Need to convert Radians to Degrees (rad → °)? The converter above delivers instant results. Below: the exact conversion factor, a reference table, real-world examples, and the history of both units — everything you need for accurate rad to ° conversion.
The History of the Radian
The radian was formalized by Roger Cotes in 1714, though the concept was implicit in Leonhard Euler's earlier work. 1 radian = the angle where arc length equals radius ≈ 57.296°. 2π radians = 360°. The radian's mathematical elegance is profound: it's the only angle unit where d(sin θ)/dθ = cos θ without a correction factor. This makes radians essential in calculus, Fourier analysis, wave mechanics, and any discipline involving periodic functions.
The History of the Degree
The 360° circle traces to Babylon (~1500 BCE), where astronomers used a base-60 number system and divided the year into ~360 days, then divided the sky circle into 360 corresponding parts. Each degree was subdivided into 60 arcminutes and 60 arcseconds — still the basis of geographic coordinates (latitude/longitude). The 360° convention survived the metric revolution precisely because 360 has many factors (2, 3, 4, 5, 6, 8, 9, 10, 12...), making angle arithmetic unusually clean.
How to Convert Radians to Degrees
Multiply Radians by 57.2958 to get Degrees.
° = rad × 57.2958Step-by-Step Example
- Start with your value in Radians — for example, 25 rad.
- Multiply: 25 × 57.2958 = 1,432.4 °.
Pro Tip: For quick rad to ° conversions without arithmetic, bookmark this page. The interactive tool above updates instantly as you type.
Radian to Degree Reference Table
| Radian (rad) | Degree (°) |
|---|---|
| 1 | 57.2958 ° |
| 2 | 114.5916 ° |
| 5 | 286.479 ° |
| 10 | 572.958 ° |
| 25 | 1,432.4 ° |
| 50 | 2,864.8 ° |
| 100 | 5,729.6 ° |
Real-World Examples — rad to °
- 57.2958 ° — the equivalent of 1 rad (the smallest reference point)
- 572.958 ° — a practical mid-range value (10 rad)
- 5,729.6 ° — a common large-quantity reference (100 rad)
Applications of Radian-to-Degree Conversion
The rad to ° conversion is needed in mathematics, navigation, surveying, and astronomy. Here's where it specifically matters:
- International specifications: Products designed in one unit system must be documented for users who work in the other.
- Scientific and technical work: Research papers and engineering drawings specify angle in a particular unit — accurate conversion prevents costly errors.
- Education: Physics, chemistry, and applied math curricula require fluency in angle unit conversion.
- Everyday tasks: Cooking, construction, fitness, and travel all involve angle conversions when switching between unit systems.
Common Mistakes When Converting Radian to Degree
- Mistake: Forgetting to switch calculator to radians mode for trigonometry
- Mistake: Confusing degrees and gradians — both use decimal notation but 90° = 100 grad
- Mistake: Using degree-based trig identities in physics formulas that expect radians
Frequently Asked Questions — Radian to Degree
How many Degrees are in 1 Radian?
Exactly 57.2958 °. The conversion factor is 57.2958 — this is derived from the precise SI definitions of both units.
What is the formula to convert Radians to Degrees?
° = rad × 57.2958. For example: 5 rad × 57.2958 = 286.479 °.
How do I convert Degrees back to Radians?
Divide by 57.2958: rad = ° ÷ 57.2958. Or multiply by 0.017453.
Why would I convert Radians to Degrees?
Radians and Degrees are both used in mathematics, navigation, surveying, and astronomy, but different countries and industries prefer different units. Converting between them is necessary when reading foreign specifications, using international recipes, or collaborating across measurement systems.
Is this Radian-to-Degree converter accurate?
Yes — the factor 57.2958 is derived from official SI definitions and international standards. All calculations use full floating-point precision.
What are some real-world examples of rad to ° conversion?
1 rad = 57.2958 °; 10 rad = 572.958 °; 100 rad = 5,729.6 °.
Conclusion
Converting Radians to Degrees: multiply by 57.2958; 1 rad = 57.2958 °. The converter above handles any value instantly. Refer to the table above for quick reference values, and bookmark this page for fast rad to ° access.