# Scale, Ratio, and Unit Conversions

Use ratios, scale factors, and unit conversions to move between drawings, material lists, sensor readings, and real dimensions.

## Outcome
Convert a drawing, measurement, or material estimate into the units the project actually needs.

## Safe first step
Write the starting unit and target unit before multiplying anything.

## Ladder steps
### 1. Write the units
Most mistakes are unit mistakes, not arithmetic mistakes.

Check: The starting and ending units are visible in the note.

### 2. Use one scale factor at a time
A clean ratio makes the conversion reviewable.

Check: Each multiplication cancels one unit or changes one scale.

### 3. Estimate before calculating
A rough estimate catches impossible answers.

Check: The final answer is in the same size range as the estimate.

### 4. Add waste or tolerance deliberately
Materials and fabrication need margins, but the margin should be named.

Check: The note says why the extra amount exists.

## Examples
### Convert a drawing measurement to real size
```sh
actual = drawing_measurement * scale_factor
```
Expected signal: The answer uses the real-world unit

### Estimate lumber board feet
```sh
board_feet = thickness_in * width_in * length_ft / 12
```
Expected signal: A material quantity with the right unit meaning

### Add a named 10 percent waste factor
```sh
total = estimate * 1.10
```
Expected signal: The final number is larger for a stated reason

## Common traps
- Dropping units halfway through the calculation.
- Adding waste twice.
- Trusting exact-looking decimals when the source measurement is rough.

## Practice task
Convert one small project dimension from a sketch into real size, then write the estimate, exact conversion, and a named tolerance.

## Next steps
- Use construction layout geometry for square corners.
- Use vectors when direction matters.
- Use fabrication notes when the material choice affects tolerance.

## Related
- [Fabrication and materials](/topics/fabrication/)
- [CAD constraints first sketch](/learn/cad-constraints-first-sketch/)
- [Maker Math](/topics/math/)
- [Project paths](/projects/)

## Obsidian backlinks

Use these wiki links to connect this note inside a local maker vault:

- [[TopicLadder]]
- [[Maker Learning]]
- [[Scale Ratio and Unit Conversions]]
- [[Maker Math]]
- [[math]]
- [[measurement]]
- [[Write the units]]
- [[Use one scale factor at a time]]
- [[Estimate before calculating]]
- [[Add waste or tolerance deliberately]]
- [[Fabrication and materials]]
- [[CAD constraints first sketch]]

## Source and next routes

Source: https://topicladder.com/learn/scale-ratio-and-unit-conversions/

- [Fabrication and materials](/topics/fabrication/)
- [CAD constraints first sketch](/learn/cad-constraints-first-sketch/)
- [Maker Math](/topics/math/)
- [Project paths](/projects/)