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Angle
Angle Converter
Convert degrees, radians, gradians, and more
Conversion Formula
Target = Value × (From Ratio / To Ratio)
Angle conversions use linear ratios. Target = Value × (Source Ratio / Target Ratio). To convert degrees to radians: multiply by 1 / 57.29578.
Angle conversion is important in mathematics, navigation, engineering, and astronomy. Convert between degrees, radians, gradians, arcminutes, and arcseconds.
Radians are the SI standard for angular measurement. A full circle is 2π radians (≈ 6.283 rad). Arcminutes and arcseconds are used in astronomy and navigation.
All Supported Angle Units
| Unit | Symbol | Definition |
|---|---|---|
| Degree | ° | The most common angular unit, dividing a circle into 360 equal parts. |
| Radian | rad | The SI unit of angle, defined by the radius of a circle. |
| Milliradian | mrad | One-thousandth of a radian, used in targeting and optics. |
| Gradian | grad | A unit dividing a right angle into 100 parts, used in surveying. |
| Arcminute | ' | One-sixtieth of a degree, used in astronomy and navigation. |
| Arcsecond | " | One-sixtieth of an arcminute, used in precision astronomy. |
| Revolution / Turn | rev | A complete 360° rotation, also known as a full turn or cycle. |
Common Angle Conversions
| From | To | Value |
|---|---|---|
| 1° | rad | 0.01745 |
| 1 rad | ° | 57.296 |
| 1° | arcmin | 60 |
| 1 arcmin | arcsec | 60 |
| π rad | ° | 180 |
Frequently Asked Questions
To convert degrees to radians, multiply by π/180 (approximately 0.01745). For example, 90° × π/180 = π/2 ≈ 1.571 radians. This is essential for trigonometry and calculus.
Radians are the natural unit for angular measurement in calculus and trigonometry because they simplify derivative formulas. For example, d/dx sin(x) = cos(x) only works in radians.
A gradian divides a right angle into 100 parts. There are 400 gradians in a full circle. It is used in surveying and some European engineering fields.
There are 360 degrees in a full circle. This dates back to ancient Babylonian mathematics, which used a base-60 number system.
Arcminutes (1/60 of a degree) and arcseconds (1/3600 of a degree) are used in astronomy for measuring celestial object positions and in navigation for precise angular measurements.
There are 2π radians (approximately 6.283 radians) in a full circle. One radian is the angle created when the arc length equals the radius.
A revolution (or full turn) equals 360 degrees, 2π radians, or 400 gradians. It represents one complete rotation and is used in engineering and physics for rotational measurements.