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Angle Converter

Convert between different units of angle Convert between 16 different units instantly with our free online tool.

Angle Converter
Convert between different units of angle
To
1 rad =57.29578 °

Formula: 1 rad × 57.29578 = 57.29578 °

1 Radian in all Angle units
Click a unit to convert to it.

Available Angle Units

16 units supported for instant conversion

Radianrad
Degree°
Gradian (Gon)grad
Arcminute′
Arcsecond″
Milliradianmrad
Turn (Revolution)tr
Quadrantquad
Sextantsext
Octantoct
Signsign
Mil (NATO)mil
Mil (USSR)mil (USSR)
Binary Degreebrad
Centesimal Minutec′
Centesimal Secondc″

About Angle Conversion

Our free online angle converter helps you quickly and accurately convert between 16 different units of angle. Whether you're a student, professional, or simply need everyday conversions, you get instant, precise results with the formula displayed.

Convert between different units of angle This converter supports both metric and imperial units, making it ideal for international use. All conversions use internationally recognized standards and formulas.

Did You Know?

A full circle = 360°. This number was chosen by ancient Babylonians because 360 is divisible by 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180 — making fractions easy.

The small-angle approximation (sin θ ≈ θ in radians) is accurate to within 1% for angles up to about 14°. Engineers and physicists use it constantly to simplify calculations.

One arcminute of latitude on Earth's surface equals exactly 1 nautical mile (1,852 m). This is why nautical miles exist — it made navigation by sextant beautifully simple.

The angle subtended by your little fingernail at arm's length is about 1° — a useful rough ruler for estimating angles in the sky.

Why Use Our Angle Converter?

Instant Results

Conversions update as you type — no button clicks needed.

High Precision

Uses internationally standardized conversion factors (SI & NIST).

16+ Units

Convert between 16 angle units used around the world.

API & AI Ready

REST API and MCP server let apps and AI assistants convert programmatically.

Common Angle Conversion Table

Quick reference: Radian (rad) to other common units.

Radian (rad)Degree (°)Gradian (Gon) (grad)Arcminute (′)Arcsecond (″)
157.2957863.661983437.747206264.8
2114.5916127.3246875.494412529.6
5286.4789318.309917188.731031324
10572.9578636.619834377.472062648
251432.3941591.54985943.675156620
502864.7893183.099171887.310313240
1005729.5786366.198343774.720626481

How to Use This Angle Converter

1

Enter Value

Type the number you want to convert

2

Select From Unit

Choose your starting unit

3

Select To Unit

Pick your target unit

4

View Result

See instant conversion with formula

5

Copy Result

Click to copy to clipboard

Frequently Asked Questions — Angle

How many degrees are in a radian?
1 radian = 180/π ≈ 57.2958°. A full circle is 2π radians = 360°.
How many radians are in a full circle?
A full circle = 2π radians ≈ 6.28318 radians = 360°. A half circle = π radians = 180°.
How many arcminutes are in a degree?
Exactly 60 arcminutes (') = 1 degree (°). And 60 arcseconds (") = 1 arcminute. These subdivisions mirror the base-60 time system.
How many arcseconds are in a degree?
Exactly 3,600 arcseconds = 1 degree (60 arcminutes × 60 arcseconds).
How many gradians are in a right angle?
100 gradians (or grads/gon) = 1 right angle = 90°. A full circle = 400 gradians. Gradians are used in surveying because right angles become round numbers.
What is π radians in degrees?
π radians = exactly 180°. This is why sin(π) = 0 and cos(π) = −1.
How do you convert degrees to radians?
Multiply degrees by π/180. Example: 90° × π/180 = π/2 ≈ 1.5708 radians.
What is a right angle in radians?
A right angle (90°) = π/2 radians ≈ 1.5708 radians.

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