Shaft Torque Calculator Formula
Understand the math behind the shaft torque calculator. Each variable explained with a worked example.
Formulas Used
Shaft Torque
torque = power_kw * 1000 * 60 / (2 * pi * rpm)Variables
| Variable | Description | Default |
|---|---|---|
power_kw | Shaft Power (P)(kW) | 15 |
rpm | Rotational Speed(RPM) | 1500 |
How It Works
Shaft Torque from Power and Speed
When power and speed are known, torque can be back-calculated.
Formula
T = P / omega = P x 60 / (2 pi N)
where P is power in watts, N is speed in RPM, and T is torque in N-m. This is essential for sizing shafts, couplings, and gearboxes.
Worked Example
A 15 kW motor running at 1500 RPM.
- 01P = 15,000 W
- 02T = 15,000 x 60 / (2 x pi x 1500)
- 03T = 900,000 / 9424.8 = 95.49 N-m
Frequently Asked Questions
Why does torque increase when speed decreases?
For a constant power source, torque and speed are inversely related: T = P/omega. Gearboxes exploit this by reducing speed to increase torque for heavy-duty applications.
How do I size a shaft for this torque?
The shaft diameter depends on the allowable shear stress: d = (16T / (pi tau_allow))^(1/3). For solid circular shafts, this comes from the torsion formula tau = Tc/J.
What is the relationship between torque in N-m and lb-ft?
1 N-m = 0.7376 lb-ft. Multiply N-m by 0.7376 to convert to lb-ft, or divide lb-ft by 0.7376 to get N-m.
Learn More
Guide
How to Calculate Gear Ratios: Complete Engineering Guide
Learn how to calculate gear ratios for spur gears, compound gear trains, and planetary systems. Covers speed, torque, and efficiency relationships with practical examples.
Ready to run the numbers?
Open Shaft Torque Calculator