Angle Unit Converter

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Reference angles

	°	rad	gon	turn
Full circle	360	2π ≈ 6.2832	400	1
Half circle (straight angle)	180	π ≈ 3.1416	200	0.5
Right angle	90	π/2 ≈ 1.5708	100	0.25
Equilateral triangle angle	60	π/3 ≈ 1.0472	66.67	0.167
45° angle (π/4)	45	π/4 ≈ 0.7854	50	0.125
30° angle (π/6)	30	π/6 ≈ 0.5236	33.33	0.0833

rad

gon

turn

Full circle

360

2π ≈ 6.2832

400

Half circle (straight angle)

180

π ≈ 3.1416

200

0.5

Right angle

π/2 ≈ 1.5708

100

0.25

Equilateral triangle angle

π/3 ≈ 1.0472

66.67

0.167

45° angle (π/4)

π/4 ≈ 0.7854

0.125

30° angle (π/6)

π/6 ≈ 0.5236

33.33

0.0833

How to use?

Enter a value Type in any unit field — degrees, radians, gradians or turns. All other fields update instantly.

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FAQ

How do you convert degrees to radians?

Multiply degrees by π/180 (≈ 0.017453). For example, 90° × π/180 = π/2 ≈ 1.5708 rad. To go the other way, multiply radians by 180/π (≈ 57.296).

What is a gradian (gon)?

A gradian (also called gon or grad) divides the full circle into 400 equal parts. It is used in surveying and civil engineering. A right angle = 100 gradians = 90 degrees = π/2 radians.

What is an arcminute and arcsecond?

1 degree is divided into 60 arcminutes (′) and each arcminute into 60 arcseconds (″). These are used in astronomy, navigation (GPS coordinates), and optics. 1° = 60′ = 3 600″.

Angle Units Explained

Angles can be measured in several units depending on the field. The most common are degrees (°) for everyday use, radians (rad) for mathematics and physics, and gradians (gon) for surveying.

Degrees vs Radians

A full circle is 360° or 2π radians. Radians are the SI-derived unit and are required in most mathematical and scientific formulas. The conversion: radians = degrees × π / 180.

Arcminutes and Arcseconds

Used in astronomy and GPS coordinates, 1° = 60 arcminutes (′) = 3 600 arcseconds (″). GPS latitude/longitude is often expressed in degrees, minutes and decimal seconds (DMS format).

Gradians (Gon)

The gradian system divides a right angle into 100 parts, making the full circle 400 gon. It is used in land surveying and civil engineering across Europe. A slope of 1% equals 0.01 gon ≈ 0.573°.

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