§ 01 / TOOL
Angle Converter.
STATUS READYUNITS 6BASE RADIAN
> CONVERT
// FROM
=
// TO
1.570796
RESULT.
° → rad
1.570796 rad.
90 ° = 1.570796 rad
§ 02 / ABOUT
How it works.
An angle is the rotation between two rays. Different fields measure it differently — everyday math uses degrees, mathematics and physics use radians, surveying uses gradians.
// THE KEY CONVERSIONS
- 1 full turn = 360° = 2π rad ≈ 6.2832 rad = 400 gon
- 1 radian ≈ 57.2958°
- 1 degree = π/180 rad ≈ 0.01745 rad = 60 arc minutes = 3600 arc seconds
- 1 gradian = π/200 rad = 0.9°
// USE IT FOR
- Trigonometry — your calculator wants radians, the problem gives degrees.
- Programming — JavaScript’s Math.sin/cos/tan all take radians.
- Astronomy — arc minutes and arc seconds for celestial measurements.
- Surveying — converting site plans between degree and gradian conventions.
§ 03 / FAQ
Common questions.
How do I convert degrees to radians?+
Multiply by π/180 (≈ 0.01745). So 90° = π/2 ≈ 1.571 rad. The reverse: rad × 180/π ≈ rad × 57.296 = degrees. A full circle is 360° or 2π rad.
Why do scientists use radians instead of degrees?+
Because radians are the "natural" angle unit — defined as the arc length divided by the radius. This makes calculus and trigonometry much cleaner: derivative of sin(x) is cos(x) only when x is in radians. In degrees you’d need extra conversion factors.
What’s a gradian / gon?+
A unit where a full circle is 400 gradians (so 100 gradians = a right angle). Used mostly in surveying and some European engineering disciplines because the decimal subdivision (10s of gradians) maps cleanly onto base-10 grids.
What are arc minutes and arc seconds?+
1 degree = 60 arc minutes (′). 1 arc minute = 60 arc seconds (″). Used in astronomy and high-precision navigation. The Hubble Space Telescope can resolve ~0.05 arc seconds; the moon is about 30 arc minutes wide as seen from Earth.
§ 04 / TOOLS
Related calculators.
§ 05 / READING