Convert signed degrees-minutes-seconds to radians, reverse radians to normalized DMS, or carry oversized minutes and seconds into a valid angle.
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DMS To Radians Formula
The following formula is used to convert degrees, minutes, and seconds (DMS) to radians.
Variables:
- R is the value in radians
- D is the degree component
- M is the minutes component
- S is the seconds component
To calculate radians, add the nonnegative degree magnitude, arcminutes divided by 60, and arcseconds divided by 3600. Apply the angle sign once to the entire sum, then multiply by π/180. Direct mode requires whole degrees and arcminutes and components below 60; Normalize carries fractional or oversized components.
| Degrees (°) | Minutes (′) | Seconds (″) | Radians (rad) |
|---|---|---|---|
| 0 | 0 | 0 | 0.000000 |
| 1 | 0 | 0 | 0.017453 |
| 5 | 0 | 0 | 0.087266 |
| 10 | 0 | 0 | 0.174533 |
| 15 | 0 | 0 | 0.261799 |
| 22 | 30 | 0 | 0.392699 |
| 30 | 0 | 0 | 0.523599 |
| 35 | 15 | 0 | 0.615229 |
| 40 | 0 | 0 | 0.698132 |
| 45 | 0 | 0 | 0.785398 |
| 50 | 0 | 0 | 0.872665 |
| 60 | 0 | 0 | 1.047198 |
| 75 | 0 | 0 | 1.308997 |
| 90 | 0 | 0 | 1.570796 |
| 120 | 0 | 0 | 2.094395 |
| 135 | 0 | 0 | 2.356194 |
| 150 | 0 | 0 | 2.617994 |
| 180 | 0 | 0 | 3.141593 |
| 270 | 0 | 0 | 4.712389 |
| 360 | 0 | 0 | 6.283185 |
| * Rounded to 6 decimals. Formula: radians = (degrees + minutes/60 + seconds/3600) × (π / 180). Constants: π ≈ 3.141593. | |||
What Does “DMS to Radians” Mean?
DMS stands for Degrees, Minutes, and Seconds, which is a method of expressing geographic coordinates or measurements of angles. Converting DMS to radians involves changing the angle measurement from degrees, minutes, and seconds to a decimal form in radians. This is often necessary in mathematical and scientific calculations, as radians are a more universally applicable unit of measurement in these fields.
How to Calculate DMS To Radians?
The following steps outline how to calculate the DMS To Radians.
- First, determine the degree component (D).
- Next, determine the minutes component (M).
- Next, determine the seconds component (S).
- Next, gather the formula from above = R = sign × (D + M/60 + S/3600) × (π/180).
- Finally, calculate the DMS To Radians.
- After inserting the variables and calculating the result, check your answer with the calculator above.
Example Problem :
Use the following variables as an example problem to test your knowledge.
Degree component (D) = 45
Minutes component (M) = 30
Seconds component (S) = 15. With a positive sign, the angle is 45.5041666667° or approximately 0.7941975317 rad.
