DC Motor and Generator Calculator: Back EMF, Torque, Speed and Efficiency

Work out the armature current, EMF, torque, efficiency and the change of speed for a DC motor or generator.

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

Choose the machine: shunt motor, series motor, shunt generator or separately excited generator. Enter the terminal voltage, the line current, the armature resistance, the field resistance and the brush drop.

The calculator finds the field and armature currents, the back EMF (E = V - Ia Ra - brush drop for a motor, the generated EMF for a generator), the power developed, the torque and the efficiency, with your stray losses taken out.

For a motor, enter a second line current to find the new speed. A shunt motor has constant flux so speed follows the back EMF. A series motor has flux proportional to current, so its speed changes a great deal with load.

Formulas used

  • E_b = V - I_aR_a - V_b
  • E_g = V + I_aR_a + V_b
  • T = \frac{E I_a}{\omega}
  • \frac{N_2}{N_1} = \frac{E_{b2}}{E_{b1}}\ \ (\text{shunt})
  • \frac{N_2}{N_1} = \frac{E_{b2}}{E_{b1}}\frac{I_1}{I_2}\ \ (\text{series})

Worked example

With the default numbers in the calculator above:

  1. Shunt field current: 1.00 A
  2. Armature current: 39.00 A
  3. Back EMF: 208.50 V
  4. Electrical power converted to mechanical power: 8131.50 W (8.13 kW)
  5. Armature (developed) torque: 77.65 N m
  6. Shaft output power and torque: 7.63 kW and 72.88 N m
  7. Efficiency: 82.95 %
  8. Speed at the second load (the field flux is constant): 1047.96 rev/min

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: Machine Shunt generator; Terminal voltage 250 V; Line (or load) current 100 A; Armature resistance 0.1 ohm; Field resistance: the shunt field for a shunt machine, the series field for a series motor 100 ohm.

  1. Shunt field current: 2.50 A
  2. Armature current: 102.50 A
  3. Generated EMF: 262.25 V
  4. Electrical power developed in the armature: 26880.63 W (26.88 kW)
  5. Armature (developed) torque: 256.69 N m
  6. Power delivered to the load: 25.00 kW
  7. Efficiency (the mechanical input is the power developed plus the stray losses): 91.31 %

Common questions

What is back EMF?

The voltage generated in the armature of a motor as it turns. It opposes the supply and it limits the armature current. The supply voltage minus the back EMF is what drives current through the armature resistance.

Why does a series motor race with no load?

Its field is the armature current, so with no load the current and flux fall, and the speed rises until something fails. Never run one unloaded.

What is the difference in current for a shunt generator?

The armature carries the load current plus the shunt field current, so the armature current is larger than the current delivered to the load.

Is armature reaction included?

No. Armature reaction and magnetic saturation are ignored, so the speed and torque are for an ideal machine.

Related calculators

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

Further reading: Fitzgerald, Kingsley and Umans, Electric Machinery (DC machines); Theraja, A Textbook of Electrical Technology.

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