Angle Conversion Chart
Quick-reference angle conversion chart. The tables below compare the most common units side by side. Download the free PDF for offline and printable use.
Standards and method
Values are calculated from the shared conversion-factor library. Exact defined relationships are preserved; displayed results are rounded only for readability.
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Printable angle conversion chart
Degrees, radians, gradians, arcminutes and arcseconds, plus slope and roof pitch. Includes the exact definition, formulas, a worked example and sources. Conversion values are checked against the defining constants, and reference data is cited to its source, before the PDF is published.
Free to print, share and use in teaching materials with attribution (CC BY 4.0).
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Angle Conversion Table
| Unit | per 1 ° | per 1 rad |
|---|---|---|
| Degree (°) | 1 ° | 57.2958 ° |
| Radian (rad) | 0.0174533 rad | 1 rad |
| Gradian (grad) | 1.11111 grad | 63.662 grad |
| Arcminute (′) | 60 ′ | 3437.75 ′ |
| Arcsecond (″) | 3600 ″ | 206265 ″ |
Values are calculated from the shared conversion-factor library. Exact defined relationships are preserved; displayed results are rounded only for readability.
Full angle conversion chart
Degrees, radians, gradians, arcminutes and arcseconds, plus slope and roof pitch. These are the same tables as the printable PDF. For: Students, surveyors, roofers, engineers and programmers.
- Exact definition
- 360° = 2π rad = 400 gon; 1° = 60′ = 3600″
- Formula
- rad = ° × π ÷ 180; slope % = tan(°) × 100
- Reverse
- ° = rad × 180 ÷ π; ° = arctan(slope % ÷ 100)
- Worked example
- A 6/12 roof pitch = 26.57° = 50 % slope
- Rounding
- Matrix values use 6 significant figures; slope angles to 2 decimal places.
Conversion factor matrix
Read across: 1 unit in the left column equals the value shown in each column unit.
| 1 unit = | ° | rad | gon | ′ | ″ |
|---|---|---|---|---|---|
| 1 ° | 1 | 0.0174533 | 1.11111 | 60 | 3,600 |
| 1 rad | 57.2958 | 1 | 63.662 | 3,437.75 | 206,265 |
| 1 gon | 0.9 | 0.015708 | 1 | 54 | 3,240 |
| 1 ′ | 0.0166667 | 2.90888 × 10⁻⁴ | 0.0185185 | 1 | 60 |
| 1 ″ | 2.77778 × 10⁻⁴ | 4.84814 × 10⁻⁶ | 3.08642 × 10⁻⁴ | 0.0166667 | 1 |
Common angles
| Degrees (°) | Radians (exact) | Radians (rad) | Gradians (gon) |
|---|---|---|---|
| 0 | 0 | 0.00000 | 0 |
| 15 | π/12 | 0.26180 | 16.667 |
| 30 | π/6 | 0.52360 | 33.333 |
| 45 | π/4 | 0.78540 | 50 |
| 60 | π/3 | 1.04720 | 66.667 |
| 90 | π/2 | 1.57080 | 100 |
| 120 | 2π/3 | 2.09440 | 133.333 |
| 135 | 3π/4 | 2.35619 | 150 |
| 150 | 5π/6 | 2.61799 | 166.667 |
| Degrees (°) | Radians (exact) | Radians (rad) | Gradians (gon) |
|---|---|---|---|
| 180 | π | 3.14159 | 200 |
| 210 | 7π/6 | 3.66519 | 233.333 |
| 225 | 5π/4 | 3.92699 | 250 |
| 240 | 4π/3 | 4.18879 | 266.667 |
| 270 | 3π/2 | 4.71239 | 300 |
| 300 | 5π/3 | 5.23599 | 333.333 |
| 315 | 7π/4 | 5.49779 | 350 |
| 330 | 11π/6 | 5.75959 | 366.667 |
| 360 | 2π | 6.28319 | 400 |
Slope percentage to angle (ramps, roads, drainage)
Slope % = rise ÷ run × 100. 8.33 % is a 1:12 wheelchair ramp.
| Slope (%) | Angle (°) | Ratio (1 in …) |
|---|---|---|
| 1 | 0.57 | 100.0 |
| 2 | 1.15 | 50.0 |
| 2.5 | 1.43 | 40.0 |
| 4 | 2.29 | 25.0 |
| 5 | 2.86 | 20.0 |
| 6 | 3.43 | 16.7 |
| 8 | 4.57 | 12.5 |
| 8.33 | 4.76 | 12.0 |
| 10 | 5.71 | 10.0 |
| 12 | 6.84 | 8.3 |
| Slope (%) | Angle (°) | Ratio (1 in …) |
|---|---|---|
| 15 | 8.53 | 6.7 |
| 20 | 11.31 | 5.0 |
| 25 | 14.04 | 4.0 |
| 30 | 16.70 | 3.3 |
| 33.3 | 18.42 | 3.0 |
| 40 | 21.80 | 2.5 |
| 50 | 26.57 | 2.0 |
| 60 | 30.96 | 1.7 |
| 75 | 36.87 | 1.3 |
| 100 | 45.00 | 1.0 |
Roof pitch (rise per 12 run) to angle
Pitch is the rise for every 12 units of run (6 = 6/12 pitch).
| Pitch | Angle (°) | Slope (%) |
|---|---|---|
| 1 | 4.76 | 8.3 |
| 2 | 9.46 | 16.7 |
| 3 | 14.04 | 25.0 |
| 4 | 18.43 | 33.3 |
| 5 | 22.62 | 41.7 |
| 6 | 26.57 | 50.0 |
| 7 | 30.26 | 58.3 |
| 8 | 33.69 | 66.7 |
| Pitch | Angle (°) | Slope (%) |
|---|---|---|
| 9 | 36.87 | 75.0 |
| 10 | 39.81 | 83.3 |
| 11 | 42.51 | 91.7 |
| 12 | 45.00 | 100.0 |
| 13 | 47.29 | 108.3 |
| 14 | 49.40 | 116.7 |
| 15 | 51.34 | 125.0 |
| 16 | 53.13 | 133.3 |
| Pitch | Angle (°) | Slope (%) |
|---|---|---|
| 17 | 54.78 | 141.7 |
| 18 | 56.31 | 150.0 |
| 19 | 57.72 | 158.3 |
| 20 | 59.04 | 166.7 |
| 21 | 60.26 | 175.0 |
| 22 | 61.39 | 183.3 |
| 23 | 62.45 | 191.7 |
| 24 | 63.43 | 200.0 |
Sources for this chart
Conversion values on this sheet are generated by the AllUnitConversions conversion library and automatically checked against the exact definitions above before the PDF is produced; reference tables are taken from the sources listed.
- BIPM SI Brochure, 9th edition — Definitions of the SI units, including the kelvin
- NIST Special Publication 811 — Guide for the Use of the International System of Units
Related Converters & Charts
Angle Conversion Chart FAQs
Common questions about the angle conversion chart.
What does this angle conversion chart include?
It lists the most common angle units side by side with their conversion factors, plus a free printable PDF you can download for offline reference.
What exact definition is this angle chart based on?
360° = 2π rad = 400 gon; 1° = 60′ = 3600″. Formula: rad = ° × π ÷ 180; slope % = tan(°) × 100. Matrix values use 6 significant figures; slope angles to 2 decimal places.
Can I download this chart as a PDF, CSV, or JSON?
Yes. Use the Download A4 PDF or US Letter PDF buttons for a printable version, or download the same tables as CSV or JSON from the links on this page.