degrees to radians

Unit Converters

Instantly convert angles between Degrees and Radians with exact Pi fractions and trigonometric values.

Exact Pi Fraction

2π3
2.094395 rad

Unit Circle (2D)

Trigonometric Context

sin(θ)√32
cos(θ)-12
tan(θ)-√3
r = d × (
π 180
)
  • r (Radians): The angular measurement in radians.
  • d (Degrees): The angular measurement in degrees.
  • π (Pi): Approximately 3.14159.

Degree to Radian Conversion Table

Degree [°]Radian [rad]
0.01 °0.0001745329 rad
0.1 °0.0017453293 rad
1 °0.0174532925 rad
2 °0.034906585 rad
3 °0.0523598776 rad
5 °0.0872664626 rad
10 °0.1745329252 rad
20 °0.3490658504 rad
50 °0.872664626 rad
100 °1.745329252 rad
1,000 °17.4532925199 rad

What is degrees to radians?

Instantly convert angles between Degrees and Radians with exact Pi fractions and trigonometric values. This calculator goes beyond simple decimals, giving you the precise mathematical output required for advanced geometry, physics, and programming. Toggle your input to instantly see the angle plotted on the interactive unit circle, providing vital spatial awareness. Furthermore, the engine automatically calculates the corresponding sine, cosine, and tangent ratios in pure fractional form, eliminating rounding errors from your workflow.
Practical Calculation Example
A mechanical engineer in Seattle is designing a custom cam mechanism and needs to program the CNC machine using precise radian measurements. They enter 120 into the DEGREES (°) field. The tool instantly outputs the EXACT PI FRACTION as 2π/3. By checking the TRIGONOMETRIC CONTEXT panel, they quickly verify the sin(θ) and cos(θ) ratios to determine the exact cutting vector before hitting Copy Exact Math to paste the pure formulas directly into their G-code script.
Reference Zones
Interface Element Mathematical Function Practical Application
RADIANS (RAD) Angular Measurement The standard unit of angular measure used in calculus and computer graphics.
EXACT PI FRACTION Algebraic Output Displays the unrounded, pure mathematical fraction (e.g., 2π/3) alongside its decimal equivalent.
UNIT CIRCLE (2D) Spatial Visualization Plots the angle on a Cartesian coordinate system to instantly verify the vector's quadrant and direction.
TRIGONOMETRIC CONTEXT Ratio Calculation Provides the exact sine, cosine, and tangent values (e.g., √3/2) for the inputted angle.

History and Origin

The division of a circle into 360 degrees dates back to the ancient Babylonians, who used a sexagesimal (base-60) number system. The radian, however, is a much more recent concept, first proposed by the British mathematician Roger Cotes in 1714. He recognized that measuring angles by the arc length they subtend provides a more natural and mathematically elegant unit, which is exactly why radians are the absolute standard in modern calculus and physics today.

What is Degree?

Definition & Usage

A degree (symbol: °) is a measurement of a plane angle in which one full rotation is 360 degrees.

What is Radian?

Definition & Usage

The radian (symbol: rad) is the SI unit for measuring angles, and is the standard unit of angular measure used in many areas of mathematics.

Frequently Asked Questions

How accurate is this degrees to radians tool?

Our tools utilize high-precision floating point math guaranteeing accuracy up to the 6th decimal place.

Is this free to use?

Yes, all converters and calculators on ToolsMetrics are 100% free with no limits.

More Frequently Asked Questions