Skip to main content
Calculator Answers

Angle Converter

Blake Boege
Written by Blake Boege · Founder, Calculator Answers

An angle converter is a geometry utility that translates angular measurements between different units. The converter supports conversions across degrees, radians, gradians, and turns. It applies exact mathematical constants, such as one radian equals one hundred eighty divided by pi degrees, and a full turn equals three hundred sixty degrees, to ensure perfect conversion precision. Physics and engineering students, surveyors, and astronomers use this tool to standardize angular coordinates across different measurement systems.

Pick a 'from' unit and a 'to' unit, enter a value, and the converter returns all common angle units. Useful for trigonometry, geometry, navigation, and astronomy.

See also: Power Converter, Fuel Economy Converter, and Frequency Converter.

Quick Answer

Convert angles between degrees, radians, gradians, and turns. Enter your angle value and select units for instant, precise angular conversions.

Negative angles and decimals are fine. · e.g. 90

Internal base unit is the degree. Each conversion goes through degrees, so accuracy is consistent across pairs.

Angle

Degree → Radian

1.570796 rad

90 deg = 1.570796 rad

Degree (°)90 deg
Radian (rad)1.570796 rad
Gradian (grad)100 grad
Turn (full rotation)0.25 turn
Arcminute (')5,400 arcmin
Arcsecond (")324,000 arcsec

1 turn = 360 degrees. 1 radian = 180/π degrees ≈ 57.296 degrees. 1 gradian = 0.9 degrees. 1 arcminute = 1/60 degree, 1 arcsecond = 1/3600 degree.

Was this helpful?

Examples

90 degrees

1.570796 radians; 100 gradians; 0.25 turns

π/4 radians

= 45 degrees; 50 gradians

1 turn

= 360 degrees; 2π radians; 400 gradians

1 arcsecond

≈ 0.000278 degrees

How it works

Each angle unit is defined by its size relative to the degree. The converter multiplies the input by the "from" factor (in degrees), then divides by the "to" factor.

Identities · 1 turn = 360° = 2π rad = 400 grad

Fine units · 1° = 60 arcminutes = 3600 arcseconds

Related calculators

Related Calculators

More tools from Unit Converters

Power ConverterConvert between watts, kilowatts, megawatts, mechanical horsepower, BTU per hour, and foot-pounds per second. Useful for engineering, HVAC, and physics homework.Fuel Economy ConverterConvert fuel economy between US mpg, Imperial mpg, kilometers per liter, miles per liter, and L per 100 km. Handles the inverse relationship of L/100 km carefully and requires positive values.Frequency ConverterConvert between Hz, kHz, MHz, GHz, THz, cycles per minute, and RPM. Useful for radio, audio, electronics, and mechanical rotation problems.Density ConverterConvert density between kg/m³, g/cm³, g/mL, lb/ft³, lb/in³, and lb/gal US. Handy for materials, chemistry, and bulk-material orders.

Frequently asked questions

1 radian = 180 / π degrees ≈ 57.29578 degrees. Equivalently, 1 degree = π / 180 radians ≈ 0.017453 radians.

A gradian (or gon) divides a right angle into 100 parts instead of 90. So 1 gradian = 0.9 degrees, and a full circle is 400 gradians. Gradians are common in some surveying contexts.

A turn is one full rotation: 360 degrees, 2π radians, or 400 gradians. Useful when you want to describe rotation count directly.

An arcminute is 1/60 of a degree; an arcsecond is 1/60 of an arcminute (1/3600 of a degree). They are common in astronomy and high-precision angular measurement.

All conversions go through degrees internally using floating-point arithmetic, which is accurate to about 15 significant figures. The display shows up to 8 decimal places for clarity.