the two numbers are equal when rpm is exactly 5,252. Below that speed the torque number is bigger than the horsepower number; above it, horsepower is bigger. That is why every dyno chart plotted in hp and lb-ft on one scale shows the curves crossing at 5,252 rpm.
Nothing physical happens at that speed; it comes from the units. Plot kW and N·m instead and the curves cross at 9,549 rpm.
Gearbox: speed down, torque up
A reducer divides the speed by its ratio and multiplies the torque by the ratio, less the losses. With a 10:1 reducer at 95% efficiency, 1,750 rpm and 30 lb-ft in become 175 rpm and 30 × 10 × 0.95 = 285 lb-ft out.
Power never goes up through a gearbox: 10.00 hp in becomes 9.50 hp out, and the difference turns into heat. The efficiency box starts at 95% as a placeholder; take the real figure from the gearbox catalogue, because worm gears can be much lower, especially at high ratios.
Electric motor: shaft horsepower from volts and amps
Electrical input for a three-phase motor is √3 × volts × amps × power factor, and the shaft gets that times the motor efficiency. At 480 V, 12 A, a power factor of 0.85 and 90% efficiency: 8.48 kW in, 7.63 kW (10.23 hp) at the shaft, and 30.54 lb-ft at 1,760 rpm. Read all four values off the nameplate; the ones here are an example.
hp here means mechanical horsepower, 745.7 W. The metric horsepower on European data sheets (PS or CV) is 735.5 W, so 1 PS is 0.986 hp, and 1 kW is 1.341 hp.
Sources
Unit conversions: NIST Special Publication 811, Guide for the Use of the International System of Units, Appendix B (1 lbf·ft = 1.355818 N·m, 1 hp = 745.6999 W, 1 metric horsepower = 735.4988 W). Single- and three-phase power: IEEE Std 141 (Red Book), chapter 3. Gearbox and motor efficiencies are figures you enter from the manufacturer's catalogue or the motor nameplate.
Results are for steady running at the speed you enter. Starting torque, service factors and duty cycles are not included. Size motors, reducers and couplings from the manufacturer's catalogue and the application's service factor.
Selling motors, drives or power transmission parts? See what a sales engineer does, manufacturers' reps, industrial distributor sales, selling to engineers.
Keep the duty point from the plant walk
On a plant walk or a call, the customer reads out horsepower, speed and the torque they need faster than you can type it. Record the conversation with ParrotNotes and you get a transcript, a summary and the action items, so the numbers for the quote are already written down.
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