Angle conversion chart
The angle conversion chart: turns, degrees and gradians, plus a formula card for radians. Edit, print and share.
The angle conversion chart: one turn is 360 degrees or 400 gradians, and everything else follows from that. Radians, which appear in trigonometry, have their own formula card further down the page. Made for the classroom and home.
| 1 turn | = | 360 degrees |
|---|---|---|
| 1 turn | = | 400 gon |
| 0.5 turn | = | 180 degrees |
| 0.25 turn | = | 90 degrees |
| 360 degrees | = | 1 turn |
| 90 degrees | = | 100 gon |
| 180 degrees | = | 200 gon |
| 45 degrees | = | 50 gon |
| 1 gon | = | 0.9 degrees |
| 100 gon | = | 90 degrees |
| 400 gon | = | 1 turn |
How the table works
Every row is a unit conversion: a quantity and unit on the left, the same quantity expressed in another unit on the right. The table is live – drag the handle to reorder, click a row to change the quantity or units, remove rows with the cross and add your own at the bottom.
Everything you change lands in the page address. Copy the link and others open exactly your table – handy when the whole class needs the same sheet. Your changes are also kept in your browser until you reset them, but only there: to share or keep them permanently, the link is what counts.
Print puts the table on a single portrait A4 and Download PDF gives you the same sheet as a file. Print practice sheet gives the table with empty answer cells and name/date lines – the normal printout is the answer key.
Degrees, gradians and turns
A full turn is 360 degrees. A right angle is 90 degrees, a quarter turn, and a straight line is 180 degrees, a half turn. The gradian (also called the gon) splits the same turn into 400 parts instead of 360, so a right angle is exactly 100 gradians. Gradians are used mostly in surveying and construction.
Common mistake: mixing up gradians and degrees. 100 gradians is 90 degrees, not 100 degrees. One gradian is 0.9 degrees.
Radians
Radians belong to trigonometry. A full turn is 2π radians, so π radians is 180 degrees. Because π cannot be written exactly in decimals, no radian value can sit as a row in the table above. Radians have their own formula card instead.
Formulas
- Degrees to radiansrad = ° × π/180
- Radians to degrees° = rad × 180/π
| ° | rad |
|---|---|
| 30 | 0.52 |
| 45 | 0.79 |
| 60 | 1.05 |
| 90 | 1.57 |
| 180 | 3.14 |
| 360 | 6.28 |
π radians is 180°, so a right angle is π/2 radians. Radians go through π, so no radian value is exact in decimals - that is why they sit in a formula and not in the table above.
Download PDFRoughly how big an angle?
- A right angle, like the corner of a sheet of paper, is 90 degrees.
- A clock’s minute hand turns 6 degrees per minute.
- A half turn is a U-turn, 180 degrees.
Frequently asked questions
How many degrees are in a turn?
360 degrees, or 400 gradians.
How many degrees is 1 radian?
Roughly 57.3 degrees. It is the angle where the arc is as long as the circle’s radius.
How do I convert degrees to radians?
Multiply by π and divide by 180. 90 degrees becomes roughly 1.57 radians.
More tables: Time · Length · Prefix ladder · Angle converter