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Convert between degrees, radians, and gradians.
📐 Used in math, engineering, and navigation. 1 revolution = 360° = 2π rad.
This tool converts between angle units: degrees, radians, gradians, arc minutes, arc seconds, and full revolutions.
Radians are the "natural" angle unit because they relate directly to circle geometry: an angle of 1 radian cuts an arc equal to the radius. Calculus formulas (derivatives of sine and cosine) only work cleanly in radians.
The Angle Converter converts angle converterfrom one unit to another using the exact internationally defined conversion factors. Type a value, choose your source and target units, and the converted result is shown instantly — no waiting, no page reload.
Manual conversion is error-prone because it means memorizing ratios (how many feet in a meter, how many pints in a liter). This tool removes that friction: the conversion factor is built in, and the math is done to full precision with no rounding until the final displayed number.
Common uses: people reach for this tool when they need to look up a degrees to radians converter, radians to degrees calculator, gradians to degrees online, or arcminutes to degrees.
Browser-based tools like this one have a few real advantages over installed software or manual methods:
The Angle Converter is based on the following formula:
rad = deg × π/180 deg = rad × 180/π 1 rev = 360° = 2π rad = 400 grad 1° = 60 arcmin, 1 arcmin = 60 arcsec 1 grad = 0.9°
Variables: deg (°) = degrees rad = radians grad = gradians, 400 per full circle arcmin (′) = arcminutes, 60 per degree arcsec (″) = arcseconds, 60 per arcminute rev = full revolutions
A full circle is 360°, 2π rad, or 400 grad. Radians are the natural unit for math because arc length equals radius times the angle in radians; gradians split the circle into 400 parts so a right angle is exactly 100 grad.
Worked example: Convert 90° to radians and gradians: rad = 90 × π/180 = π/2 ≈ 1.5708 rad grad = 90 ÷ 0.9 = 100 grad Convert 0.5° to arcunits: 0.5 × 60 = 30 arcmin = 30 × 60 = 1800 arcsec Reverse: 1.5708 rad × 180/π ≈ 90°
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