15 degrees is approximately 0.2618 radians.
To convert degrees into radians, multiply the degree value by π and then divide by 180. This converts the angular measurement from a circle divided into 360 parts (degrees) into the radian system, which measures angles by the length of the arc.
Conversion Tool
Result in radians:
Conversion Formula
The formula to convert degrees to radians is: radians = degrees × (π / 180). Degrees divide a full circle into 360 parts, while radians measure the angle based on the radius of the circle’s arc. Since the circumference of a circle is 2π times the radius, 360 degrees equals 2π radians.
When you multiply degrees by π/180, you scale the degree measure into the radian measure, because 180 degrees equals π radians.
Example calculation for 15 degrees:
- Start with 15 degrees
- Multiply 15 × π = 15π
- Divide by 180: (15π) / 180 = π / 12
- Numerical value: π / 12 ≈ 0.2618 radians
Conversion Example
- Convert 45 degrees to radians:
- Multiply 45 × π = 45π
- Divide by 180: 45π / 180 = π / 4
- Result: π/4 ≈ 0.7854 radians
- Convert 90 degrees to radians:
- Multiply 90 × π = 90π
- Divide by 180: 90π / 180 = π / 2
- Result: π/2 ≈ 1.5708 radians
- Convert 120 degrees to radians:
- Multiply 120 × π = 120π
- Divide by 180: 120π / 180 = 2π / 3
- Result: 2π/3 ≈ 2.0944 radians
- Convert 0 degrees to radians:
- Multiply 0 × π = 0
- Divide by 180: 0 / 180 = 0
- Result: 0 radians
Conversion Chart
| Degrees | Radians |
|---|---|
| -10.0 | -0.1745 |
| -5.0 | -0.0873 |
| 0.0 | 0.0000 |
| 5.0 | 0.0873 |
| 10.0 | 0.1745 |
| 15.0 | 0.2618 |
| 20.0 | 0.3491 |
| 25.0 | 0.4363 |
| 30.0 | 0.5236 |
| 35.0 | 0.6109 |
| 40.0 | 0.6981 |
This chart converts degrees from negative to positive values into radians, so users can quickly find the radian equivalent without calculation. Look up the degree value in the table, and the corresponding radian value is right beside it.
Related Conversion Questions
- What is 15 degrees converted into radians exactly?
- How do I change 15° to radians in calculator?
- Why does 15 degrees equal about 0.26 radians?
- Is 15 degrees closer to 0.25 or 0.3 radians?
- How many radians are in 15 degrees and why?
- Can you show me the step to convert 15 degrees into radians?
- What’s the difference between degrees and radians when converting 15?
Conversion Definitions
Degrees: A degree is a unit to measure angles, dividing a circle into 360 equal parts. It allows easy representation of angles in everyday use, from navigation to geometry. Each degree corresponds to 1/360th of a full rotation around a point.
Radians: A radian measures angles based on the arc length of a circle. One radian is the angle made when the arc length equals the radius length. It connects angle measurement directly with circle geometry, and there are about 6.283 radians in a full circle.
Conversion FAQs
What is the practical reason to convert degrees to radians?
Many mathematical formulas and programming functions, like trigonometric functions, require input in radians because it aligns with the natural properties of circles and periodic functions. Degrees are easier for humans to read, but radians simplify calculations.
Does converting 15 degrees to radians lose precision?
Converting between degrees and radians can introduce small rounding errors, especially if decimals are truncated. Using exact values like π/12 maintains precision, but decimal approximations like 0.2618 radians may be slightly off by a tiny margin.
Can negative degrees be converted to radians the same way?
Yes, negative degrees convert using the same formula. A negative degree means rotation in the opposite direction, so negative radians represent the same opposite angle on the circle.
How do I convert radians back to degrees?
To convert radians back to degrees, multiply the radian value by 180 and then divide by π. This reverses the formula, turning the radian measure into degrees, which is more familiar for many users.
Why is π involved in the conversion formula?
π relates the circle’s circumference to its diameter, linking linear and angular measurements. Since degrees divide a circle into 360 parts and radians measure the angle by arc length, π connects these two systems by expressing 180 degrees as π radians.
