CALCULATORS / EMBEDDED TIMING AND DIGITAL SYSTEMS

UART baud-rate divider and error calculator

Integer-divider UART baud error; oversampling factor supplied.

embedded-uart-baud.napkin / editable

SCENARIO COMPARISON

Compare the numbers.

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

Scenario	divider	actualHz	relativeError
	9	111111	0.0354938
	7	114286	0.00793651

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.

baud error budget0.04 × fails

BASELINE INPUTS

clock16000000 Hzbaud115200 Hzoversampling16

CALCULATED

divider9

actual111110 Hz

relativeError0.035494

Edits change the baseline source.

THE SOURCE

Edits below update the same model.

# UART baud-rate divider and error
# Scope: Integer-divider UART baud error; oversampling factor supplied.
# Status: illustrative worked example; engineering review pending.
# Inputs are example values. Checks are editable example requirements, not standards.

clock = 16000000 Hz
baud = 115200 Hz
oversampling = 16

divider := round(clock/(oversampling*baud))
actual := clock/(oversampling*divider) [Hz]
relativeError := abs(actual-baud)/baud

check baud error budget: relativeError <= 0.03

scenario alternative: clock = 1.28e+07 Hz

Calculated from your source · not saved

Baseline · Baseline

baud error budget0.04 × fails

alternative · alternative

baud error budget0.01 ✓ 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.

divider: divider = round(clock/(oversampling*baud))
actual: actual = clock/(oversampling*divider) [Hz]
relative error: relativeError = abs(actual-baud)/baud

Original worked example

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

Given

clock: 16000000 Hz
baud: 115200 Hz
oversampling: 16

Calculated

divider: 9
actual: 111111 Hz
relative error: 0.0354938

Assumptions and limits

Integer-divider UART baud error; oversampling factor supplied.

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: UART baud-rate divider and error. Inputs: clock; target baud; divider mode. Outputs: divider; achieved baud; percentage error. Model scope: Declared clock, peripheral and execution assumptions. 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: clock, target baud, divider mode
Outputs: divider, achieved baud, percentage error
Modes: calculate, compare, sweep
Drawing: Timing diagram or event simulation

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