Angle Converter
Turn any angle into a different unit — degrees, radians, gon, arcminutes, arcseconds, and turns — using exact, published factors.
Degree-based
Every unit is a fixed multiple of the degree, so the converter pivots through degrees for one consistent rule.
Display rounding
Results are shown to six decimal places, so values like π rad may round the last digit.
What is an angle converter?
One value, any unit
An angle converter changes a value from one unit into another — degrees to radians, radians to degrees, degrees to gon, arcminutes to degrees, and back. It works by translating every value through a single shared pivot, the degree (°), so any pair of units converts with one consistent rule. This tool covers the six units used in math, trigonometry, navigation, surveying, and astronomy: degree, radian, gradian (gon), arcminute, arcsecond, and turn.
Angle units share a zero point, so converting is purely multiplicative — scale by the factor in, then by the factor out.
result = value × (degrees per from-unit) ÷ (degrees per to-unit)Each unit has a fixed number of degrees: a full circle is 360°, 2π rad, 400 gon, or 1 turn; one degree is 60 arcminutes and 3600 arcseconds. The converter turns your value into degrees first, then into the unit you want — so a single rule handles every direction.
Suppose you want to convert 180° into radians.
Convert to degrees
The value is already in degrees: 180 × 1 = 180°.Convert out to radians
Divide by the radian factor: 180 ÷ 57.29578 = 3.141593.Read the result
180° converts to 3.141593 rad — exactly π radians, half a full turn around a circle.
Angle conversion is a simple ratio, so the everyday anchors are easy to remember: a full circle is 360° = 2π rad ≈ 6.283185 rad = 400 gon = 1 turn, and half a circle is 180° = π rad ≈ 3.141593 rad. The right unit depends on the job: radians are the natural choice for math and trigonometry because they are arc length divided by radius, degrees are the everyday unit for geometry and navigation, gon is used in surveying because a right angle is a round 100 gon, and arcminutes and arcseconds measure the tiny angles in astronomy and optics. As a quick sanity check, a right angle is 90° = π/2 rad ≈ 1.5708 rad = 100 gon. If a converted number looks far off by a factor like π or 200, check that the from-unit and to-unit are not swapped — the swap arrow flips them in one click.
The arithmetic is exact; the limits are about precision and how angles wrap.
Precision and angle wrapping
The radian factor uses 180/π, which is irrational, so conversions to or from radians carry a long decimal tail; results are rounded to six decimal places and may lose the last digit. This tool converts the raw numeric value and does not wrap angles into a 0–360° range, so 450° stays 450° rather than folding to 90°. Subtract full turns yourself first if you need a value within a single revolution.