Angle Converter: Degrees, Radians, Gradians

Last updated: October 2026

From

Formula

1 ° = 0.01745329 rad

The arc is 0.01745 times as long as the radius, so the angle is 0.01745 rad.

A radian is the angle whose arc is exactly as long as the radius. Each colored piece of the arc is one radius long, and a whole circle takes 2π ≈ 6.28 of them; the numbers around the circle count whole radii.

All Results

° 1

rad 0.0174533

grad 1.11111

Quick Reference Table: Degree → Radian

Value (°)	Result (rad)
1 °	0.017453 rad
5 °	0.087266 rad
10 °	0.174533 rad
15 °	0.261799 rad
30 °	0.523599 rad
45 °	0.785398 rad
60 °	1.0472 rad
90 °	1.5708 rad
120 °	2.0944 rad
180 °	3.1416 rad
270 °	4.7124 rad
360 °	6.2832 rad

About Angle Conversions

Angles are basic to mathematics, engineering, navigation and physics. The degree (°) is the most common unit: a full circle is 360°. The radian (rad) is the SI unit of angle, used in mathematics and physics. One radian equals about 57.296°, and a full circle equals 2π radians. To convert degrees to radians, multiply by π/180. The gradian (grad or gon) divides a full circle into 400 parts, so a right angle is exactly 100 gradians. The gradian is used mainly in surveying and civil engineering.

Common Angles

Angles from construction, transport and geography. A full circle is 360°, or 2π radians, or 400 gradians.

Angle	°	rad	grad
Wheelchair ramp, max (1:12)	4.76	0.08308	5.289
Road gradient of 10%	5.71	0.09966	6.344
Earth's axial tilt	23.44	0.4091	26.04
Typical roof pitch	30	0.5236	33.33
Equilateral triangle corner	60	1.047	66.67
Right angle	90	1.571	100
Straight angle	180	3.142	200
Full circle	360	6.283	400

History of the radian

Degrees split a circle into 360 parts by convention. The radian needs no convention: it measures an angle by how many radii fit along its arc.

1722 Roger Cotes died in 1716; this year his cousin Robert Smith published his mathematical work, Harmonia mensurarum. Cotes is usually credited with inventing radian measure (angles measured by how many radii fit along the arc), though the name came much later.
1873 James Thomson used the word "radian" in examination questions at Queen's College, Belfast. It is the earliest printed use usually cited. The mathematician Thomas Muir had been looking for a name for the same unit and adopted "radian" after consulting him.
1960 The new International System of Units (SI) included the radian as a supplementary unit, together with the steradian for solid angles.
1995 The General Conference on Weights and Measures made the radian and the steradian derived units, ending the separate class of supplementary units.

Sources:

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