Angle Converter
Convert between degrees, radians, gradians, arcminutes, arcseconds, and turns instantly.
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Popular conversions
About this angle converter
This tool converts between 6 common angle units, from everyday degrees to the radians used in calculus and the arcseconds used in astronomy. Pick any two units, enter a value, and the result updates instantly — every conversion happens with simple arithmetic directly in your browser, so there's no network request, no waiting, and it keeps working even if you lose your internet connection.
Common real-world uses
Degrees are the everyday choice for navigation, construction, and geometry; radians show up constantly in trigonometry, physics, and programming (most languages' math libraries expect radians, not degrees); gradians appear in some surveying software; and arcminutes/arcseconds are the standard for precise astronomical measurements like a telescope's field of view or the parallax of a star.
Units covered
- Degree (°) — the everyday unit for angles, dividing a full circle into 360 parts — a convention that traces back to ancient Babylonian base-60 mathematics.
- Radian (rad) — the SI unit of angle, defined so a full circle equals 2π radians — the natural unit for calculus and most programming math functions (Math.sin, Math.cos, etc.).
- Gradian (gon) — divides a full circle into 400 parts instead of 360, making a right angle exactly 100 gradians — used in some surveying and civil engineering software.
- Arcminute (′) — one sixtieth of a degree, used in astronomy and optics to describe very small angular separations, like the resolving power of a telescope.
- Arcsecond (″) — one sixtieth of an arcminute (1/3600 of a degree), the standard unit for extremely precise angular measurements in astronomy, such as stellar parallax.
- Turn (turn) — one full rotation, equal to 360 degrees — used in fields like robotics and audio (turntable speed) where counting full revolutions is more intuitive than degrees.
Frequently asked questions
Why does a circle have 360 degrees?
It traces back to ancient Babylonian mathematics, which used a base-60 (sexagesimal) counting system — 360 divides evenly by 60, along with many other small numbers, which made it convenient for the astronomical calculations of the time.
When would I use radians instead of degrees?
Radians are the standard unit in calculus and most programming languages' trig functions (Math.sin, Math.cos, etc. in JavaScript all expect radians), because they make many formulas simpler by directly relating an angle to arc length on a unit circle.
What are gradians used for?
Gradians divide a circle into 400 parts instead of 360, making a right angle exactly 100 gradians — a decimal-friendly convention still used in some European surveying and civil engineering software.
Does this work offline?
Yes — every conversion is a simple multiplication done in your browser, so it keeps working without an internet connection once loaded.