Angle Converter
Convert any value from degree to radian with full precision. Use the converter above for instant results, or read on for the exact formula, worked examples, common uses, and answers to frequently asked questions.
π Quick Reference Table
About the Degree to Radian conversion
Angle conversions are needed in mathematics, engineering, navigation, astronomy, and surveying. The radian is the SI unit and is defined as the angle made by an arc equal in length to the radius. The degree, arcminute, and arcsecond are older units that survive in navigation, geography, and astronomy.
This page focuses specifically on converting degree to radian. Use the converter above for instant results, or read on for what each unit is, the exact formula, a worked example, and answers to common questions.
Understanding degree and radian
What is a degree?
The degree divides a full circle into 360 equal parts, a convention inherited from ancient Babylonian astronomy and its base-60 counting. It is the everyday unit for angles in geometry, navigation, and construction.
What is a radian?
The radian is the SI unit of angle, defined as the angle subtended by an arc equal in length to the radius, so a full circle is two pi radians. It is the natural unit for calculus, physics, and trigonometry.
How a degree compares to a radian
The radian is the larger of the two units: it takes about 57.29577951 degree to make a single radian. Because the degree is smaller, the same length or quantity works out to a larger number when you measure it with that unit. Knowing which unit is larger is a quick way to sanity-check a conversion: if the numbers move in the wrong direction, the two units have probably been swapped.
Conversion formula
The exact mathematical relationship between degree and radian is:
1 degree = 0.01745329 radian
So to convert a value V from degree to radian, use:
Vradian = Vdegree Γ 0.01745329
To go in the opposite direction:
Vdegree = Vradian Γ 57.29577951
These factors come from the international definitions published by NIST, BIPM, and ISO 80000 and are exact within their respective standard systems. The converter applies them with full floating-point precision.
Worked example
Using the formula above, here are some common values converted from Degree to Radian:
| Degree | Radian |
|---|---|
| 1 | 0.017453 |
| 5 | 0.087266 |
| 10 | 0.174533 |
| 25 | 0.436332 |
| 50 | 0.872665 |
| 100 | 1.745329 |
Sources and accuracy
One full revolution equals 2Ο radians = 360 degrees = 400 gradians. The degree is traditionally divided into 60 arcminutes, each of 60 arcseconds. The radian is dimensionless but is given its own unit by the SI (BIPM).
Conversion factors are cross-checked against the NIST SP 811 guide, the BIPM SI brochure, and ISO 80000, plus published historical references for older unit systems. For mission-critical work such as medical dosing, legal-for-trade measurement, aerospace, or large-scale engineering, always verify independently with the original source.
Practical tips
When entering values for trigonometric functions in spreadsheets or code, use radians unless the function explicitly accepts degrees. Most calculators have a "DRG" or "MODE" button to switch between degrees, radians, and gradians.
Frequently asked questions
How many radian are in one degree?
One degree equals 0.01745329 radian. To convert, multiply your degree value by 0.01745329.
Which is bigger, a degree or a radian?
The radian is bigger. One degree is only about 0.01745329 radian.
How accurate is this degree to radian converter?
It uses the official international conversion factors from NIST and BIPM with full double-precision floating-point accuracy. For everyday use the result is precise to many more decimal places than any practical measurement requires.
Can I convert radian back to degree as well?
Yes. Use the swap button above to reverse the From and To fields, or change either dropdown to any unit in the angle category. The calculation runs entirely in your browser, so it also works offline once the page has loaded.
About Angle Conversions
Convert between degrees, radians, gradians, arcminutes, and arcseconds.
UnitSwiftPro uses internationally standard conversion factors maintained by NIST and ISO. For critical applications (medical, engineering, legal), always verify against an authoritative source.