Convert Degrees to Radians
Degrees to radians is the conversion you need when you leave everyday angles behind and step into math and physics, where radians are the standard. One degree is approximately 0.017453292519943295 radians, so the number always comes out much smaller when you switch from degrees to radians.
Degrees to Radians conversion table
| Degrees (°) | Radians (rad) |
|---|---|
| 1 | 0.017453 |
| 2 | 0.034907 |
| 3 | 0.05236 |
| 5 | 0.087266 |
| 10 | 0.174533 |
| 20 | 0.349066 |
| 50 | 0.872665 |
| 100 | 1.745329 |
| 500 | 8.726646 |
| 1,000 | 17.453293 |
The formula
To convert degrees to radians, multiply the number of degrees by 0.017453292519943295 (which is π/180):
radians = degrees × 0.017453292519943295
A worked example
Say you have a right angle of 90 degrees and want it in radians:
90 × 0.017453292519943295 = 1.5707963 rad
So 90 degrees is about 1.5707963 radians — which is exactly π/2.
Why it's an approximation
The factor here is π divided by 180, and π is irrational: its decimals run on forever without ever settling into a repeating pattern. That means no decimal number can capture it perfectly — 0.017453292519943295 is already rounded, and adding more digits only gets you closer, never all the way there. This is why math and physics usually leave radians written as multiples of π (like π/2 or 2π) instead of decimals: that form is exact, while the decimal never is.
When you'll use it
Feeding angles into trigonometry, calculus, and physics formulas, which nearly all expect radians, and working with programming languages whose sin, cos, and tan functions take radians rather than degrees.
Frequently asked questions
How many radians are in a degree?
About 0.017453292519943295 radians. That's π divided by 180, and because π never ends or repeats, the figure is rounded — you just take as many decimals as you need.
What is 90 degrees in radians?
About 1.5707963 radians, which is π/2 — a right angle. Half a circle, 180 degrees, is π radians, so a quarter of that is π/2.
Is the degrees to radians conversion exact?
No. The factor is π/180, and π is irrational — it goes on forever without repeating — so any decimal you write down is rounded. The clean way to write it is as a multiple of π.