Degrees to Radians Converter
Convert degrees to radians and radians to degrees instantly. Type an angle in either box and see the exact result with up to 10 decimals, plus the answer in terms of pi.
Two-Way Angle Converter
Common Angles: Degrees to Radians Table
The most-used conversions, shown both in terms of pi and as decimals (10 decimal places).
| Degrees | Radians (in terms of π) | Radians (decimal) |
|---|---|---|
| 0° | 0 | 0 |
| 30° | π/6 | 0.5235987756 |
| 45° | π/4 | 0.7853981634 |
| 60° | π/3 | 1.0471975512 |
| 90° | π/2 | 1.5707963268 |
| 120° | 2π/3 | 2.0943951024 |
| 135° | 3π/4 | 2.3561944902 |
| 150° | 5π/6 | 2.6179938780 |
| 180° | π | 3.1415926536 |
| 270° | 3π/2 | 4.7123889804 |
| 360° | 2π | 6.2831853072 |
The Degrees to Radians Formula
π / 180180 / πWorked examples of degree radian conversion:
- 180° to radians: 180 × π/180 = π ≈ 3.1415926536
- 90° to radians: 90 × π/180 = π/2 ≈ 1.5707963268
- 45° to radians: 45 × π/180 = π/4 ≈ 0.7853981634
- 1 radian to degrees: 1 × 180/π ≈ 57.2957795131°
- π/6 radians to degrees: π/6 × 180/π = 30°
Why Radians? (Trigonometry and Programming Context)
Degrees are a human convention - a full circle is 360° because 360 divides nicely. Radians are the natural mathematical unit: one radian is the angle that subtends an arc exactly as long as the radius, and a full turn is 2π ≈ 6.2831853072 radians.
- Calculus: d/dx sin(x) = cos(x) holds only when x is in radians. In degrees, an awkward factor of π/180 appears in every derivative.
- Physics: arc length = rθ and angular velocity (rad/s) formulas work directly only with radians.
- Programming: Math.sin, Math.cos, Math.tan in JavaScript, Python math.sin, and C's sin() all expect radians. Convert first: Math.sin(deg * Math.PI / 180). Python also ships math.radians() and math.degrees() helpers, and Excel has RADIANS() and DEGREES().
Frequently Asked Questions
How do I convert degrees to radians?
Multiply degrees by pi/180. For example, 90 degrees x pi/180 = 1.5707963268 radians. The converter above does it instantly - type any angle in degrees to see the exact radian value with up to 10 decimals.
What is the formula to convert degrees to radians?
The formula is radians = degrees x pi / 180, where pi is approximately 3.1415926536. To go the other way, degrees = radians x 180 / pi. So 1 degree equals 0.0174532925 radians, and 1 radian equals 57.2957795131 degrees.
What is 180 degrees in radians?
180 degrees equals exactly pi radians, approximately 3.1415926536 radians. That is why pi shows up in angle math - half a full turn (360 degrees) is pi radians.
What is 90 degrees in radians?
90 degrees equals pi/2 radians, approximately 1.5707963268 radians. A right angle is one quarter of a full turn, and a full turn is 2pi radians, so 90 degrees = 2pi/4 = pi/2.
What is 1 degree in radians?
1 degree equals 0.0174532925 radians (exactly pi/180). Search engines show this exact value - 0.0174532925 - when you search for "degrees to radians", because it is the most common conversion factor in trigonometry.
How many degrees is 1 radian?
1 radian equals 57.2957795131 degrees (exactly 180/pi). In practice people often use the approximation 57.2958 degrees: converting 57.2958 degrees gives 1.0000003576 radians, only 0.000036 percent off from 1.
How do I convert radians to degrees?
Multiply radians by 180/pi. For example, pi radians x 180/pi = 180 degrees, and pi/4 radians x 180/pi = 45 degrees. The converter above handles both directions - enter radians to get degrees instantly.
What is pi/4 radians in degrees?
pi/4 radians = 45 degrees (exactly). It equals about 0.7853981634 radians, a common angle in the unit circle table: 45 degrees sits exactly between the x and y axes.
Why do mathematicians prefer radians over degrees?
Radians make calculus formulas clean. The derivative of sin(x) is cos(x) only when x is in radians - in degrees an ugly factor of pi/180 appears. Many physics formulas (arc length = r times theta, angular velocity in rad/s) also only work directly with radians. Degrees are a human convenience (360 is divisible by many numbers); radians are the natural unit.
Why do Math.sin and Math.cos in programming use radians?
Every major language (JavaScript Math.sin, Python math.sin, C sin) expects radians. If you have degrees, convert first: Math.sin(deg * Math.PI / 180). Forgetting this is one of the most common bugs in graphics and game code - sin(90) returns 0.8940, not 1, because 90 radians is not 90 degrees.
What is the difference between degrees and radians?
Both measure angles, but they slice the circle differently. Degrees split a full turn into 360 parts. Radians measure by arc length: one radian is the angle where the arc length equals the radius, and a full turn is 2pi, approximately 6.2831853072 radians. 360 degrees and 2pi radians describe the exact same turn.
How do I convert degrees to radians on a calculator?
Most scientific calculators have a DEG/RAD mode button. Type the degrees, then press the conversion (often labeled D-R or 2nd + ANGLE). Or just multiply by 0.0174532925 (which is pi/180): 45 x 0.0174532925 = 0.7853981625 radians.
Can angles be negative when converting?
Yes. Negative degrees convert to negative radians with the same formula: -45 degrees x pi/180 = -0.7853981634 radians. Negative angles just mean clockwise rotation instead of counter-clockwise; angles over 360 degrees also work, for example 720 degrees = 4pi, approximately 12.5663706144 radians.
What is 360 degrees in radians?
360 degrees equals exactly 2pi radians, approximately 6.2831853072 radians. One full rotation is the definition of 2pi radians - that is also why the frequency tool Hz to rad/s multiplies by 2pi.
Common Conversions: Quick Reference
This free degrees to radians calculator handles both directions instantly: type degrees on the left, radians on the right, and the table shows degrees to radians in terms of pi (π/6, π/4, π/3...) alongside decimals. Think of this page as a degree to radian converter plus its reverse in one tool: the degrees to radians conversion never changes - multiply by π/180 going down, by 180/π going up.
A degree to radian calculation is a single multiplication: degrees times pi over 180. A radian to degree calculation is the mirror image: multiply by 180 over pi to turn radians to degrees. Use this angle converter whenever you switch between the two units - in geometry homework, unit-circle work, or code.
| Conversion | Exact | Decimal |
|---|---|---|
| 1 degree to radians | π/180 | 0.0174532925 |
| 30 degrees to radians | π/6 | 0.5235987756 |
| 45 degrees to radians | π/4 | 0.7853981634 |
| 60 degrees to radians | π/3 | 1.0471975512 |
| 90 degrees to radians | π/2 | 1.5707963268 |
| 180 degrees to radians | π | 3.1415926536 |
| 360 degrees to radians | 2π | 6.2831853072 |
| pi radians to degrees | - | 180 |
| pi/4 radians to degrees | - | 45 |
The degrees to radians chart above doubles as a radians in terms of pi chart and covers the classic unit circle degrees to radians mapping used in radians in trigonometry classes: 0, π/6, π/4, π/3, π/2, π, 3π/2, 2π.
What is 0.0174532925? It is simply 1 degree expressed in radians (π/180) - the number search engines show for "degrees to radians". What is 1 radian in degrees? It is 180/π ≈ 57.2957795131 degrees; the handy estimate 57.2958 degrees to radians ≈ 1.0000003576 radians is accurate to 0.000036%.
In degree radian measure, angles scale linearly: a full circle in radians is 2π ≈ 6.2831853072, so every extra 360° just adds another 2π. Why use radians instead of degrees in math? Because calculus and physics formulas stay clean. And yes - degrees can be negative in radians form too: -45° = -0.7853981634 rad.
How to Convert in Code and on Calculators
How to convert degrees to radians in code
- JavaScript degrees to radians: rad = deg * Math.PI / 180
- Python: to convert degrees to radians in Python use math.radians(deg); the reverse is math.degrees(rad). Python's math.radians() helper is just deg × π/180.
- Excel degrees to radians: =RADIANS(A1) (and =DEGREES(A1) back).
Remember that Math.sin expects radians - sin and cos use radians in every major language, so convert degree values first or results will be wrong.
Learning how to convert radians to degrees is the same idea in reverse - multiply by 180/π instead of π/180.
How to convert degrees to radians on a calculator
For degrees to radians on a calculator, the steps depend on the model:
- TI-84 degrees to radians: enter the value, press 2nd > ANGLE > DMS/R conversion, or multiply by 0.0174532925.
- Casio calculator degrees to radians: switch mode to RAD (SHIFT > MODE > 4), or use the angle conversion menu to change degrees to radians.
- How to change degrees to radians on a calculator manually: just multiply by 0.0174532925 (π/180) - e.g. 45 × 0.0174532925 = 0.7853981625. For radians to degrees, multiply by 57.2957795131 (180/π): the radian to degree formula is deg = rad × 180/π.
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