Degrees to Radians Converter
Convert an angle into degrees, minutes, seconds, radians and multiples of π at once. Negative angles and degrees-minutes-seconds conversion are supported.
Degrees, minutes and seconds
Convert between degrees-minutes-seconds (written like 35°41′22″) and decimal degrees (written like 35.68944°). The sign goes on the whole angle, once. Enter 0 or a positive number in the degrees, minutes and seconds fields, and choose the minus sign for a negative angle.
Angle units and their definitions
The size of each unit in degrees is listed below. Degrees are the base unit.
| Unit | Size of one unit | Definition and source |
|---|---|---|
| Degrees, minutes and seconds | ||
| degree (°) | 1 ° | 1/360 of a full turn. NIST lists 1.745 329 E−02 rad. NIST SP 811 |
| minute of arc (′) | 1/60 ° (about 0.01666667 °) | 1/60 of a degree. NIST lists 2.908 882 E−04 rad. NIST SP 811 |
| second of arc (″) | 1/3600 ° (about 0.0002777778 °) | 1/3,600 of a degree. NIST lists 4.848 137 E−06 rad. NIST SP 811 |
| Radians | ||
| radian (rad) | 5625000000000000000000000000000000000000000000000000000000000/98174770424681038701957605727484465131161543730472056905467 ° (about 57.29578 °) | The angle at the center of a circle that cuts off an arc as long as the radius. 1 rad = 180/π degrees (about 57.29578°), calculated with an approximation of π |
| π radians (multiples of π) | 180 ° | 1 π rad = 180°. Shows how many times π the angle is |
- Conversions among degrees, minutes, seconds and multiples of π are calculated exactly.
- A value in radians cannot be exact, because it involves π. This tool calculates with an approximation of π (to the 60th decimal place), and labels every value that involves radians as a "rounded value".
- "Multiple of π" is an exact fraction when you start from degrees (90° = π/2, −60° = −π/3). When you start from radians the calculation uses the approximation, so the fraction is not shown.
- Negative angles are rounded by their absolute value and then given the sign back, so positive and negative angles are mirror images.
Examples
- 180° = π radians = about 3.141593 rad
- 90° = π/2 radians = about 1.570796 rad
- −90° = −π/2 radians = about −1.570796 rad
- 1 rad = about 57.29578°
- 0.5° = 30′ = 1,800″
- 35°41′22″ = about 35.689444°, and −35°41′22″ = about −35.689444°
Notes
- You can enter decimals (up to 12 digits before the decimal point and 6 decimal places). Use a period as the decimal separator. Commas are accepted only as thousands separators.
- You can enter angles above 360° and negative angles. The tool does not reduce them to the remainder after dividing by 360° (720° stays 720°).
- Enter the minutes and seconds as 0 or more and less than 60. An entry such as 59′60″ is rejected.
- The radian is the SI unit of plane angle. NIST SP 811 Appendix B.8 lists the degree, the minute and the second of arc as factors to the radian (1.745 329 E−02, 2.908 882 E−04 and 4.848 137 E−06), which agree with the values used here.
Sources
The definitions on this page come from the source below (checked on November 1, 2026). The degree, minute and second (angle) rows of NIST SP 811 Appendix B.8 were read word for word. The B.8 page does not list the radian as a unit to convert from, so the radian and the multiple of π are defined here by their usual meaning (an arc as long as the radius; 1 π rad = 180°) and are not attributed to a source.
Frequently asked questions
How do I convert degrees to radians?
Multiply by π/180. For example, 180° is π radians (about 3.141593 rad) and 90° is π/2 radians (about 1.570796 rad).
How do I convert radians to degrees?
Multiply by 180/π. One radian is about 57.29578°.
How are negative angles converted?
The tool converts the absolute value and then adds the sign. −90° is −π/2 radians (about −1.570796 rad). For degrees-minutes-seconds, the sign is written once at the start, as in −35°41′22″.
How do I turn degrees-minutes-seconds into decimal degrees?
Calculate degrees + minutes/60 + seconds/3,600. For 35°41′22″, that is 35 + 41/60 + 22/3,600 = about 35.689444°.
How many minutes and seconds are in one degree?
One degree is 60 minutes, or 3,600 seconds. One minute is 60 seconds.