60 degrees is equal to approximately 1.0472 radians.
To convert degrees into radians, you multiply the degree value by π divided by 180, because a full circle has 360 degrees which equals 2π radians. So, 60 degrees times π/180 gives the radian equivalent.
Conversion Tool
Result in radian:
Conversion Formula
Degrees convert to radians by multiplying the degree amount by π divided by 180. This works because 360 degrees equals 2π radians, so 1 degree equals π/180 radians. Thus, the formula is:
radians = degrees × (π / 180)
Example with 60 degrees:
- Start with 60 degrees
- Multiply 60 by π (approximately 3.1416)
- Divide the result by 180
- So, 60 × 3.1416 / 180 = 1.0472 radians
Conversion Example
- 45 degrees to radians:
- Multiply 45 by π: 45 × 3.1416 = 141.372
- Divide by 180: 141.372 / 180 = 0.7854 radians
- 90 degrees to radians:
- Multiply 90 by π: 90 × 3.1416 = 282.744
- Divide by 180: 282.744 / 180 = 1.5708 radians
- 120 degrees to radians:
- Multiply 120 by π: 120 × 3.1416 = 376.992
- Divide by 180: 376.992 / 180 = 2.0944 radians
- 30 degrees to radians:
- Multiply 30 by π: 30 × 3.1416 = 94.248
- Divide by 180: 94.248 / 180 = 0.5236 radians
Conversion Chart
The chart below shows values from 35.0 to 85.0 degrees converted into radians. You can use this table to quickly find the radian value for these degrees without calculation.
| Degrees | Radians |
|---|---|
| 35.0 | 0.6109 |
| 40.0 | 0.6981 |
| 45.0 | 0.7854 |
| 50.0 | 0.8727 |
| 55.0 | 0.9599 |
| 60.0 | 1.0472 |
| 65.0 | 1.1345 |
| 70.0 | 1.2217 |
| 75.0 | 1.3090 |
| 80.0 | 1.3963 |
| 85.0 | 1.4835 |
Related Conversion Questions
- How many radians are in 60 degrees exactly?
- What is the radian equivalent of a 60-degree angle in trigonometry?
- How to convert 60 degrees to radians by hand?
- Is 60 degrees equal to 1 radian or more?
- Why does 60 degrees convert to 1.047 radians and not 1?
- What formula should I use to change 60 degrees into radians?
- Are radians bigger or smaller than degrees when converting 60 degrees?
Conversion Definitions
Degrees: Degrees measure angles based on dividing a circle into 360 equal parts. Each degree is 1/360th of a circle, which makes it easy for dividing full rotations. Degrees are commonly used in geometry, navigation, and daily applications involving angles.
Radian: Radian is the standard unit of angular measure in mathematics defined by the angle at the center of a circle subtending an arc equal in length to the radius. There are 2π radians in a full circle, making it useful for calculus and trigonometric functions.
Conversion FAQs
Why is π involved in converting degrees to radians?
The pi (π) comes from the definition of a radian. A radian measures the angle by the length of the arc divided by the radius of the circle. Since the circumference of a circle is 2π times the radius, π naturally appears in the conversion between degrees and radians.
Can radians be negative when converting from degrees?
Yes, radians can be negative if the degree measure is negative. Negative angles often represent clockwise rotation, so converting a negative degree like -60 degrees results in a negative radian value.
Is the conversion formula the same for angles larger than 360 degrees?
The formula works for any angle size, even larger than 360 degrees. Because radians and degrees both measure rotation, multiplying degrees by π/180 always gives the correct radian equivalent regardless of size.
Why do calculators sometimes show radian values with decimals?
Since π is an irrational number, its decimal form is infinite and non-repeating. Calculators approximate π to a certain decimal place, so radian results are shown as decimal numbers rounded to a few places.
Does converting degrees to radians affect the angle’s direction?
No, converting degrees to radians only changes the unit of measurement, not the actual angle or its direction. The angle stays the same, just expressed differently.