# `Angle`

An angle, held in radians to 9 places, written `90deg` or `1.5rad`.

[Physical quantities](types.md#physical-quantities); ordered; since Jadpo 0.1.0.

## Make one

`text.parse(raw, as: Angle)` reads one from its text; text that isn't one at all fails `malformed`, such as `5`, `""` or `1.2.3`.

These operations give one: `units.of` and `units.sum`.

## Text, JSON and storage

`text.from` writes its canonical text, the one form `text.parse` reads back. JSON sends an object of its parts.

| Text | JSON |
|---|---|
| `0 rad` | `{"value":"0","unit":"rad"}` |
| `1.570796327 rad` | `{"value":"1.570796327","unit":"rad"}` |
| `3.141592654 rad` | `{"value":"3.141592654","unit":"rad"}` |

It is stored in one column named for the field, of type `numeric(38, 9)`, holding the angle in radians (rad). `1.570796327 rad` is stored as `1.570796327`.

## Shown to people

`text.format(value, locale:)` shows it to people in their locale. A call may also give `unit:`.

With `locale: Locale.en_gb`:

| Value | Shown |
|---|---|
| `0 rad` | `0 rad` |
| `1.570796327 rad` | `1.570796327 rad` |
| `3.141592654 rad` | `3.141592654 rad` |

## Operations

- `colour.from_hsl(hue: Angle, saturation: Percentage, lightness: Percentage) -> Colour`: The colour of a CSS Color 4 HSL hue, saturation and lightness, the percentages clamped to 0% to 100%: `colour.from_hsl(120deg, 100%, 25%)` is `#008000`.
- `colour.from_oklch(lightness: Percentage, chroma: Decimal, hue: Angle) -> Colour`: The colour of an OKLCH lightness, chroma and hue, clipped into sRGB, the lightness clamped to 0% to 100% and the chroma to 0 or more: `colour.from_oklch(62.8%, 0.2577, 29.23deg)` is `#ff0000`.
- `units.in(value: Quantity, unit: QuantityUnit, scale: Int, rounding: Rounding) -> Decimal`: `value` in `unit`, a unit of its kind, as a `Decimal` of `scale` places rounded by `rounding`: `units.in(5km, LengthUnit.mile, scale: 2, rounding: Rounding.half_even)` is `3.11`.
- `units.of(value: Number, unit: QuantityUnit) -> Quantity`: `value` of `unit`, an `Int` or a `Decimal`, as the quantity of `unit`'s kind, converted exactly to the base unit and rounded half to even to the kind's scale: `units.of(5, LengthUnit.mile)`.
- `units.sum(items: List<Quantity>) -> Quantity`: The items added up, all of one kind; nothing for no items. A `Temperature` or a `SoundLevel` doesn't add to itself, so neither is summed.

Like every standard type, it also has the contract's own operations: `text.parse`, `text.from`, `text.format`, `json.read`, `json.write` and `==`. It is ordered, so `<` and sorting take it. [Every standard type meets one contract](../topics/every-standard-type-meets-one-contract.md) says how they work.