Math
Degrees to Radians Converter
Convert degrees to radians and back, keeping the exact π form whenever it exists: 150° = 5π/6, 22.5° = π/8, 1° = π/180.
The converter also handles degrees-minutes-seconds in both directions and shows gradians and turns for completeness.
Degrees accept decimals and fractions (180/7). Radians accept π/6, 5pi/6, or decimals like 2.618. DMS accepts 30° 15′ 30″, 30d 15m 30s, or 30:15:30.
Try an example
Result
Converted angle
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- Degrees
- —
- Radians
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- Degrees-minutes-seconds
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- Gradians
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- Turns
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Student quick launch
Grade planning, algebra checks, and formulas students reach for most.
Study path
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Follow these when you want the formula behind the answer, a short lesson, or nearby tools in the same topic.
The conversion formulas
A full circle is 360° and also 2π An angle unit where a full turn is 2π instead of 360 degrees., because the circumference of a unit circle is 2π. So 180° = π radians, and every conversion is a proportion against that fact.
Common conversions
| Degrees | Radians (exact) | Radians (decimal) |
|---|---|---|
| 30° | π/6 | 0.5236 |
| 45° | π/4 | 0.7854 |
| 60° | π/3 | 1.0472 |
| 90° | π/2 | 1.5708 |
| 120° | 2π/3 | 2.0944 |
| 135° | 3π/4 | 2.3562 |
| 150° | 5π/6 | 2.6180 |
| 180° | π | 3.1416 |
| 270° | 3π/2 | 4.7124 |
| 360° | 2π | 6.2832 |
How to use it
- Pick the direction: degrees to radians, radians to degrees, or a DMS conversion.
- Type the angle. For radians you can write π/6, 5pi/6, or a decimal.
- Read the converted angle in the header; the other units appear below it.
How to read the answer
- An answer like 5π/6 (2.618) is exact on the left and rounded on the right. Use the The answer kept as a fraction or radical instead of a rounded decimal. in trig class.
- If the degree measure is not a nice fraction of 180 (for example 1.234°), only the decimal radian value is shown.
- 1 radian is about 57.2958°, and 1° is about 0.0174533 radians.
Common mistakes and edge cases
- Multiplying by 180/π when going from degrees to radians (that is the radians-to-degrees factor).
- Leaving the fraction unreduced: 150/180 π should be simplified to 5π/6.
- Writing minutes as decimals: 30° 30′ is 30.5°, not 30.30°.
- Forgetting that negative angles convert the same way: -45° = -π/4.
Worked examples
150° to radians
Converted angle
5π/6 (2.617994)
22.5° to radians
decimal degrees still reduce to π/8
Converted angle
π/8 (0.392699)
Negative angle
-45° = -π/4
Converted angle
-π/4 (-0.785398)
Radians to degrees
5π/6 = 150°
Converted angle
150°
Decimal radians to degrees
2 rad ≈ 114.59°
Converted angle
114.591559°
DMS to decimal
30° 15′ 30″
Converted angle
30.258333°
Decimal to DMS
12.2583°
Converted angle
12° 15′ 29.88″
Zero
Converted angle
0 (0)
Unreadable input
Converted angle
—
Frequently asked questions
How do I convert degrees to radians?+
Multiply by π/180. For 150°: 150 × π/180 = 150π/180 = 5π/6 ≈ 2.618 radians.
How do I convert radians to degrees?+
Multiply by 180/π. For 5π/6: 5π/6 × 180/π = 5 × 30 = 150°. For a decimal such as 2 rad: 2 × 57.2958 ≈ 114.59°.
What is 1 radian in degrees?+
180/π ≈ 57.2958°. A radian is the angle whose arc length equals the radius, and 2π of them make a full turn.
Why do teachers want radians in terms of π?+
Because the exact form keeps the relationship to the circle visible (π/6 is one twelfth of a turn) and avoids rounding errors in later steps.
How do I convert degrees-minutes-seconds to decimal degrees?+
Divide minutes by 60 and seconds by 3600, then add: 30° 15′ 30″ = 30 + 15/60 + 30/3600 = 30.2583°.
What is a gradian?+
A unit where a right angle is 100 grad and a full circle is 400 grad. Multiply degrees by 10/9 to get gradians.
About this calculator
- Written by
- mathcheck editorial team
- Last reviewed
- September 4, 2026
Method
- Uses the values entered by the user and stable formulas documented on the page.
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Last updated: September 4, 2026