About this calculator
The Radians to Degrees Calculator converts decimal radians or pi fractions into degrees. It is useful when a formula, graph, or calculator gives an angle in radians but the answer needs to be understood or presented in degrees.
radians to degrees calculator method
Since pi radians equals 180 degrees, the calculator multiplies the radian value by 180 / pi. If you enter a pi fraction, it first turns that fraction into a radian value.
- degrees = radians x 180 / pi
- pi radians = 180 degrees
- 2pi radians = 360 degrees
How to use the radians to degrees calculator
- Choose decimal radians or pi fraction input.
- Enter the radian value.
- Multiply by 180.
- Divide by pi.
- Read the degree result.
- Compare against the common angle table if the value is familiar.
Worked examples
Convert pi radians
Input: 1pi / 1
Calculation: pi x 180 / pi
Result: 180 degrees
Convert pi over 6
Input: 1pi / 6
Calculation: (pi / 6) x 180 / pi
Result: 30 degrees
Pi fraction inputs
Many exact radian answers are written as fractions of pi, such as pi / 6, pi / 4, pi / 3, or 3pi / 2. The pi-fraction input makes those conversions faster and avoids typing long decimals.
Decimal radian inputs
Decimal radians often appear in programming, spreadsheets, scientific calculators, and numerical outputs. Convert them back to degrees when the context is easier to understand in a 0 to 360-degree scale.
Common mistakes to avoid
- Mixing degrees and radians
- Most wrong trigonometry answers come from using the wrong angle unit. Check whether the question, calculator, or exam setting is using degrees or radians before comparing results.
- Rounding too early
- Keep extra decimal places during working, then round the final answer. Rounding sine, cosine, or tangent too early can noticeably change a side length or angle.
- Using trig on a non-right triangle
- SOHCAHTOA only applies directly to right-angled triangles. Other triangles may need the sine rule, cosine rule, or a split into right triangles.
Edge cases
- Tangent is undefined where cosine is zero, such as 90 degrees and 270 degrees.
- Inverse sine and inverse cosine only accept inputs from -1 to 1.
- Angles that differ by 360 degrees can have the same sine, cosine, and tangent values.
- A calculated triangle side should not be negative. Recheck the selected side labels if that happens.
Limitations
This calculator is for educational maths support. It uses standard trigonometric formulas and JavaScript Math functions, so results are numerical approximations. For coursework, exams, engineering, surveying, or safety-critical work, follow the required method, units, precision, and marking guidance.
Frequently asked questions
Should I use degrees or radians?
Use the unit given in the question. GCSE-style triangle questions usually use degrees. A-Level maths, calculus, circular motion, and many scientific formulas often use radians.
What does SOHCAHTOA mean?
SOHCAHTOA is a memory aid: sine equals opposite over hypotenuse, cosine equals adjacent over hypotenuse, and tangent equals opposite over adjacent.
Why is tan 90 degrees undefined?
Tangent is sine divided by cosine. At 90 degrees, cosine is zero, so the division is not defined.
Why do inverse trig calculators sometimes give only one angle?
Inverse trig functions return a principal value. Some trig equations have multiple valid angles over a larger interval, so the calculator result may be one of several possible angles.
Can I use these calculators for GCSE and A-Level revision?
Yes, they are useful for checking working and building confidence. Always practise writing the full method because exam marks often depend on the steps, not just the final number.
Related calculators
- Degrees to Radians Calculator
- Trigonometry Calculator
- Inverse Trig Calculator