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Technical guide · method and practical tips

Torque, power and rotational speed: understanding the relations

Torque describes rotational effort, speed describes how fast the shaft turns, and power combines both. The main trap is assuming that high torque always means a more powerful motor.

Reviewed

Low gearHigh gearcranksetwheelwheel speed ↓wheel torque ↑cranksetwheelwheel speed ↑wheel torque ↓At comparable power: gaining torque means losing speed.
The transmission ratio exchanges speed for torque; it does not create power.

Three different quantities

Torque T, expressed in N·m, measures the ability of a force to rotate a shaft. Speed n, commonly expressed in rpm, counts revolutions per minute. Power P, expressed in W or kW, measures the rate of mechanical energy transfer.

Two motors with the same power can therefore deliver very different torque if they rotate at different speeds.

The fundamental relation

P = T · ω = 2π · T · n / 60

The formula P = T·ω uses angular speed ω in rad/s. When a motor plate gives n in rpm, use ω = 2πn/60 before multiplying by torque.

A quick engineering check is T(N·m) ≈ 9550 × P(kW) / n(rpm).

What a reducer actually does

A reducer lowers output speed and increases theoretical torque approximately in proportion to its ratio. It does not create energy: output power is below input power because of losses.

Keep the kinematic ratio, which links speeds, separate from mechanical efficiency, which represents losses.

Common mistakes

The most common errors come from incorrect conversion or comparisons made at different speeds.

  • Using rpm directly in P = T·ω.
  • Comparing two torque values without comparing their speeds.
  • Confusing rated power with transmitted power.
  • Ignoring motor, reducer or belt efficiency.

Numerical application

Worked example: finding motor torque

A motor delivers 15 kW at 1,500 rpm. Find the torque available on its shaft before the reducer.

  1. Convert power: P = 15,000 W.
  2. Convert speed: ω = 2π × 1,500 / 60 = 157.08 rad/s.
  3. Apply T = P/ω = 15,000 / 157.08.
  4. Keep a number of digits consistent with the input data.

Result: Torque is approximately 95.5 N·m. With a 5:1 reducer at 90% efficiency, corrected output torque would be about 430 N·m.

Method adapted from the OpenStax chapter on rotational work and power. Open exact source ↗

For checking and further study

Direct references

Each link points to the exact course, standard or publication page used, rather than a generic homepage.

  1. Work and Power for Rotational MotionOpenStax — University Physics Volume 1Open textbook section on work, torque and rotational power.
  2. Mechanics & Materials IMIT OpenCourseWareUniversity course on applied mechanics and mechanics of materials.
  3. The International System of Units, 9th editionInternational Bureau of Weights and Measures (BIPM)Official reference for coherent units, symbols and conversions.
  4. NIST Special Publication 811 — Guide to the SINational Institute of Standards and TechnologyPractical rules for writing and converting physical quantities correctly.

Power transmission

Relations between torque, power, speed and ratio

A ratio trades speed for torque without creating power. Efficiency reduces available torque.

Torque from P and n

With P in kW and n in rpm, the result is in N·m.

T = 9 549,3 · P / n

Ratio

Gears: Z₂/Z₁. Pulleys: D₂/D₁ without slip.

n₂ = n₁ / i

Output torque

Apply ratio and then efficiency.

T₂ = T₁ · i · η