Visual Degrees vs Radians

By dan • June 1, 2026 • 1 min read

# Visual Degrees vs Radians

Canonical public lesson for degrees and radians.

## One picture
Degrees slice a circle into human-friendly parts. Radians measure how much radius-length fits along the arc.

## Simple idea
A radian is an angle measured by arc distance.

```text
radian angle = arc length / radius
```

On a unit circle where `radius = 1`, the radian measure equals the arc length.

## Key conversions
- `360° = 2π radians`
- `180° = π radians`
- `90° = π/2 radians`
- `1 radian ≈ 57.3°`

## Code without math libraries
```python
PI = 3.141592653589793

def deg_to_rad(deg):
return deg * PI / 180

def rad_to_deg(rad):
return rad * 180 / PI
```

Source task: `21d1aa06-cd00-4313-b981-ad415e47e22b`