About Torque, Horsepower & RPM Calculator
The torque, horsepower and RPM calculator solves the fundamental shaft-power relation P = T × ω in whichever direction you need: enter any two of torque, speed, and power, and it returns the third — always in both unit systems. In imperial units HP = T(ft·lb) × RPM ÷ 5252.113, where 5252.113 is exactly 33,000 ÷ 2π: one horsepower is 33,000 ft·lb of work per minute by definition, and a shaft turning at N RPM sweeps 2πN radians per minute.
The metric twin is kW = T(N·m) × RPM ÷ 9549.297, with 9549.297 exactly 60,000 ÷ 2π. The 5252 constant explains dyno-chart folklore: torque (in ft·lb) and horsepower curves always cross at 5252 RPM, because that is where T × RPM ÷ 5252.113 = T. Below the crossover an engine makes more torque than horsepower; above it, the reverse.
How It Works
- Pick what to solve for: power from torque and speed (the dyno direction), torque from power and speed (the motor-sizing direction — what twist does a 100 HP motor deliver at 5252 RPM?), or speed from power and torque.
- Pick the unit system for your inputs: imperial takes ft·lb and HP, metric takes N·m and kW. The results always show both systems, converted through 1 ft·lb = 1.35582 N·m and 1 hp = 745.6999 W (NIST values).
- The math is one identity in three arrangements: HP = T×RPM/5252.113, T = HP×5252.113/RPM, RPM = HP×5252.113/T — and identically with kW, N·m, and 9549.297. No efficiency enters; this is the shaft-side relation, so apply motor or gearbox efficiency separately.
- Read the chart for intuition: at 1800 RPM (the 4-pole induction-motor speed) every 100 ft·lb of torque is about 34.3 HP. Halve the speed and the same torque makes half the power.
Worked Example
A dyno pull shows 300 ft·lb at 2626 RPM. Power = 300 × 2626 ÷ 5252.113 = 150.0 HP — exactly half the crossover speed, so horsepower reads exactly half the torque number. The same operating point in metric: 300 ft·lb = 406.7 N·m, and 406.7 × 2626 ÷ 9549.297 = 111.8 kW, which is 150.0 HP × 0.7457. Running the identity backwards for motor sizing: a 100 HP motor at 5252 RPM delivers 100 × 5252.113 ÷ 5252 = 100.0 ft·lb — the crossover in action.
Torque to horsepower chart at 1800 RPM
Shaft power for common torque values at 1800 RPM — the synchronous speed of a 4-pole 60 Hz induction motor and the most common industrial shaft speed. At this speed the shortcut is HP ≈ torque ÷ 2.92. Enter your own speed in the tool; power scales linearly with RPM.
| Torque (ft·lb) | Power (HP) | Power (kW) |
|---|---|---|
| 50 ft·lb | 17.14 | 12.78 |
| 100 ft·lb | 34.27 | 25.56 |
| 200 ft·lb | 68.54 | 51.11 |
| 300 ft·lb | 102.82 | 76.67 |
| 500 ft·lb | 171.36 | 127.78 |
Formulas
- Horsepower from torque and speed
HP = T × RPM / 5252.113- Kilowatts from torque and speed
kW = T × RPM / 9549.297- Rearrangements
T = P × 5252.113 / RPM; RPM = P × 5252.113 / T- Unit bridges
1 ft·lb = 1.35582 N·m; 1 hp = 0.745700 kW
Standards & References
- P = T·ω shaft-power identity; 1 mechanical horsepower = 33,000 ft·lb/min = 550 ft·lb/s (definition, per NIST SP 811 and any machine-design text)
- Constants stated exactly: 5252.1131 = 33000/(2π) and 9549.2966 = 60000/(2π) — derivations in the calculator source
- Unit conversions per NIST SP 811 Appendix B: 1 ft·lbf = 1.355818 N·m, 1 hp = 745.6999 W
Frequently Asked Questions
How do I convert torque and RPM to horsepower?
Multiply torque (in ft·lb) by RPM and divide by 5252.113: a shaft carrying 300 ft·lb at 2626 RPM transmits 300 × 2626 ÷ 5252.113 = 150 HP. The constant is exactly 33,000 ÷ 2π — one horsepower is defined as 33,000 ft·lb of work per minute, and each revolution is 2π radians. In metric, divide T(N·m) × RPM by 9549.297 to get kilowatts.
Why do torque and horsepower curves always cross at 5252 RPM?
Because HP = T × RPM ÷ 5252.113: when RPM equals 5252, HP equals T numerically, so the two curves (plotted in ft·lb and HP on the same axis) must intersect there. It is an artifact of the imperial units, not engine physics — plot the same engine in N·m and kW and the curves cross elsewhere (at 9549 RPM, beyond most engines).
How much torque does an electric motor produce?
Rearrange to T = HP × 5252.113 ÷ RPM. A 100 HP motor at 1800 RPM delivers about 292 ft·lb continuously; the same 100 HP at 3600 RPM only 146 ft·lb. That inverse relation is why slow, high-torque loads (mixers, crushers, conveyors) pair motors with gear reductions rather than buying bigger motors — a 3:1 reduction triples shaft torque at a third the speed, keeping power constant.
Does this calculation include efficiency?
No — P = T·ω is the relation at one shaft, exact by definition. Losses appear between shafts: a motor's electrical input exceeds its shaft output by the motor efficiency, and a gearbox's output power is input × efficiency. Apply those separately (the gear ratio calculator handles the gearbox side); this tool converts among torque, speed, and power at the point where you know two of them.
What is the metric equivalent of the 5252 rule?
kW = T(N·m) × RPM ÷ 9549.297, with the constant exactly 60,000 ÷ 2π. Handy anchors: 100 N·m at 3000 RPM is 31.4 kW; at the common 1500 RPM (4-pole, 50 Hz) each 100 N·m is 15.7 kW. The calculator always displays both systems, so dyno sheets and motor nameplates from either tradition reconcile instantly.
Which horsepower does this calculator use?
Mechanical (imperial) horsepower: 550 ft·lb/s = 745.6999 W. That is the HP on US motor nameplates and dyno charts. Metric horsepower (PS/CV, 735.5 W) is about 1.4% larger per unit; if you need PS, convert from the kW readout (PS = kW ÷ 0.7355) rather than the HP one.