Converters
Angle Converter
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.
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
Related calculators
- 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.
- All converters.
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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