Octants to Radians (oct → rad)
Formula
1 oct = 0.7853981633974483 radConversion Table
| oct | rad |
|---|---|
| 0 | 0 |
| 1.0000 | 0.78540 |
| 2.0000 | 1.5708 |
| 3.0000 | 2.3562 |
| 4.0000 | 3.1416 |
| 5.0000 | 3.9270 |
| 6.0000 | 4.7124 |
| 7.0000 | 5.4978 |
| 8.0000 | 6.2832 |
| 9.0000 | 7.0686 |
| 10.000 | 7.8540 |
| 11.000 | 8.6394 |
| 12.000 | 9.4248 |
| 13.000 | 10.210 |
| 14.000 | 10.996 |
| 15.000 | 11.781 |
| 16.000 | 12.566 |
| 17.000 | 13.352 |
| 18.000 | 14.137 |
| 19.000 | 14.923 |
| oct | rad |
|---|---|
| 20.000 | 15.708 |
| 21.000 | 16.493 |
| 22.000 | 17.279 |
| 23.000 | 18.064 |
| 24.000 | 18.850 |
| 25.000 | 19.635 |
| 26.000 | 20.420 |
| 27.000 | 21.206 |
| 28.000 | 21.991 |
| 29.000 | 22.777 |
| 30.000 | 23.562 |
| 31.000 | 24.347 |
| 32.000 | 25.133 |
| 33.000 | 25.918 |
| 34.000 | 26.704 |
| 35.000 | 27.489 |
| 36.000 | 28.274 |
| 37.000 | 29.060 |
| 38.000 | 29.845 |
| 39.000 | 30.631 |
| oct | rad |
|---|---|
| 40.000 | 31.416 |
| 41.000 | 32.201 |
| 42.000 | 32.987 |
| 43.000 | 33.772 |
| 44.000 | 34.558 |
| 45.000 | 35.343 |
| 46.000 | 36.128 |
| 47.000 | 36.914 |
| 48.000 | 37.699 |
| 49.000 | 38.485 |
| 50.000 | 39.270 |
| 51.000 | 40.055 |
| 52.000 | 40.841 |
| 53.000 | 41.626 |
| 54.000 | 42.412 |
| 55.000 | 43.197 |
| 56.000 | 43.982 |
| 57.000 | 44.768 |
| 58.000 | 45.553 |
| 59.000 | 46.338 |
| oct | rad |
|---|---|
| 60.000 | 47.124 |
| 61.000 | 47.909 |
| 62.000 | 48.695 |
| 63.000 | 49.480 |
| 64.000 | 50.265 |
| 65.000 | 51.051 |
| 66.000 | 51.836 |
| 67.000 | 52.622 |
| 68.000 | 53.407 |
| 69.000 | 54.192 |
| 70.000 | 54.978 |
| 71.000 | 55.763 |
| 72.000 | 56.549 |
| 73.000 | 57.334 |
| 74.000 | 58.119 |
| 75.000 | 58.905 |
| 76.000 | 59.690 |
| 77.000 | 60.476 |
| 78.000 | 61.261 |
| 79.000 | 62.046 |
Octants to Radians Conversion
Converting Octants (oct) to Radians (rad) is a common angle conversion. 1 oct equals 0.785398 rad. For example, 100 oct is equal to 78.539816 rad.
Quick Mental Math: Octants to Radians
1 octant is about 0.7854 radians, so use that as a quick check.
Why is converting Octants to Radians tricky?
octants to radians hides a pi-based factor, so treating the step as a clean base-10 shift gives the wrong size.
Quick Reference Values
1 oct = 0.785398 rad. 5 oct = 3.926991 rad. 10 oct = 7.853982 rad. 25 oct = 19.634954 rad. 50 oct = 39.269908 rad. 100 oct = 78.539816 rad.
What is Octants?
Octants (oct) is a unit of angle. An octant is a unit of angular measurement equal to 45 degrees or one-eighth of a full circle (360 degrees). It is used in historical and navigational contexts to describe angular divisions. One octant corresponds to π/4 radians according to angular standards [iso-80000]. The octant dates to early navigation instruments developed in the 18th century, notably the reflecting octant invented by John Hadley in 1731. It was adopted to improve celestial navigation accuracy before the sextant became widespread [iso-80000]. While largely replaced by degrees and radians, octants remain referenced in historical navigation and maritime heritage. Some naval training and museums preserve knowledge of octants as part of seafaring traditions [nist-sp-811].
What is Radians?
Radians (rad) is a unit of angle. A radian is the SI unit of plane angle defined as the angle subtended at the center of a circle by an arc equal in length to the radius. One radian equals approximately 57.2958 degrees or exactly 1 rad = radius/arc length ratio. It is a dimensionless unit used extensively in mathematics, physics, and engineering [bipm-si-brochure]. The radian concept was formalized in the 19th century, with mathematicians like Roger Cotes contributing to its development. The radian was adopted as the standard angular unit in the SI system to provide a natural measure of angles based on circle geometry [bipm-si-brochure]. Radians are the standard unit of angular measurement in science, engineering, and technology worldwide. They are used in trigonometry, rotational dynamics, and signal processing, with formal adoption by the BIPM and ISO 80000 standards [bipm-si-brochure, iso-80000].
Common Misspellings
People often search for this conversion using these alternate spellings: octent, octent angle, octons, octancts, radianes, radias, radans, radiens. All of these refer to the Octants to Radians conversion.