Direct conversion
Result
—
—
Exact / normalized context
—π form
—turns
—0–360°
—−180–180°
The π form recognizes useful rational multiples of π when the value is sufficiently close.
All equivalents
Slope / grade laboratory
—slope %
—rise : run
—‰ grade
—radians
Slope % is nonlinear: slope % = tan(angle) × 100. It is undefined at ±90°.
DMS ↔ decimal degrees
Decimal degrees
—
—
—
Trigonometric inspector
—sin θ
—cos θ
—tan θ
—quadrant
Trig values are evaluated from the exact underlying radian value, not from the rounded display.
Angle normalizer
—[0, 360)
—(−180, 180]
—whole turns
—residual °
Definitions
| Unit | Degrees per unit |
|---|
Key identities
360° = 2π rad = 400 gon = 1 turn.
1° = 60 arcmin = 3,600 arcsec.
1 mrad = 0.001 rad.
NATO mil here means exactly 6,400 mil per full turn.
Negative angles are preserved as signed rotations. Normalized forms are shown separately so conversion never silently changes direction.