FORMULA
How to convert
rad = ° × 0.01745329252Example: 10 ° = 0.17453293 rad.
° → RAD
Degrees to Radians
Convert degrees to radians with an exact, deterministic calculation.
LIVE CONVERSIONDECIMAL ENGINE EXACT_
1 ° = 0.01745329252 rad
MULTI-CONVERT
QUICK ANSWER
1 Degree
0.01745329252 rad
REFERENCE TABLE
Degree to Radian
| degrees | radians |
|---|---|
| 1 ° | 0.01745329 rad |
| 5 ° | 0.08726646 rad |
| 10 ° | 0.17453293 rad |
| 25 ° | 0.43633231 rad |
| 50 ° | 0.87266463 rad |
| 100 ° | 1.74532925 rad |
ABOUT THIS CONVERSION
Convert degrees to radians
This page converts degrees (°) to radians (rad). Convertor4U first interprets the input using Degree's definition, then expresses the same quantity in Radian. The result is calculated from the stored factor and offset definitions, not from a rounded lookup table.
Real-world example
For working with a drawing, bearing, machine setting, or rotation, an input of 90 ° converts to 1.57079633 rad. Keep extra digits while calculating, then round only the final value to the precision the task actually needs.
Rounding and precision
Small angular errors can produce large position errors over distance. Preserve sufficient digits for navigation or machining, and round only to the instrument's angular resolution. Decimal degrees and degrees-minutes-seconds require separate formatting steps.
Regional context
Degrees are widely understood, while mathematical formulas often require radians. The word 'mil' is ambiguous across military and engineering angular systems; this converter provides the SI milliradian and labels it mrad.
Common mistake
Keep angular units separate from angular speed; radians and radians per second describe different quantities.
Editorial method
Definitions and sources are listed below. Calculations retain more precision than the default display and round only for presentation.
USEFUL ANSWERS
° to rad FAQs
How do I convert degrees to radians?
Enter the ° value in the calculator. It applies the stored factor and offset definitions and returns the equivalent in rad; the formula and common-value table are shown on this page.
Is the ° to rad conversion exact?
Defined measurement relationships are calculated with decimal arithmetic from stored standards. The displayed answer may be rounded for readability. Currency results instead depend on the dated reference rate shown.
How many decimal places should I keep?
Small angular errors can produce large position errors over distance. Preserve sufficient digits for navigation or machining, and round only to the instrument's angular resolution. Decimal degrees and degrees-minutes-seconds require separate formatting steps.
What should I check before using the result?
Keep angular units separate from angular speed; radians and radians per second describe different quantities.
FROM UNIT
Degree
A degree (°) is one 360th of a complete revolution. It measures plane angle or rotation.
BIPM SI Brochure and exact international definitions ↗Definition verified 14 August 2026TO UNIT
Radian
The radian (rad) is the SI unit of plane angle; one full revolution is 2π radians. It measures plane angle or rotation.
BIPM SI Brochure and exact international definitions ↗Definition verified 14 August 2026Content reviewed by Convertor4U Editorial Team · 16 August 2026 · Report an error on this page