What is the base SI unit for angle?

The primary reference unit for angle in this converter is the Degree (°). All 7 supported angle units are anchored to this standard.

Are these angle conversion factors verified?

Yes, all angle conversion constants on UnitConvertersGo are verified against NIST Special Publication 811 and ISO/IEC 80000 international metrology standards.

Angle Converter

Enter a value below to convert between metric, imperial, and standard angle units.

Convert Angle

Enter a value and select the units to convert between degrees, radians, and gradians.

Instant conversion

Value

From

Result

0.17453 rad

10 ° = 0.17453 rad

10 ° = 0.17453 rad = 11.11111 gradGet Widget

You can change the units using the dropdowns above or click on a unit button.

Suggested Conversions

Common Angle Reference Points

Here are some common angle values in Degree (°), Radian (rad), and Gradian (Gon) (grad). Click any preset value or arrow to load it into the converter.

Description	Degree (°)	Radian (rad)	Gradian (Gon) (grad)
30° acute angle (π/6 rad)	30	0.5236	33.33333
45° diagonal angle (π/4 rad)	45	0.7854	50
1 Radian (~57.2958°)	57.29578	1	63.66198
90° right angle (π/2 rad)	90	1.5708	100
180° straight angle (π rad)	180	3.14159	200
360° full circle (2π rad)	360	6.28319	400

Angle Conversion Formulas

Use the following formulas to convert between degrees, radians, and gradians.

Degrees to Radians

rad = deg × π / 180

Radians to Degrees

deg = rad × 180 / π

Degrees to Gradians

grad = deg ÷ 0.9

Example: Convert 180 Degrees to Radians

rad = 180 × (π ÷ 180)

rad = 3.141593 rad (π rad)

A full circle equals 360 degrees, 2π radians (≈ 6.283185 rad), or 400 gradians (gons).

More Degree & Radian Conversions

Convert from Degrees

Convert to Radians

Frequently Asked Questions

1 degree (°) equals 0.01745 radians (rad). Multiply your degree value by 0.01745 or enter it in the Angle Converter above for instant calculation.

Angle Converter

Quick Info

Degree (°) divides a complete circle into 360 equal parts, with each degree subdivided into 60 arcminutes (′).
Radian (rad) is the coherent SI unit of plane angle where 1 rad = 180/π ≈ 57.29578°.
Gradian (grad / gon) divides a right angle into 100 grads and a full circle into 400 grads (1 grad = 0.9°).
Arcminute & Arcsecond: 1 degree = 60 arcminutes (′) = 3,600 arcseconds (″), used in astronomy and cartography.

Angle Units Comparison

Degree (°)

Standard geometric angle unit equal to 1/360 of a full rotation.

Radian (rad)

SI angle subtended by an arc equal in length to the radius (~57.2958°).

Gradian (grad)

Metric surveying angle equal to 1/400 of a circle (0.9 degrees).

References

[1]NIST CUU · Non-SI Units Accepted for Use (deg, arcmin, arcsec)
Source
[2]NIST SI · SI Coherent Unit: Radian (rad)
Source
[3]NIST SP 811 · NIST SP 811 App. B.9 (Plane Angle)
Source

Related Categories

Add This Calculator to Your Site

Free HTML widget · 4 embed formats

Embed the interactive Angle Converter widget on your blog, classroom, or documentation page.

Customize & Get Embed Code

All Angle Conversion Calculators (6)

Select any dedicated angle pair below for worked examples and printable tables

Degrees to Radians (° to rad)Radians to Degrees (rad to °)Degrees to Gradians (° to grad)Arcminutes to Degrees (′ to °)Radians to Revolutions (rad to rev)Angular Mils (NATO) to Degrees (mil to °)

Category Conversion Matrix

Simultaneous comparison of 7 units in this category

Degree (°)

Radian (rad)

0.01745

Gradian (Gon) (grad)

1.11111

Minute of Arc (′)

Second of Arc (″)

3,600

Revolution (Turn) (rev)

0.00277777

Angular Mil (NATO) (mil)

17.77778

Angle Unit Definitions & Symbols

Degree (°)

OTHER

1/360 of a full circle.

Radian (rad)

SI angle unit (1 rad ≈ 57.29578°).

Gradian (Gon) (grad)

METRIC

1/400 of a full circle (0.9°).

Minute of Arc (′)

OTHER

1/60 of a degree.

Second of Arc (″)

OTHER

1/3600 of a degree.

Revolution (Turn) (rev)

OTHER

Complete 360° circle (2π radians).

Angular Mil (NATO) (mil)

OTHER

Artillery & compass angle unit (6,400 mils = 360°, 1 mil = 0.05625°).

References

NIST · BIPM · ISO

[1]
NIST CUU (Non-SI Units Accepted for Use (deg, arcmin, arcsec))·Angle Metrology Standards — Degree (°), Radian (rad) & Gradian (Gon) (grad)
NIST CUU Standard
[2]
NIST SI (SI Coherent Unit: Radian (rad))·International Reference Specification for Geometry & Rotation Angles
NIST SI Reference
[3]
NIST SP 811 (NIST SP 811 App. B.9 (Plane Angle))·Official Angle Conversion Factors & Rounding Rules
NIST SP 811 Tables

Measurement Navigator78 Categories9 Scientific Domains

Browse All 78 Measurement Categories

A–Z Directory →Sitemap

Common ConvertersEveryday metric, imperial, and US customary converters for length, weight, volume, temperature, area, pressure, energy, speed, time, and data.