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MODULE 1 · UNIT 1 OF 5

Torque, Power, and Speed

approx. 6 min · Learning goals, example, knowledge check

Learning goals — after this unit, you will be able to …

  • Apply the relationship between torque M, power P, and speed n using the formula M = 9550 · P / n;
  • Rearrange the formula according to the variable you are looking for (M, P, or n);
  • Classify the terms “rated speed” and “rated torque” as reference values for motor selection.

Three variables, one formula

Torque, power, and speed are related in every rotating drive via a single formula. If you know two of the three quantities, you can calculate the third—the basis of every motor design. In drive technology, the following formula has become standard for the commonly used units (torque M in Nm, power P in kW, speed n in min⁻¹):

M = 9550 · P / n

M = Torque (Nm) · P = Power (kW) · n = Speed (min⁻¹)

The number 9550 is not a measured quantity, but a conversion constant (60 · 1,000 / 2π ≈ 9,549.3)—it is solely responsible for ensuring that the formula works with the units commonly used in practice, kW and min⁻¹. Depending on which quantity is being calculated, the same formula can be rearranged to find P or n:

P = M · n / 9550 ·  n = 9550 · P / M

The same three quantities, each expressed in terms of the variable of interest.

Rated Speed and Rated Torque

The rated speed is the speed at which a motor can continuously deliver its rated power and rated torque under specified rated conditions—it is indicated on the nameplate and serves as the reference point for all other performance data of the drive. The rated torque is the corresponding torque that can be transmitted continuously. For short periods, a motor can deliver more than its rated torque. The magnitude and duration are specified in the data sheet and depend on the motor type (standard motors according to IEC 60034-1 deliver at least 1.6 times the rated torque for 15 seconds; servo motors often deliver significantly more). The breakdown torque of an induction motor—typically 2 to 3 times the rated torque—is the limit at which it stops; it is not an operating value.

Mnemonic

M = 9550 · P / n – At a given power, torque decreases as speed increases. The rated torque is the continuous value; the data sheet specifies the maximum short-term overload allowed (for standard motors, at least 1.6 × for 15 s according to IEC 60034-1). The 2.0(3.0 × for an induction motor) is the breakdown torque; it is not a permissible operating value.

Worked example

Sketch: Motor with output shaftRotating arrow on the shaft with speed n (top) and torque M (bottom), both in the same direction of rotation; the block arrow P represents the power output.

Given

A motor delivers a power output of P = 7.5 kW at a speed of n = 1,450 min⁻¹.

Calculation

M = 9550 · P / n = 9550 · 7.5 / 1,450 ≈ 49.4 Nm

To verify calculations using your own values: Torque calculator (opens in a new tab)

Knowledge check

Answer all three questions, then click "Check". From 2 of 3 correct answers, the unit counts as completed. You can retry at any time.

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Question 1 of 3: A motor delivers P = 5.5 kW at n = 1,750 min⁻¹. What torque M does it deliver? (M = 9550 · P / n)
Nm
Explanation

M = 9550 · P / n = 9550 · 5.5 / 1,750 ≈ 30.0 Nm.

Source: Torque Calculator →
Question 2 of 3: What is the form of M = 9550 · P / n when expressed in terms of power P?
Explanation

Rearranging for P yields P = M · n / 9550—the same formula, but with the unknown variable isolated.

Source: Torque Calculator →
Question 3 of 3: A motor with a rated speed of 1,500 min⁻¹ drives a shaft via a gearbox with a gear ratio of i = 10. What is the output speed in min⁻¹?
min⁻¹
Explanation

The output speed is calculated by dividing the rated speed by the gear ratio: 1,500 / 10 = 150 min⁻¹.

Source: Glossary: Rated speed →

Please answer all three questions to activate "Check".

Further reading (optional)

Online Calculator: Torque Calculator (opens in a new tab) Glossary: Rated torque (opens in a new tab) Glossary: Rated speed (opens in a new tab)

Learning purpose: calculation methods and figures are simplified teaching examples. For a real machine, the manufacturer’s specifications, the relevant standards and a check by a qualified person apply.

Curriculum v0.1 (Beta) · Status 17.09.2026 · content carefully prepared and reviewed – final sign-off to follow

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