Angle Converter – Degrees, Radians & Gradians

This angle unit converter routes every input through exact definitions — π radians = 180° exactly, so 1 radian = 57.2957795°. Enter a value, pick the source and target units, and the result appears instantly with the factor applied shown beside it. Degrees divide the circle into 360 familiar parts, radians measure arc length per radius and belong to every serious formula, gradians split quadrants into 100, and turns wrap everything into clean multiples of one. The bridge is the exact identity π rad = 180°, so 1 radian = 57.295779513° and every degree–radian conversion inherits mathematical exactness. A mini table of the head factor makes spot-checks immediate: 1 rad = 57.2958 °; 5 rad = 286.4789 °; 10 rad = 572.9578 °; 50 rad = 2,865 °; 100 rad = 5,730 °. Calculus demands radians: sin x ≈ x and derivatives like d/dx sin = cos hold only there, which is why textbooks switch the instant limits and series appear.

1. 1

   Step 1

   Enter the value you want to convert

2. 2

   Step 2

   Select the source unit you are converting from

3. 3

   Step 3

   Select the target unit you want as the result

4. 4

   Step 4

   Read the exact result, then swap or copy as needed

• 1

  π rad = 180° is the only constant you need — derive the rest

• 2

  Calculator mode check: DEG/RAD mismatches cause silent factor-of-57 errors

• 3

  Gradians: 400/turn, used in European surveying

• 4

  Mils for artillery: NATO divides the circle into 6400

• Feeding degree values into radian-based series without the π/180 factor

• Confusing gradians (400 per turn) with degrees (360 per turn)

• Losing the π when calculator mode is DEG while formulas assume RAD