How do you convert degrees to radians?

To convert degrees to radians, multiply the degree value by π/180 (approximately 0. 01745). For example: 1) 180° = π radians, 2) 90° = π/2 radians, 3) 360° = 2π radians, 4) 45° = π/4 radians. Our calculator handles this automatically.

What is 1 degree equal to in radians?

1 degree equals π/180 radians (approximately 0.01745 radians). Common conversions include: 1) 30° = π/6 rad, 2) 45° = π/4 rad, 3) 60° = π/3 rad, 4) 90° = π/2 rad, 5) 180° = π rad, 6) 360° = 2π rad.

What are common degree to radian conversions?

Common degree to radian conversions include: 1) 30° = π/6 ≈ 0.524 rad, 2) 45° = π/4 ≈ 0.785 rad, 3) 60° = π/3 ≈ 1.047 rad, 4) 90° = π/2 ≈ 1.571 rad, 5) 180° = π ≈ 3.142 rad, 6) 360° = 2π ≈ 6.283 rad.

Why do we use both degrees and radians?

Different angle units serve different purposes: 1) Degrees are intuitive for everyday use, 2) Radians are preferred in mathematics and physics, 3) Radians simplify many mathematical formulas, 4) Degrees are easier for non-technical measurements, 5) Some calculations require radians for accuracy.

What's the easiest way to estimate degrees to radians?

For quick estimates of degrees to radians: 1) Remember that 180° = π radians, 2) 90° = π/2 radians, 3) 60° = π/3 radians, 4) 45° = π/4 radians, 5) For other angles, multiply degrees by π/180 (≈0. 01745).

How are degrees and radians used in real life?

Degrees and radians are used in various contexts: 1) Navigation and mapping (degrees), 2) Mathematics and physics (radians), 3) Engineering calculations (both), 4) Computer graphics (both), 5) Astronomy (both), 6) Trigonometry (both), 7) Surveying (degrees).

Degrees to Radians Conversion Calculator

Degrees (°) to Radians (rad) Converter

Symbol: ° (degree), rad (radian)

Degrees and radians are units for measuring angles. A degree is 1/360 of a full circle, while a radian is the angle formed when the arc length equals the radius.

Formula: 1 radian = 180/π degrees ≈ 57.2958°

Common Conversions:

30° = π/6 rad
45° = π/4 rad
90° = π/2 rad
180° = π rad
360° = 2π rad

From:

Degree (°)

To:

Radian (rad)

Conversion Result

1 °=

1.000 rad

Use the converter above to calculate different values and units

What are Angle Measurements?

Angle measurements quantify the amount of rotation between two intersecting lines or planes. Degrees and radians are two standard units used for measuring angles, with degrees being more common in everyday use and radians being preferred in mathematics and scientific calculations.

The relationship between degrees and radians is based on the properties of a circle: a complete circle spans 360 degrees or 2π radians. This relationship gives us the conversion factor: 1 degree equals π/180 radians (approximately 0.01745). This conversion is fundamental in trigonometry, calculus, physics, and engineering.

Common Degrees to Radians Conversions

Degrees (°)	Radians (rad)	Common Reference
30°	π/6	Angle in a 30-60-90 triangle
45°	π/4	Diagonal angle in a square
60°	π/3	Angle in an equilateral triangle
90°	π/2	Right angle
180°	π	Straight angle
270°	3π/2	Three-quarter circle
360°	2π	Full circle
1°	0.01745 rad	One degree (standard unit)

Practical Use Cases

Mathematics: Converting degrees to radians for calculus problems, trigonometric equations, and series expansions where radians are the natural unit
Physics: Converting angle measurements for calculating angular velocity, frequency, and wave properties in oscillations
Engineering: Designing circular components, gears, and mechanical systems that involve rotational motion
Computer Graphics: Programming animations, rotations, and perspective transformations in 2D and 3D environments
Navigation: Converting between coordinate systems and mapping applications
Astronomy: Converting angle measurements for celestial calculations, orbital mechanics, and telescope positioning

Educational Resource

This educational video explains the relationship between degrees and radians and demonstrates how to convert between these units with practical examples and applications.

Conversion Tools

Download Conversion Chart (PDF)

Get our comprehensive degrees to radians conversion chart for quick reference when you're offline.

Degrees to Radians Conversion FAQs

Find answers to common questions about converting between degrees and radians.