30 kW at 1200 rpm: What Torque Reaches the Shaft?

Power alone does not size a shaft or coupling. Pair it with rotational speed to find the twisting moment the drivetrain must transmit.

1. Record Power and Speed

The shaft delivers 30 kW at 1200 rpm. Keep the units visible before substituting anything into the rotational power equation.

2. Convert Kilowatts to Watts

Use coherent SI units: 30 kW becomes 30,000 W. Mixing kilowatts with newton-metres and radians per second creates a thousandfold error.

3. Use Rotational Power

For a rotating shaft, power equals torque times angular speed: P = Tω. Rearranging gives T = P/ω.

4. Convert rpm to Angular Speed

Use ω = 2πN/60. At 1200 rpm, the shaft turns at about 125.66 radians per second.

5. Divide Power by Speed

T = 30,000/125.66, so the transmitted torque is about 238.7 N·m. A quick unit check leaves newton-metres.

6. Reject the rpm Shortcut

Do not divide watts directly by rpm. Revolutions per minute must become radians per second before P = Tω is dimensionally consistent.

7. Test the Inverse Trend

At constant power, halving speed to 600 rpm doubles torque to about 477.5 N·m. That inverse trend is a strong reasonableness check.

Convert First. Calculate Once. Check the Trend.

Write P = Tω, convert kW and rpm, solve for torque, then verify that lower speed means higher torque at the same power.