Angular Resolutions.
Angular Conversions
Accu have compiled a series of basic tables for conversion of angular measurements between degrees, radians and arcminutes.
A circle is divided into 360 degrees, and each degree is divided up into 60 smaller measurements, called arcminutes. Radians are an alternative unit of angular measurement which are favourable in certain applications. Degrees are commonly used and widely understood, but radians are a more natural form of angular measurement which relate more closely with pi, making them favourable in certain mathematical formulae.
| Degrees | Radians | Milliradians | Microradians | Arcminutes | % of a Rev. |
|---|---|---|---|---|---|
| 1 | 0.0174556 | 17.4555712 | 17455.57 | 60 | 0.2777778 |
| 57.2883514 | 1 | 1000 | 1000000 | 3437.3 | 15.9134309 |
| 0.0572884 | 0.0010000 | 1 | 1,000 | 3.4373011 | 0.0159134 |
| 0.0000573 | 0.0000010 | 0.0010000 | 1 | 0.0034373 | 0.0000159 |
| 0.0166666 | 0.0002909 | 0.2908656 | 290.8656195 | 1 | 0.0046296 |
| 0.0002778 | 0.0000048 | 0.0048478 | 4.8477797 | 0.0166667 | 0.0000772 |
| 3.6 | 0.0628571 | 62.8571 | 62857.143 | 216 | 1 |
| 360 | 6.2857143 | 6286 | 6285714 | 21600 | 100 |
Rotary Encoders
The following table applies the previous measurements to figures which are commonly used alongside rotary encoders, which are used for digitised angular positioning:
| Binary Digits (Bits) | Counts per Rev. | Arcminutes per Bit | Milliradians per Bit |
|---|---|---|---|
| 7 | 128 | 168.75 | 49.087 |
| 8 | 256 | 84.375 | 24.544 |
| 9 | 512 | 42.188 | 12.272 |
| 10 | 1024 | 21.094 | 6.1359 |
| 11 | 2048 | 10.547 | 3.0680 |
| 12 | 4096 | 5.2734 | 1.5340 |
| 13 | 8192 | 2.6367 | 0.76699 |
| 14 | 16384 | 1.3184 | 0.38350 |
| 15 | 32768 | 0.65918 | 0.19175 |
| 16 | 65536 | 0.32959 | 0.095874 |
| 17 | 131072 | 0.16479 | 0.047937 |
| 18 | 262144 | 0.0823397 | 0.023968 |
| 19 | 524288 | 0.041199 | 0.011984 |
| 20 | 1048576 | 0.020599 | 0.0059921 |