Shaft Power & Torque Calculator
Calculate shaft torque from power and speed, power from torque and speed, or the shaft speed from power and torque. Supports kW/W/hp/PS, N·m/kgf·m/lb·ft/lb·in and rpm/rad·s⁻¹/Hz, reports every result in both metric and imperial units, and adds the input power a drive must supply at a given efficiency.
Input
Any two of power, torque and speed determine the third.
Combined motor/gearbox/coupling efficiency. Sets the input power a drive must supply. Leave at 100% for the ideal case.
Output
| Quantity | Value | Other units |
|---|---|---|
| No data yet | ||
Guides
Power, torque and rotational speed on a shaft are three faces of one relationship: P = T × ω. Give this calculator any two of them and it returns the third, along with every result restated in the units the rest of your paperwork uses.
How to use it
- Pick what you want to solve for — torque, power, or speed.
- Enter the two values you already know, each with its own unit. Power takes kW, W, mechanical horsepower (hp) or metric horsepower (PS); torque takes N·m, kgf·m, lb·ft or lb·in; speed takes rpm, rad/s or Hz.
- Optionally drop the drive efficiency below 100% to see the input power a motor has to supply once gearbox, coupling and belt losses are accounted for.
The results table gives torque, shaft power, rotational speed and angular velocity, each with the equivalent value in every other supported unit, plus a formula breakdown you can copy into a calculation sheet. The table downloads as CSV.
The formulas
The single relationship behind all three modes is:
ω = 2π × N / 60— angular velocity in rad/s from speed in rpmP = T × ω— power in watts from torque in N·m and ω in rad/s
Rearranged into the shortcut engineers actually memorise, with power in kW and speed in rpm:
T (N·m) = 9549.3 × P (kW) / N (rpm)P (kW) = T (N·m) × N (rpm) / 9549.3N (rpm) = 9549.3 × P (kW) / T (N·m)
Why does efficiency matter?
The bare formula describes an ideal shaft. A real drive train loses power in the motor, the gearbox, the couplings and the belts, so the motor has to supply more than the shaft delivers: P_input = P_shaft / η. Set the efficiency slider to your combined drivetrain efficiency (85–95% is typical for a geared motor) and the calculator adds the required input power and the power lost as heat.
Is this enough to size a motor?
No — it's the starting point. Real motor selection also needs a service factor for shock loading, duty cycle, starting torque, and ambient/thermal derating. Use this figure as the continuous-running requirement and apply your standard's service factor on top.
mechanical hp or metric PS?
They aren't the same: 1 hp = 745.70 W, 1 PS = 735.50 W, a difference of about 1.4%. The calculator reports both so you never have to guess which one a datasheet meant.
Privacy
Everything is calculated in your browser. No values are sent to a server.
Related tools
Sizing a belt drive off the back of this figure? The Belt Length Calculator works out belt length, wrap angles and belt speed from your pulley diameters. For tightening the fasteners that hold the assembly together, use the Bolt Torque Calculator, and to move a torque figure between unit systems on its own, the Torque Converter does just that.