Controlled engineering worksheet
Shaft Power–Torque–Speed
Calculate one positive magnitude from two compatible mechanical shaft quantities at the same shaft section and operating point. This worksheet does not convert electrical input power into shaft output.
Đầu vào
Result record
- Mechanical shaft power P
- —
- Shaft torque T
- —
- Rotational speed n
- —
- Angular velocity ω
- —
- Mechanical horsepower
- —
- Torque in lbf·ft
- —
Scope and limitations
What is calculated
For rotation about one axis, mechanical power transfer is the dot product of torque and angular velocity. For aligned positive magnitudes at a compatible operating point:
ω = 2πn / 60
P[kW] = 2π · n[r/min] · T[N·m] / 60000
Rearranging gives T = 60000P/(2πn) and n = 60000P/(2πT). The familiar factor 9549.296… is 60000/(2π); it is a unit-conversion constant, not an ISO tolerance or design rule.
What is not calculated
- Electrical input, hydraulic input, fuel power, motor efficiency or transmission losses.
- Starting torque, accelerating torque, inertia, duty cycle, thermal rating, service factor or available torque from a machine curve.
- Conformity with a motor, gearbox, coupling, shaft or safety standard.
T(t)ω(t). It is not necessarily the product of average torque and average speed. Use synchronized time histories or a justified cycle model.Independent worked example
For mechanical shaft power P = 15 kW và tốc độ n = 1500 r/min at the same point:
T = 15000 / 157.0796327 = 95.49296586 N·m
Displayed digits do not create measurement accuracy. Round the result according to the uncertainty and resolution of the input data.
Sources and normative status
| Nguồn | Verified use on this page | Status / boundary |
|---|---|---|
| MIT OpenCourseWare, 2.004, Lecture 14 | Derives rotational mechanical power P = TΩ and explains the sign of power flow. | Open university course note; formula basis, not a conformity standard. |
| BIPM SI Brochure, 9th edition, version 4.01 (2026) | SI units: torque N·m, angular velocity rad/s, power W; distinguishes angular velocity from ordinary frequency. | Official SI publication. |
| NIST SP 811, Appendix B.8 | Published factors: 1 hp (550 ft·lbf/s) = 745.6999 W; 1 lbf·ft = 1.355818 N·m; 1 r/min = 0.1047198 rad/s. | Official conversion table; factors are printed to stated precision. |
| ISO 80000-3:2019 + Amd 1:2025 | Official lifecycle and scope card for space/time quantities and units. | Published. Clause-level use requires the licensed controlled text. |
| ISO 80000-4:2019 + Amd 1:2025 | Official lifecycle and scope card for mechanics quantities and units. | Published; edition 3 is under development as ISO/AWI 80000-4. No ISO compliance claim is made here. |
Practical questions
Can motor electrical input power be entered?
No. Obtain mechanical shaft output at the same operating point, or apply a separately justified efficiency/loss model before using this worksheet.
Why are zero values rejected?
Each solve mode divides by speed or torque, and the worksheet is deliberately limited to positive operating magnitudes. At standstill, the relationship can report zero instantaneous shaft power even when nonzero torque exists; it cannot infer speed or torque by division.
Can average torque and average speed be multiplied?
Only when a justified steady or cycle model makes them compatible. Otherwise calculate or measure the time average of the instantaneous product.
