Lift and Hoist Motor Power Calculator: Steady Speed, Friction, Counterweight and Acceleration

Find the motor power for a lift, hoist or elevator from the load, the speed and the friction.

Calculated from standard textbook formulas, with every step shown. The formulas are fixed, so the working does not need checking: what matters is the numbers you type in. Use these calculators only if you are competent to choose the inputs (loads, material strength, dimensions, supports) and check your units and assumptions. For learning and checking your own working: design and sign-off are for a qualified engineer. Drafting Central does not store the numbers you type.

How this calculator works

Enter the mass of the car and load, the lifting speed, the friction force and, if there is one, the mass of the counterweight.

At a steady speed there is no acceleration, so the force is the weight plus the friction (less the counterweight). The power is that force times the speed, which is the power at the rope.

Enter the drive efficiency to get the power the motor must deliver, an acceleration to get the peak power at the end of the start, and the height for the energy in one trip.

Formulas used

  • F = mg - m_cg + f
  • P = Fv
  • P_{motor} = \frac{Fv}{\eta}
  • F_a = F + (m + m_c)a

Worked example

With the default numbers in the calculator above:

  1. Weight of the car and load: 13734.00 N
  2. Force the motor must supply at a steady speed (acceleration is zero): 15734.00 N
  3. Power at the rope at a steady speed: 47.20 kW
  4. How the power splits: against gravity and against friction: 41.20 kW against gravity and 6.00 kW against friction
  5. Power the motor must deliver, with the losses in the drive: 47.20 kW

Change the numbers in the calculator to see the full working, every step, for your own case.

A second worked example

A different case, with these numbers: Gravity (the problem may use 10) 10 m/s2.

  1. Weight of the car and load: 14000.00 N
  2. Force the motor must supply at a steady speed (acceleration is zero): 16000.00 N
  3. Power at the rope at a steady speed: 48.00 kW
  4. How the power splits: against gravity and against friction: 42.00 kW against gravity and 6.00 kW against friction
  5. Power the motor must deliver, with the losses in the drive: 48.00 kW

Common questions

Why is the acceleration zero at a steady speed?

A constant speed means no change in speed, so there is no net force and the pull on the rope balances the weight and the friction.

What does the counterweight do?

It balances part of the weight of the car, so the motor only lifts the difference. That cuts the motor size and the energy a lot.

How do I choose the motor?

Use the power for the full rated load at the top speed, including the drive efficiency, and check the acceleration and the starting duty. Then pick the next standard size up.

Does this work for a hoist or crane?

Yes. Use the mass lifted and the hoist speed, and set the counterweight to 0.

Related calculators

Got a question about this? Ask an engineering question and get a plain-language answer with references.

Further reading: AS 1735 Lifts, escalators and moving walks; any university physics text (work, energy and power).

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