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120 degrees is approximately 2.0944 radians. When converting degrees to radians, you multiply the degree value by π divided by 180. So, 120 degrees equals 2.0944 radians because 120 × (π / 180) = 2.0944.

Converting 120 degrees to radians involves multiplying the degree value by π (pi) divided by 180. Since π is approximately 3.1416, the calculation is 120 × (3.1416 / 180), which simplifies to roughly 2.0944 radians. This conversion is essential in mathematics and physics where radian measure is standard.

What is the conversion from degrees to radians?

The process of converting degrees to radians is based on the fact that a full circle is 360 degrees or 2π radians. To switch from degrees to radians, you multiply the degree measure by π/180. This ratio converts the angular measure from one unit to the other, maintaining the same angle size in different units. For example, converting 120 degrees to radians involves multiplying 120 by π/180, resulting in 2.0944 radians. This method works because it relates the linear measure of angles in degrees to the radian measure, which is based on the radius of a circle.

Conversion Tool

Conversion Formula

The formula to convert degrees to radians is radians = degrees × (π / 180). This works because π radians equal 180 degrees, which means 1 degree equals π/180 radians. By multiplying the degree value by π/180, you scale the measure to radians, preserving the angle’s size in a different unit. For example, converting 60 degrees: 60 × (π / 180) = π / 3 ≈ 1.0472 radians.

Conversion Example

• Convert 90 degrees to radians:
• Multiply 90 by π / 180.
• 90 × (3.1416 / 180) = 1.5708 radians.
• So, 90 degrees equals approximately 1.5708 radians.
• Convert 45 degrees to radians:
• 45 × (π / 180) = 0.7854 radians.
• This shows that 45 degrees is roughly 0.7854 radians.
• Convert 150 degrees to radians:
• 150 × (π / 180) = 2.6180 radians.
• Therefore, 150 degrees is approximately 2.6180 radians.

Conversion Chart

This chart helps you quickly find the radian equivalent for degrees between 95 and 145. To read, find your degree value in the first column, then look across to find the corresponding radian in the second column. It makes comparing angles faster and easier.

Related Conversion Questions

• How many radians is 120 degrees exactly?
• What is the radian measure of 120 degrees?
• Can I convert 120 degrees to radians using a calculator?
• What is 120 deg expressed in radians in decimal form?
• How do I convert degrees to radians for angles like 120°?
• What is the radian equivalent of a 120-degree angle?
• Is there an easy way to convert 120 degrees into radians manually?

Conversion Definitions

deg

Deg, short for degrees, is a unit measuring angles where a full circle equals 360 degrees. It is commonly used in navigation, geometry, and everyday measurements, representing how much an angle opens or turns around a fixed point.

rad

Rad, short for radians, is a measurement for angles based on the radius of a circle. One radian equals the angle at which the arc length equals the radius. It’s widely used in mathematics and physics because it simplifies many formulas involving angles and circles.

Conversion FAQs

Why is converting degrees to radians important in mathematics?

Converting degrees to radians is crucial because many mathematical formulas involving trigonometry, calculus, and physics are based on radian measure. Radians provide a natural way to describe angles in relation to the circle’s radius, simplifying calculations and expressions.

How accurate is the approximation of π in these conversions?

Using π approximations like 3.1416 gives sufficiently accurate results for most practical purposes, but for high-precision calculations, more decimal places of π can be used. The slight difference doesn’t significantly affect the outcome in typical applications.

Can I convert any degree measure to radians using this method?

Yes, the formula radians = degrees × (π / 180) applies universally for converting any degree measure to radians, regardless of whether the number is whole or fractional. It works because of the relationship between the circle’s circumference and angle measures.

What is the significance of the radian measure in trigonometry?

In trigonometry, radian measure simplifies the derivatives and integrals of trigonometric functions. It ensures that the functions are expressed in their most natural form, making the calculations more straightforward and the results more consistent across various mathematical contexts.