About this calculator
The Degrees to Radians Calculator converts degree measure into radians, including decimal radians and a pi-form result. It is useful for A-Level maths, calculus, circular motion, graphs, and any formula that expects angles in radians.
degrees to radians calculator method
A full turn is 360 degrees or 2pi radians, so one degree equals pi / 180 radians. The calculator multiplies the degree value by pi / 180.
- radians = degrees x pi / 180
- 180 degrees = pi radians
- 360 degrees = 2pi radians
How to use the degrees to radians calculator
- Enter the angle in degrees.
- Multiply the degree value by pi.
- Divide by 180.
- Read the decimal radian answer.
- Use the pi-form result where exact working is preferred.
- Check the reference table for common angles.
Worked examples
Convert 180 degrees
Input: 180 degrees
Calculation: 180 x pi / 180
Result: pi radians
Convert 45 degrees
Input: 45 degrees
Calculation: 45 x pi / 180
Result: pi / 4, about 0.785 radians
Why radians matter
Radians measure angle by arc length on a circle. They are the natural angle unit for calculus, trigonometric graphs, angular speed, and many physics formulas.
Exact form vs decimal form
For maths working, pi-form is often cleaner. Decimal radians are useful for calculator entry, code, and numerical modelling.
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
- Radians to Degrees Calculator
- Trigonometry Calculator
- Inverse Trig Calculator