° to rad — convert degrees to radians
Exact 1 ÷ 57.29578 = 0.01745329
1 degree in other units
| Radians | 0.01745329 | rad |
|---|---|---|
| Milliradians | 17.453293 | mrad |
| Gradians | 1.111111 | gon |
| Arcminutes | 60 | ′ |
| Arcseconds | 3,600 | ″ |
| Turns | 0.002777777778 | turn |
° to rad at a glance
| Degrees | Radians |
|---|---|
| 1 ° | 0.01745329 rad |
| 2 ° | 0.03490659 rad |
| 3 ° | 0.05235988 rad |
| 5 ° | 0.08726646 rad |
| 10 ° | 0.17453293 rad |
| 20 ° | 0.34906585 rad |
| 25 ° | 0.43633231 rad |
| 50 ° | 0.87266463 rad |
| 100 ° | 1.745329 rad |
| 250 ° | 4.363323 rad |
| 500 ° | 8.726646 rad |
| 1,000 ° | 17.453293 rad |
How to convert degrees to radians
Multiply by 0.01745329 — one degree is 0.01745329 radians. That factor is exact: it comes from the definition of the units rather than from a measurement, so it will not change and does not need rounding.
Working 1 ÷ 57.29578 = 0.01745329
Questions
How many radians are in a degree?
One degree is 0.01745329 radians. This figure is exact — it comes from the definition of the unit, not a measurement.
What is 1 degree in radians?
1 degree is 0.01745329 radians. The working is 1 ÷ 57.29578 = 0.01745329.
How many degrees is one radian?
About 57.3°, or exactly 180/π. A radian is the angle you get when the arc along a circle is as long as its radius, which is why the number is awkward: it comes from the geometry rather than from someone choosing a round figure.
Why does maths use radians instead of degrees?
Because the calculus only comes out clean in radians. The derivative of sine is cosine only when the angle is in radians; in degrees a factor of π/180 turns up everywhere. Degrees are a human convention, radians are the circle's own unit.
Why 360 degrees in a circle?
Babylonian arithmetic, most likely, and it stuck because 360 divides so willingly — by 2, 3, 4, 5, 6, 8, 9, 10, 12 and more. Halves, thirds and quarters of a circle all land on whole numbers, which is more than can be said for 100.
What is a gradian for?
It is the metric attempt at angle: 100 gradians in a right angle, 400 in a full circle. It never displaced the degree in general use but survives in surveying in parts of Europe, and most scientific calculators still have a GRAD mode next to DEG and RAD.