Angle Converter
Convert between degrees, radians, gradians and turns.
Formula and sources updated · Data sources · 1View algorithm, constants and default inputs (JSON)
1 rad ≈ 57.2957795131 °
About this calculator
A full turn is 360 degrees, 2π radians, 400 gradians or 1 turn. Radians are the natural unit in calculus and are what most programming languages expect.
Worked example
calculated with the default values below
Value 90 · From Degrees (°) · To Radians (rad) · Decimal places 4 Result 1.5708 · Degrees 90.0000 ° · Radians 1.57079633 rad · Gradians 100.0000 grad
Method and assumptions
Formula basis and scope
Convert plane angle via degrees and radians; 180 degrees = π radians.
Only the displayed unit definitions are converted; rounding and measurement uncertainty are separate.
Data sources
Disclaimer
These calculators give general conversion results. Rounding and the precision of the value you enter both affect the output, so treat displayed decimals as indicative rather than exact.
Implementation source
This record describes the implementation used by this page. It is not independent validation. External references, when available, support only the stated formula or definition; estimates and custom rules retain their own assumptions.
Formula and variables
a₂ = a₁ × f₁ ÷ f₂
- a₂
- result angle
- a₁
- input value
- f₁
- source-unit factor expressed in degrees
- f₂
- target-unit factor expressed in degrees
Factors: degree 1, radian 57.2958, gradian 0.9, turn 360, arcminute 1/60, arcsecond 1/3600; radians = degrees × π ÷ 180.
Frequently asked questions
Why are there 400 gradians (gon) in a full turn, rather than 360 degrees?
A gradian (also called a gon) divides a right angle into 100 equal parts, so a full turn is 400 gradians. One gradian equals 0.9 degree; therefore a right angle is 100 gradians, 90 degrees, or π/2 radians. Select the target unit to choose how the converted value is displayed.