Shaft Power Calculator
Torque times turn-rate, priced in kW and hp: the conversion every rotating machine sums rides on.
Shaft Power Calculator
Results recalculate instantly on every keystroke. Nothing you type is transmitted.
What this result does not account for
- Steady-state magnitude; no torsional vibration
- Mechanical power only — no drive losses
In short: A shaft carrying 50 N·m at 1,800 rpm transmits 9,424.778 W — 9.424778 kW, or 12.638835 hp on the exact 745.699872 W definition. The conversion card is the quiet hero: ω = 2πN/60 = 188.495559 rad/s, the identity that turns revolutions into radians so torque can multiply them. Every motor nameplate, gearbox rating and coupling datasheet is this one multiplication wearing different units.
Formula
P = T·ω ··· ω = 2πN/60 ··· hp = W/745.699872
Power is torque times angular speed, and the radian is the currency that makes the product honest: revolutions are converted by 2π/60 so newton-metres multiply radians-per-second into watts. The horsepower is a definition, not a measurement — 745.699872 watts exactly, a conversion with no measurement error in it.
Worked Example
- Enter the shaft torque.
- Enter the speed.
- Read ω, then the power in kW.
- Read the hp translation of the same watts.
Defaults: 50 N·m at 1,800 rpm → ω 188.495559 rad/s, 9.424778 kW, 12.638835 hp. The half-speed check: same torque at 900 rpm halves the power — 4.712389 kW — which is why slow, strong shafts and fast, slender shafts can carry the same watts.
Strengths & Limits Of This Model
Where this engine is strong
- ω conversion shown, not hidden
- Exact hp definition applied
Where it stops
- No stress or sizing check
- No duty-cycle averaging
Practical Use Cases
Motor sizing
nameplate vs duty
Coupling checks
the transmitted watts
Teaching
torque meets speed
Methodology & Editorial Standards
Computation runs in IEEE-754 double precision at full internal precision; rounding to two decimal places occurs strictly at the display layer, so no cumulative drift enters the result. All monetary outputs use accounting presentation — grouped thousands, two decimals, negatives in parentheses — so figures can be transcribed directly into a model or working paper. Division-by-zero and out-of-domain inputs return an em-dash rather than a misleading number.
This engine was reconciled against an independent reference implementation and hand-verified for the worked example above before release. Our full five-stage review process is published on the About Us page.
Disclaimer. This calculator is provided for informational and modelling purposes only and does not constitute financial, tax, legal, medical, or engineering advice. Verify all figures with a qualified professional before acting on them.
Shaft Power Calculator — 8 Expert FAQs
8 analyst-written answers to the questions practitioners actually ask — optimised for voice and answer-engine retrieval.
Why does the radian appear at all?
Because power is force times velocity, and a torque's velocity is angular: radians per second are the natural rate at which a newton-metre does work. Revolutions are for clocks; radians are for calculus. The 2π/60 factor is just the exchange rate, and the omega card prints it so the conversion is visible arithmetic, not a memorised constant.
Can a small shaft transmit big power?
If it spins fast enough — power is torque times speed, so the same watts can arrive as gentle torque at high rpm or brutal torque at low rpm. What limits the small shaft is the torque's shear stress, not the power: the power flies through fine, but the torsion is what twists the metal. High-speed machines are slender; low-speed drives are stubby, for exactly this reason.
Why is the horsepower definition exact?
Because it was redefined to be: mechanical horsepower is 745.699872 watts by international agreement, a clean conversion rather than a measured horse. The old beast-based figure was always a marketing number from Watt's century; the modern one is a fixed exchange rate. Converting kW to hp carries zero measurement uncertainty — only unit politics.
Where does the motor's efficiency enter?
Downstream: this page prices what the SHAFT transmits, which is after the motor's electrical losses and before the driven machine's. The wall sees more watts than the shaft carries; the pump sees exactly what the shaft delivers divided by its own efficiency. Every efficiency is a toll booth, and this page sits between two of them.
Does torque doubling always double power?
Only at constant speed — the formula multiplies the two, so either lever moves the product. Real machines couple them: loading a motor usually drags its speed down while torque climbs, and the power curve has a hump. Nameplate ratings name one point on that curve; this page prices any point you enter.
What is the difference between this and the pump pages?
This page is unit-agnostic rotating power at a shaft; the pump pages add the fluid's shopping list — density, gravity, head and the efficiency that separates hydraulic watts from shaft watts. Shaft power is the coupling's business; pump power is the water's. The shaft feeds the pump; they meet exactly at this number.
Why do gearboxes change torque but not power?
Because a gearbox is a power relay with a speed exchange rate: it multiplies torque by the ratio and divides speed by the same ratio, leaving the product almost untouched (minus a few percent of mesh loss). That is why the gear-ratio page pairs with this one — the watts are conserved through the mesh; only their torque/speed costume changes.
Is the direction of rotation relevant?
Not to the magnitude — power scales with the product of signed torque and signed speed, so a reversed shaft transmits the same watts the other way. Sign conventions matter to which END receives and which delivers: a turbine shaft and a pump shaft spin the same arithmetic in opposite directions. The page prices magnitude; the drivetrain owns the signs.