Angle Converter
Degrees, minutes, radians and slope percent, all at once.
Inputs
Result
Formula
| Degrees | 1° = 60′ = 3600″ |
| Radians | 180° = π rad, 1 rad = 57.2958° |
| Gradians | 90° = 100 gon, 1 gon = 0.9° |
| Slope percent | i = tan(θ) × 100% |
| Slope ratio | 1 : n where n = 1 ÷ tan(θ) |
| Rise per metre | h = tan(θ) × 1000 mm |
30° is 1800′ or 108000″ — 0.5236 rad, 33.33 gon, a 57.735% slope or about 1:1.73, rising 577.4 mm per metre. The usual 2% flat-roof fall is 1.1458°.
Degrees, minutes, seconds and radians
| Degrees | Minutes | Seconds | Radians | Gradians |
|---|---|---|---|---|
| 1° | 60′ | 3600″ | 0.017453 | 1.111 |
| 15° | 900′ | 54000″ | 0.261799 | 16.667 |
| 30° | 1800′ | 108000″ | 0.523599 | 33.333 |
| 45° | 2700′ | 162000″ | 0.785398 | 50.000 |
| 60° | 3600′ | 216000″ | 1.047198 | 66.667 |
| 90° | 5400′ | 324000″ | 1.570796 | 100.000 |
| 180° | 10800′ | 648000″ | 3.141593 | 200.000 |
FAQ
Are slope and angle different things?
Yes. An angle is the opening between two lines; a slope is rise over run, and tangent links them. They are close at small angles (5° is 8.75%, only 3.75 points apart) but diverge fast (30° is 57.7%). Roof “fractions of fall” and road percentages are both slopes.
Why angles for bar bending but slopes for formwork?
Bar scheduling cares about the bend, and codes specify 90° or 135° hooks that map straight onto the bender's scale. Formwork and roofs care about drainage, which depends on rise relative to run, so a slope is used. They are not interchangeable — treating 2% as 2° overstates the fall by 14%.
Why is the radian dimensionless?
Because a radian is arc length divided by radius — length over length, so the units cancel. Angular velocity is therefore per second rather than radian per second, and inertia times angular acceleration gives torque with no conversion factor, which is why physics needs radians and degrees would introduce a stray π/180.
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Results are estimating aids only and are not a design basis. Construction and final accounts must follow the drawings, the applicable standards and an approved method statement. Anything affecting structural safety, shoring or falsework must be checked by a suitably qualified engineer.