Convert degrees to radians

1. How to convert degrees to radians

The conversion is a single multiplication: rad = ° × 0.0174532925199. Both units are defined against the same base — the radian (rad) — so the factor is fixed and the result is exact to the precision shown.

Worked at the two values people ask for most: 1 ° = 0.017453293 rad and 45 ° = 0.78539816 rad. Going the other way, ° = rad × 57.2957795131, so 1 rad = 57.29578 ° — a direction with its own page, radians to degrees.

Results are given to eight significant figures. That is more precision than most jobs need — for a rough figure, treat 1 ° as about 0.017453293 rad and adjust — but rounding early and multiplying afterwards is how a small error becomes a visible one, so the full figure is what the converter carries.

2. Degrees to Radians conversion table

Every row is the same factor applied — nothing in the table is a special case, and any value in between behaves the same way. Type your own figure into the converter above and the Formula tile shows the arithmetic being used, so the result is checkable rather than taken on trust.

3. What the two units are

• Degrees (°). One ° is 0.017453293 rad.
• Radians (rad). One rad is 1 rad.

Both are converted through the radian (rad): the value is multiplied by its own unit's factor to reach the base, then divided by the target unit's factor to leave it. No direct degrees to radians factor has to exist or be kept correct, which is also why the converter can show the same value in all 7 angle units at once.

A radian is the angle subtending an arc equal to the radius, so a full turn is 2π radians and one radian is about 57.2958°. Gradians divide the right angle into 100 rather than 90, which is why 90° is 100 grad — a surveying convention that never displaced degrees.

If the pair you actually want is not this one, the full unit converter runs every 7 angle units off the same factor table, along with 11 other categories of measurement.