About Degrees to Radians Converter
This converter turns degrees into radians. One degree is 0.0174533 radians. It is free, needs no sign-up and runs in your browser, so nothing you enter is uploaded.
To convert by hand, multiply the number of degrees by 0.017453293. For example, 15 deg × 0.017453293 = 0.261799 rad. To go back, multiply radians by 57.29578. For a rough mental estimate, multiply by about 0.017, which is off by about 2.6 percent.
A full turn is 360 degrees, 400 gradians and 2π radians (about 6.283185 rad). An arcminute is 1/60 of a degree and an arcsecond is 1/60 of an arcminute. Radians are the unit calculators and programming languages expect for sin, cos and tan.
Multiply by π ÷ 180. The angles most worksheets use are 30° = π/6 (0.523599 rad), 45° = π/4 (0.785398 rad), 60° = π/3 (1.0472 rad), 90° = π/2 (1.5708 rad) and 180° = π (3.14159 rad). The decimals are rounded; the π form is exact.
How to use Degrees to Radians Converter
- Choose a group such as Length or Temperature from the Quantity picker. It opens on a worked conversion.
- Type the value you want to convert in the From box. Decimals and negative numbers are fine.
- Pick the unit you have in the From list and the unit you want in the To list. The swap button reverses the pair.
- Read the result in the result card, and use the copy button to put it on your clipboard.
- Set Precision to Auto, or to a fixed number of decimals from 0 to 10, if you need a specific rounding.
- Check the formula line and the chart of common values under the result when you want to see how the number was reached.
Features
- 102 units in 15 groups, from nanometers and light-years to square miles, and from bits to tebibytes. It includes milligrams, UK gallons and pints, cubic meters, feet and inches, degrees and radians, hertz and rpm, and bits per second to MB/s.
- Results update as you type, with a swap button to reverse the pair.
- Precision control: Auto (up to 8 significant digits) or 0 to 10 fixed decimals.
- A copy button for the result.
- The formula and the factor in both directions, shown under the result.
- A chart of common values (1, 2, 5, 10, 20, 25, 50, 75, 100, 250, 500 and 1,000) for the pair you chose.
- Temperature handled with proper offset formulas, plus the UK gas mark oven table.
- Fuel economy handled as an inverse, so US and UK miles per gallon and liters per 100 km convert correctly.
- Bangladesh land units: decimal (shotangsho), katha and bigha.
- Both decimal data units (KB, MB, GB, TB) and binary ones (KiB, MiB, GiB, TiB), clearly labeled.
Degrees to radians formula
To convert degrees to radians, multiply the value by 0.017453293.
To go the other way, multiply radians by 57.29578, which is the same as dividing by 0.017453293.
rad = deg × 0.017453293Worked examples
15 deg gives 0.261799 rad
15 × 0.017453293 = 0.261799
120 deg gives 2.0944 rad
120 × 0.017453293 = 2.0944
180 deg gives 3.14159 rad
180 × 0.017453293 = 3.14159
Degrees to radians conversion chart
| Degrees (deg) | Radians (rad) |
|---|---|
| 1 | 0.0174533 |
| 15 | 0.261799 |
| 30 | 0.523599 |
| 45 | 0.785398 |
| 60 | 1.0472 |
| 90 | 1.5708 |
| 120 | 2.0944 |
| 135 | 2.35619 |
| 180 | 3.14159 |
| 270 | 4.71239 |
| 360 | 6.28319 |
Privacy: how it works
- Every conversion is calculated by code running in your browser tab. The values you type are never sent to Ulkaa or anyone else, and nothing is stored.
- There is no account and no sign-up for this tool, and it costs nothing to use.
Tips
- Use the swap button instead of retyping when you need the reverse conversion.
- For a quick mental check, round the factor: 1 inch is about 2.5 cm, 1 kg is about 2.2 lbs, 1 mile is about 1.6 km.
- Set Precision to 2 decimals for cooking, shopping and travel, and to 6 or more for engineering work.
- Check whether a figure uses US or imperial units before converting volumes, gallons and miles per gallon.
- For land, convert for a rough size, then confirm the area from the deed or survey record.
Frequently asked questions
Is it really free?
Yes. There is no price, no trial and no credit card. Ulkaa Tool does the work with your own device, so there is no server bill to pass on to you.
Do I need an account?
No. There is no sign-up and no login. Open the page and use it. An Ulkaa account is not needed for anything on this tool.
Does it run in my browser?
Yes. Your values are processed by code running in your browser tab, on your own device.
Is my data uploaded?
No. Your values are never sent to Ulkaa or to anyone else. You can check this yourself by watching the Network tab in your browser developer tools while you use the tool.
How many radians are in a degree?
One degree is 0.0174533 radians.
How many degrees are in a radian?
One radian is 57.2958 degrees.
How do I convert degrees to radians by hand?
Multiply the value in degrees by 0.017453293. For example, 15 deg is 0.261799 rad. To reverse it, divide by 0.017453293.
How do I convert degrees to radians?
Multiply degrees by π/180, which is about 0.017453293. For example 180 degrees is π radians, about 3.14159 rad, and 90 degrees is about 1.5708 rad. To go back, multiply radians by 180/π.
How many radians is 360 degrees?
A full turn of 360 degrees is 2π radians, about 6.28319 rad.
Does my calculator want degrees or radians?
Check its mode. sin(90) is 1 in degree mode but about 0.894 in radian mode, so converting first, or switching the mode, matters.
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