Example 1
- 180°
3.141592653589793
How many radians is 180°? π, about 3.14159.
Degrees to radians
Type an angle in degrees. The calculator multiplies by π/180 and returns radians. 180° is π, about 3.14159. 90° is π/2, about 1.57080. 45° is π/4, about 0.78540.
The direction is one way: degrees to radians. There is no path back from radians to degrees here. π is the usual constant.
Results
Enter data and click Calculate.
How it works
A radian is another measure of the same angle. One radian is the angle whose arc on a circle equals the radius. A full turn is 360° or 2π radians, so 180° = π rad.
The formula is linear: radians = degrees × π / 180. 180 × π / 180 = π ≈ 3.141592653589793. 90° gives π/2 ≈ 1.57080. 45° gives π/4 ≈ 0.78540. Zero degrees stays zero radians.
The field is degrees. A comma and a dot are the same decimal. A negative angle passes and returns a negative radian, the same turn the other way. 360° gives 2π ≈ 6.28319, a full turn.
The calculator does not divide the other way. If you have radians and want degrees, you multiply by 180/π off this page. Tangent, sine and cosine on neighboring cards take an angle in their own mode, not from this field.
The header units switch does not convert the angle. A typed 180 stays 180 degrees, not 180 radians. The result is a real number, with no π letter in the box, only the decimal value.
30° is π/6 ≈ 0.52360. 60° is π/3 ≈ 1.04720. 270° is 3π/2 ≈ 4.71239. 1° is π/180 ≈ 0.01745.
Formula
radians = degrees × π / 180
How to use
- Type degrees, for example 180.
- Click Calculate. You get π, about 3.14159.
- 90° gives about 1.57080, which is π/2.
- 45° gives about 0.78540, which is π/4.
- This calculator does not go from radians back to degrees. Tangent of an angle lives on its own page.
180° = π rad
Radians = degrees × π / 180. 180° is π ≈ 3.14159. 90° is π/2 ≈ 1.57080. The calculator does not convert back.
- radian
- The measure where an arc equal to the radius is 1. 180° = π rad. A full turn is 2π.
- degrees
- The calculator input. 90° gives π/2. 45° gives π/4. Zero stays zero radians.
- π
- π from the calculator. In the formula it divides 180. The result shows the decimal, not the letter.
Examples
Example 2
- 90°
1.5707963267948966
How many radians is 90°? π/2, about 1.57080.
Example 3
- 45°
0.7853981633974483
How many radians is 45°? π/4, about 0.78540.
Related calculators
Common questions
How many radians is 180°?
π, about 3.14159. The formula 180 × π / 180 cancels to π. That is a half turn.
What does a radian mean?
An angle measure where an arc equal to the radius is 1 rad. A full circle is 2π rad, which is 360°.
How many radians are 90° and 45°?
90° is π/2 ≈ 1.57080. 45° is π/4 ≈ 0.78540. Same factor π/180.
Does the calculator also convert radians to degrees?
No. The direction is one way: degrees times π/180. The return trip is times 180/π, off this page.
How many radians is 360°?
2π ≈ 6.28319. A full turn. 0° stays 0.
Do negative degrees pass?
Yes. -90° gives about -1.57080. The sign is the turn direction. The formula does not change.
Why is there no π letter in the result?
The calculator shows the decimal value of π. 180° looks like 3.141592653589793, not the symbol π.
How many radians is 1°?
π/180 ≈ 0.01745. 30° is π/6 ≈ 0.52360. 60° is π/3 ≈ 1.04720.
Does the metric and US switch change the angle?
No. A degree stays a degree. The header label does not multiply the field.
Why do sines want radians?
Analysis formulas take the argument in radians. tan, sin and cos themselves live on their cards. Here you only change the measure.
Knowledge sources
The calculator computes the same formula as the definition below.
Page updated in 2026.