Back EMF and voltage headroom calculator

Motor electrical power balance at a supplied SI back-EMF constant.

motors-back-emf.napkin / editable

SCENARIO COMPARISON

Compare the numbers.

This source describes an analytical model. Its quantities and checks are the view.

Scenario	emfV	requiredV
	15.708	17.708
	12.5664	14.5664

All calculated quantities are listed with the inputs. Switch to Source to inspect the equations.

SCENARIOS / CALCULATED VALUESSAME SOURCE

Change an input to see the consequences.

bus voltage budget17.71 V✓ passes

BASELINE INPUTS

constant0.05 V*s/radspeed3000 rpmcurrent2 Aresistance1 ohm

CALCULATED

emf15.708 V

required17.708 V

Edits change the baseline source.

THE SOURCE

Edits below update the same model.

# Back EMF and voltage headroom
# Scope: Motor electrical power balance at a supplied SI back-EMF constant.
# Status: illustrative worked example; engineering review pending.
# Inputs are example values. Checks are editable example requirements, not standards.

constant = 0.05 V*s/rad
speed = 3000 rpm
current = 2 A
resistance = 1 ohm

emf := constant*speed [V]
required := emf+current*resistance [V]

check bus voltage budget: required <= 24 V

scenario alternative: constant = 0.04 V*s/rad

Calculated from your source · not saved

Baseline · Baseline

bus voltage budget17.71 V ✓ passes

alternative · alternative

bus voltage budget14.57 V ✓ passes

Illustrative first-order example. Checks are editable requirements, not design standards. The broader topic may require additional equations, data, and validation.

Formula and units

This example uses the following equations. Input names and units match the editable source above.

emf: emf = constant*speed [V]
required: required = emf+current*resistance [V]

Original worked example

These are the baseline values in the downloadable source. Edits above let you test your own values.

Given

constant: 0.05 V*s/rad
speed: 3000 rpm
current: 2 A
resistance: 1 ohm

Calculated

emf: 15.708 V
required: 17.708 V

Assumptions and limits

Motor electrical power balance at a supplied SI back-EMF constant.

The requirement checks use the limits written in this example. Passing a check does not establish that the model covers every load, material behavior, or operating condition in a real design.

Download this .napkin example ↓

Take it further with your agent

Napkin keeps the inputs, equations, checks and assumptions together in one study. Your agent sets it up; you change the numbers.

Try with Claude ↗

codex 'Use Napkin (https://napkin.engineering/mcp, or the local Napkin plugin) to build a study: Back EMF and voltage headroom. Inputs: speed; flux or voltage constant; resistance; current. Outputs: back EMF; bus-voltage requirement. Model scope: Motor and load parameters with explicit operating limits. Read napkin_capabilities and the current snapshot. Ask me for the values that matter, label assumptions with units, author .napkin source, validate it and apply it with napkin_source using the current revision, then open the study. Add checks for the limits I supply. Keep unsupported analyses explicit.'

Claude needs the Napkin connector; Codex needs the Napkin plugin. Set up your agent ↗

The broader study

The topic brief below describes the broader scope. The worked example above states the particular calculation it implements.

Inputs: speed, flux or voltage constant, resistance, current
Outputs: back EMF, bus-voltage requirement
Modes: calculate, compare, sweep
Drawing: Torque-speed and duty plots

EXECUTABLE WORKED EXAMPLE · FIRST-ORDER MODEL · CHECK THE SCOPE & ASSUMPTIONS