How do I calculate torque from power and speed?

Torque (Nm) = 9549 × Power (kW) / Speed (RPM). This is derived from the fundamental relationship P = T × ω, where ω = 2πn/60. The constant 9549 simplifies the calculation: 60000/(2π) ≈ 9549.

What is the relationship between kW and Nm?

Power in kW and torque in Nm are related through rotational speed: P = T × n / 9549. At any given speed, higher torque means higher power. At constant power, torque decreases as speed increases (inverse relationship).

What is the 9549 constant?

The constant 9549 comes from the unit conversion: 9549 ≈ 60000/(2π). It appears when converting between kW, Nm, and RPM. The exact value is 9549.2966... Using P(kW) = T(Nm) × n(RPM) / 9549.

How do I convert kW to hp?

1 kW = 1.341 hp (mechanical horsepower). Conversely, 1 hp = 0.7457 kW. This is the mechanical (imperial) horsepower. Metric horsepower (PS) is slightly different: 1 PS = 0.7355 kW.

Does torque change with speed?

For a given power source, yes. Electric motors have a rated torque at rated speed. At constant power output, torque is inversely proportional to speed: T = 9549 × P / n. However, actual motor torque curves vary — induction motors have peak torque (breakdown torque) at a specific slip speed.

Free Engineering Tool

Torque — Power — Speed Calculator

Convert between torque, power, and rotational speed. Given any two, calculate the third. Supports kW, Nm, RPM with imperial conversions.

kW ↔ Nm ↔ RPM hp & ft·lbf T = 9549 × P / n

Results

Calculated Value

—

Torque

—

Power

—

Speed

—

Angular Velocity ω

—

Power (Imperial)

—

Torque (Imperial)

—

Fundamental Relationship

The relationship between power, torque, and rotational speed is:

Where ω = 2πn/60 is the angular velocity in rad/s, and n is speed in RPM.

Practical Formulas (with constant 9549)

Substituting and rearranging for each unknown, using the constant 9549 ≈ 60000/(2π):

Unit Conversions

From	To	Factor
kW	hp (mechanical)	× 1.341
hp	kW	× 0.7457
Nm	ft·lbf	× 0.7376
ft·lbf	Nm	× 1.3558
RPM	rad/s	× 2π/60

Practical Example

Example — 15 kW motor at 1500 RPM

Given: P = 15 kW, n = 1500 RPM

T = 9549 × 15 / 1500 = 95.49 Nm

ω = 2π × 1500 / 60 = 157.08 rad/s

Power in hp: 15 × 1.341 = 20.12 hp

Torque in ft·lbf: 95.49 × 0.7376 = 70.44 ft·lbf

💡 The 9549 constant: This convenient number equals 60000/(2π) ≈ 9549.2966. It eliminates the need to convert RPM to rad/s explicitly. It works when power is in kW, torque in Nm, and speed in RPM.