Converters
Angle Converter
Last updated: June 19, 2026
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.
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.
Degree → Radian
1.570796 rad
90 deg = 1.570796 rad
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.
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
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- Unit circle calculator for sin, cos, tan, and the unit-circle coordinate of any angle.
- Circle calculator for radius, diameter, circumference, and area.
- Scientific calculator for trig functions in both degree and radian mode.
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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.
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