A quarter turn
90° equals π/2 radians, 0.25 turns, 100 gradians, 5400 arcminutes, or 324,000 arcseconds. The direction diagram points upward.
Convert a plane angle
Negative angles preserve their sign. Input magnitude is limited to 1 billion in the selected unit.
Conversion preserves complete rotations. The direction diagram and normalized readouts wrap those rotations separately. Counterclockwise is positive from the right-hand horizontal axis.
Converted amount
90 degrees (°)
radians (rad)
90°wrapped to [0°, 360°)
90°wrapped to [−180°, 180°)
Degrees, minutes, seconds: 90° 0′ 0.00″. Seconds rounded to two decimals.
Equivalent units
| Unit | Amount |
|---|---|
| degrees (°) | 90 |
| radians (rad) | 1.57079633 |
| turns / revolutions | 0.25 |
| gradians / gon | 100 |
| arcminutes (′) | 5,400 |
| arcseconds (″) | 324,000 |
Displayed values are rounded. CSV uses the available JavaScript numeric precision; it cannot restore precision absent from the input.
Calculations and CSV generation run locally in your browser. No measurement data is uploaded by this tool.
How to use the Angle Converter
- 01
Enter a signed decimal angle and select the source and target units. Input magnitude is limited to one billion in the source unit.
- 02
Read the full converted angle. Use the diagram and wrapped values to inspect its equivalent direction after removing complete rotations.
- 03
Choose display precision and copy the conversion or download a table. DMS output rounds arcseconds to two decimal places.
Examples
A negative multi-turn rotation
−450° is −1.25 turns. Its direction is the same as 270° in the [0°, 360°) range or −90° in the [−180°, 180°) range. The primary result keeps the original rotation count.
Decimal degrees to DMS
12.5° displays as 12° 30′ 0.00″. The sign applies to the entire angle; −12.5° is the negative of that full magnitude.
Units for complete and partial rotations
The converter uses 360 degrees or 400 gradians per complete turn. A radian relates an arc length to its radius, giving 2π radians in a turn. Arcminutes and arcseconds divide a degree into 60 and 3600 parts respectively. Their names refer to angle, not elapsed time.
Wrapping is separate from conversion
A conversion multiplies by a unit factor and preserves complete turns. Normalization takes a remainder to express only the direction. The unsigned display includes 0° and excludes 360°; the signed display includes −180° and excludes 180°. Thus +180° appears as −180° in the signed readout.
Reading the diagram
The reference axis points right, with positive rotation counterclockwise. This is the common mathematical plane-angle convention. A compass bearing usually starts at north and increases clockwise, so the diagram should not be read as a geographic bearing. It represents direction only, not the total number of turns.
What to know
- Plane angles only; solid angles, compass bearings, and military mil conventions are not included.
- DMS and normalized values use floating-point arithmetic. Very large rotations can lose fine angular detail.
- Decimal and scientific notation are supported; commas and unit text are not. Calculations use JavaScript floating-point numbers and displayed results are rounded.
Common questions
Can I paste 12° 30′ 15″?
The amount field accepts a decimal number, not a DMS expression. Convert the parts to degrees first: degrees + minutes/60 + seconds/3600, with the sign applied to the whole value.
Are gradians and degrees the same?
No. A right angle is 100 gradians or 90 degrees. The option labeled gradians / gon uses that convention.
Why does 360° show the same direction as 0°?
They differ by one complete turn. The full converted value preserves the turn; the direction diagram removes it.
Does this include military mils?
No. Several mil conventions exist. Use the exact degree or radian definition required by your source.