Angle Converter
Degrees, minutes, radians and slope percent, all at once.
Quick answer
With the default inputs: Value 30 · From unit DegreeDegrees 30°
Edit the inputs below to recalculate.Inputs
Result
Degrees
30°
| Degrees minutes seconds | 30° 0′ 0″ |
| Minutes | 1800′ |
| Seconds | 108000″ |
| Radians | 0.523599rad |
| Gradians | 33.3333gon |
| Slope | 57.735% |
| Slope ratio | 1 : 1.73 |
| Rise per metre | 577.4mm |
| Sine / cosine | 0.5 / 0.866 |
Slope percent is tangent times 100, not the angle: 45° is 100%, 30° is 57.7% and 5° is 8.75%. Trade talk of “a 2% fall” means the percentage. Beyond 90° the tangent goes negative and slope percent stops being meaningful.
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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 |
How to work it out
- Degrees, minutes, seconds: 1° = 60′ = 3600″. Setting out uses this form, but 30°15′30″ must become 30.2583° before it goes into a trigonometric function.
- Radians: 180° = π rad, and 1 rad = 57.29578°. Spreadsheets and calculators take radians only, which is the most common trap in engineering calculation.
- Gradians: 90° = 100 gon, so 1 gon = 0.9°. Common on European surveying instruments, rare in China.
- Turns: 1 turn = 360° = 2π rad, occasionally used for rotation and speed.
- Gradient percentage: i = tan(θ) × 100%, the bridge between angle and slope for roofs, roads and drainage. Note it is tan, not sin — they converge at small angles and diverge sharply at large ones.
- Rise per metre: h = tan(θ) × 1000 mm. At 30° that is 577 mm per metre, the figure used for batten spacing on pitched roofs.
Where it goes wrong
- Feeding degrees into a trigonometric function. SIN(30) in a spreadsheet computes the sine of 30 radians (−0.988), not 0.5. Use RADIANS(30) or 30×PI()/180.
- Reading degrees and minutes as a decimal. 30°15′ is 30.25°, not 30.15° — 15′ is 15/60. In setting out this error runs to metres.
- Using sin instead of tan for gradient. Below about 5° they are nearly equal; at 30° sin is 0.5 against tan at 0.577, a 15% difference.
- Treating a gradient percentage as an angle. A 20% gradient is arctan(0.2) = 11.3°, not 20°. This confusion is endemic in roofing work.
- Rounding π to 3.14. Long arc calculations accumulate error; use 3.14159265.
Material and cost
An angle error in setting out means rework: writing 30.15° for 30.25° shifts 175 mm over 100 m, enough that steelwork or curtain walling will not fit. On roofs, one degree of pitch error changes tile quantity by 1-2% per 100 m².
On site
- Memorise the special angles: 30° gives sin 0.5, cos 0.866, tan 0.577; 45° gives 0.707, 0.707, 1; 60° gives 0.866, 0.5, 1.732. These cover most hand calculations.
- Rough gradient-to-angle mapping: 10% ≈ 5.7°, 20% ≈ 11.3°, 30% ≈ 16.7°, 50% ≈ 26.6°, and 100% is exactly 45° — a useful anchor.
- Total stations and theodolites may display degrees and minutes. Confirm the export format before processing, since many packages fail silently on DMS input.
- Arc length must use radians. Using degrees is out by a factor of 57 — the classic consequence of dropping π/180.
Basis
- GB/T 3100-3102 Quantities and units series
- GB 50026-2020 Standard for engineering surveying, horizontal control surveys
- GB 50345-2012 Technical code for roof engineering, roof design
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.
Cite this page
Use this format in reports, method statements or coursework. The link is permanent.
Building Calculator. Angle Converter. 2026-10-25. https://jianzhujisuan.com/en/unit-angle
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.