45 degrees equals 0.7854 radians.
To convert 45 degrees to radians, you multiply by π and divide by 180. Since π radians equals 180 degrees, this conversion maintains the correct proportion between the two units. So, 45 × π ÷ 180 = π/4 radians, which is approximately 0.7854.
Conversion Tool
Result in radian:
Conversion Formula
The formula to convert degrees to radians is:
radians = degrees × (π / 180)
This formula works because a full circle is 360 degrees, which equals 2π radians. Dividing both sides by 2 shows that 180 degrees equals π radians. So, multiplying degrees by π/180 converts it to the corresponding radian measure.
Example calculation for 45 degrees:
- Start with 45 degrees.
- Multiply by π: 45 × π = 45π
- Divide by 180: (45π) ÷ 180 = π/4
- Approximate π as 3.1416: π/4 ≈ 3.1416 ÷ 4 = 0.7854 radians
Conversion Example
- Convert 60 degrees to radians:
- Multiply 60 × π = 60π
- Divide by 180: 60π ÷ 180 = π/3
- Approximate: π/3 ≈ 1.0472 radians
- Convert 30 degrees to radians:
- 30 × π = 30π
- 30π ÷ 180 = π/6
- π/6 ≈ 0.5236 radians
- Convert 90 degrees to radians:
- 90 × π = 90π
- 90π ÷ 180 = π/2
- π/2 ≈ 1.5708 radians
- Convert 120 degrees to radians:
- 120 × π = 120π
- 120π ÷ 180 = 2π/3
- 2π/3 ≈ 2.0944 radians
- Convert 15 degrees to radians:
- 15 × π = 15π
- 15π ÷ 180 = π/12
- π/12 ≈ 0.2618 radians
Conversion Chart
| Degrees | Radians |
|---|---|
| 20.0 | 0.3491 |
| 25.0 | 0.4363 |
| 30.0 | 0.5236 |
| 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 |
The chart lists degree values in the left column, and the equivalent radian values to the right. You can find the radian measure by locating the degrees you want, and reading across the row to get the radian result. This helps quick conversions without calculation.
Related Conversion Questions
- What is 45 degrees converted into radians?
- How to change 45 degrees to radian unit?
- Why is 45 degrees equal to 0.7854 radians?
- What formula converts 45° to radians?
- Is 45 degrees the same as π/4 radians?
- How many radians are in 45 degrees exactly?
- Can 45 degrees be converted to radians without a calculator?
Conversion Definitions
Degrees: A degree is a measurement of angles, where a full circle divides into 360 equal parts. Each part is one degree. This unit is used mostly in geometry, navigation, and everyday angle measurements. It originated from the Babylonians, who used a base-60 system for dividing circles.
Radian: A radian measures angles by the length of the arc created on a circle. One radian is the angle formed when the arc length equals the radius of the circle. It’s the standard unit in mathematics and physics because it relates angles directly to the radius and circumference of circles.
Conversion FAQs
Why is the factor π/180 used to convert degrees to radians?
The factor π/180 comes from the relation that 180 degrees equal π radians. Because a full circle is 360 degrees or 2π radians, dividing both by two gives that 180 degrees must be π radians. Multiplying degrees by π/180 scales the value into radians accordingly.
Can I convert radians back to degrees? How?
Yes, converting radians back to degrees involves multiplying the radian value by 180 and dividing by π. This reverses the original conversion formula, letting you express radians in the more familiar degree unit.
Is the radian unit more useful than degrees?
Radians are preferred in higher mathematics and physics because they simplify formulas involving trigonometric functions and calculus. The radian ties directly to a circle’s properties, making calculations with angles and periodic functions more natural than with degrees.
What happens if I use degrees instead of radians in trigonometric functions?
Most programming languages and calculators expect angle inputs in radians for trig functions. If degrees are used without conversion, results will be incorrect. Always convert degrees to radians before applying sine, cosine, or tangent functions in such contexts.
Is 45 degrees exactly equal to π/4 radians?
Yes, 45 degrees is exactly π/4 radians by definition. Since 180 degrees equal π radians, dividing both by 4 yields 45 degrees equals π/4 radians. This fraction is exact, but its decimal approximation is 0.7854.