Enter the degrees, minutes, and seconds into the calculator to determine the value in radians. This calculator can also evaluate any of the variables given the others are known.
- All Unit Converters
- DMS Calculator (Degrees, Minutes, Seconds)
- Angle To Time Calculator
- Degree to Percent Slope Calculator
Dms To Radians Formula
The following formula is used to convert degrees, minutes, and seconds (DMS) to radians.
R = (D + M/60 + S/3600) * (π/180)
Variables:
- R is the value in radians
- D is the degree component
- M is the minutes component
- S is the seconds component
To calculate the value in radians, add the degree component to the minutes component divided by 60 and the seconds component divided by 3600. Multiply the result by π/180 to convert the value from degrees to radians.
| 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 is a Dms To Radians?
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 = (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
