Conversion From Degrees to Radians Calculator

Convert angles from degrees to radians with our precise calculator. Learn the conversion formula, understand the difference between degrees and radians, and see practical examples of how this conversion is used in mathematics and science.

What is Degrees to Radians Conversion?

Degrees and radians are two different units for measuring angles. Degrees are commonly used in everyday contexts, while radians are more common in advanced mathematics and physics. The conversion between these units is essential for many calculations in trigonometry, calculus, and engineering.

Key Conversion Fact

180 degrees = π radians (approximately 3.14159 radians)

The conversion from degrees to radians allows you to use trigonometric functions in calculators and programming languages that expect radians. Many scientific calculators have a "rad" mode that automatically converts degrees to radians for trigonometric calculations.

How to Convert Degrees to Radians

The formula to convert degrees to radians is straightforward:

Conversion Formula

radians = degrees × (π / 180)

This formula works because a full circle is 360 degrees or 2π radians. Therefore, 180 degrees is exactly π radians.

Example Conversion

Convert 90 degrees to radians:

radians = 90 × (π / 180) = π/2 ≈ 1.5708 radians

This conversion is essential when working with trigonometric functions in calculus, physics, and engineering. Many programming languages and scientific calculators use radians as their default unit for trigonometric functions.

Degrees vs Radians

Degrees and radians are both units of angular measurement, but they have different origins and uses:

Feature	Degrees	Radians
Origin	Based on the 360-degree circle	Based on the radius of a circle
Full Circle	360 degrees	2π radians (≈6.2832 radians)
Common Use	Everyday measurements, navigation	Advanced mathematics, physics, engineering
Trigonometry	Used in basic trigonometry	Used in calculus and advanced math

Degrees are more intuitive for everyday use, while radians are more mathematically convenient for calculations involving rates of change and derivatives.

Common Conversion Values

Here are some common angle conversions between degrees and radians:

Degrees	Radians	Approximate Value
0°	0	0
30°	π/6	≈0.5236
45°	π/4	≈0.7854
60°	π/3	≈1.0472
90°	π/2	≈1.5708
180°	π	≈3.1416
270°	3π/2	≈4.7124
360°	2π	≈6.2832

These common values are useful for quick reference when working with trigonometric functions and circular measurements.

FAQ

Why do we need to convert degrees to radians?

Degrees and radians are used in different contexts. Degrees are more intuitive for everyday measurements, while radians are more mathematically convenient for advanced calculations in calculus and physics.

Is π/2 radians equal to 90 degrees?

Yes, π/2 radians is exactly equal to 90 degrees. This is because 180 degrees equals π radians, so half of that is π/2 radians.

Can I use degrees directly in trigonometric functions?

Many scientific calculators have a "deg" mode that allows you to use degrees directly with trigonometric functions. However, most programming languages and advanced mathematical software use radians by default.

What is the difference between a degree and a radian?

A degree is based on the 360-degree circle, while a radian is based on the radius of a circle. One radian is the angle subtended at the center of a circle by an arc equal in length to the radius.