---
jupyter:
  description: 'Units in planex2d: the geometry itself has no unit; px.mm, px.inch and the other factors convert to
    meters, and the readers of DXF and KiCad files return meters too.'
---

# Units

planex2d does not impose a unit system. A number is a length in whatever unit you choose, and an area is in that
unit squared. The factors `px.mm`, `px.cm`, `px.m`, `px.um`, `px.inch` and `px.mil` state what a number means; with
them, the geometry is in meters.

```python
import math
import planex as px
```

## The same plate twice

The example is a plate of 80 × 50 mm with a hole of 10 mm diameter, drawn twice: once in plain numbers, counting in
millimeters, and once with the factors, in meters:

```python
plain = px.QuickSketch().Rectangle(80, 50).Face() - px.Circle((40, 25), 5).Face()

mm = px.mm
metric = px.QuickSketch().Rectangle(80 * mm, 50 * mm).Face() - px.Circle((40 * mm, 25 * mm), 5 * mm).Face()
```

```python nbsphinx="hidden"
from docs_figures import Row
```

```python nbsphinx="hide-input"
Row((plain, f"Plain numbers: 80 × 50, area {plain.mass:.1f}"),
    (metric, f"With px.mm: 0.08 × 0.05, area {metric.mass:.4e}"),
    caption="The same plate in plain numbers and in meters")
```

Both are the same plate, and only the numbers differ. The first area is in mm² and the second in m². Divided by
`px.mm**2`, the second area is in mm² again:

```python
print("plain:", plain.mass)
print("metric:", metric.mass, "m²")
print("metric:", metric.mass / mm**2, "mm², exact", 80 * 50 - math.pi * 5**2)
```

## The factors

| Factor | In meters |
|---|---|
| `px.m` | 1 |
| `px.cm` | 0.01 |
| `px.mm` | 0.001 |
| `px.um` | 10⁻⁶ |
| `px.inch` | 0.0254 |
| `px.mil` | 2.54 · 10⁻⁵ (a thousandth of an inch) |

## Where units come in

- **Files.** `px.FromDXF` reads the drawing's unit from its header and returns its wires in meters; `unit=` sets the
  unit instead. `px.WriteDXF` writes meters unless `unit=` is given, for example `unit=px.mm`. KiCad boards are read
  in meters, and `px.WriteKiCad` takes `unit=` as well. See [Files](../files.md).
- **Simulations.** Material constants have to be in the same unit as the geometry. A part drawn in millimeters and
  solved in NGSolve needs a conductivity in W/(mm K), not W/(m K).
- **Resolution.** planex2d resolves lengths down to about 10⁻¹⁴ relative to the coordinates, or 10⁻¹⁴ absolute for
  coordinates below 1. OpenCASCADE works with an absolute tolerance of 10⁻⁷, so after the export, a feature smaller
  than that, in the chosen unit, is lost. See [Tolerances](tolerances.md) for details.