Trig Degree Calculator — All 6 Functions, Radians & Reference Angle
Enter any angle in degrees — positive, negative or beyond 360° — to instantly get its radian equivalent, all six trigonometric function values (sin, cos, tan, csc, sec, cot), the quadrant it falls in, and its reference angle.
degrees
45° = 0.785398 rad
- 1
Conversion factor π ÷ 180
π ÷ 180 = 0.017453Multiply any degree value by this factor to get radians. - 2
Radians
45 × 0.017453 = 0.785398
How does this calculator work?
rad = deg × π/180. Then sin, cos, tan = sin/cos (undefined at 90°, 270°), csc = 1/sin, sec = 1/cos, cot = cos/sin. The reference angle is the equivalent angle in Q1 (0–90°), found by subtracting from 180°, 180°, or 360° depending on the quadrant. All absolute values equal the Q1 values; signs follow All–Sin–Tan–Cos by quadrant.
Formula
How this is calculated
The degree-to-radian conversion multiplies the angle by π/180. The resulting radian measure is then passed directly to the standard trigonometric functions: sine and cosine are defined for all real angles; tangent (sin/cos) is undefined wherever cos = 0 (i.e. at ±90°, ±270° and their equivalents); the three reciprocal functions csc, sec and cot are undefined wherever their denominators are zero.
The quadrant is found by normalising the angle into the range [0°, 360°) and checking which 90° sector it falls in. The reference angle is the acute angle between the terminal ray and the nearest x-axis, always in [0°, 90°]. Reference angles are useful because the absolute values of all six trig functions at any angle equal the values at its reference angle — only the signs change by quadrant (remembered by the mnemonic "All Students Take Calculus": All positive in Q1, Sin positive in Q2, Tan positive in Q3, Cos positive in Q4).
Angles beyond 360° or below 0° are handled by reducing modulo 360° before computing the quadrant and reference angle, but the exact radian value (and trig function values) use the original input without reduction.
Frequently asked questions
The reference angle is the acute angle (0°–90°) between the terminal side of your angle and the nearest x-axis. Trig functions at any angle have the same absolute value as their reference angle — you only adjust the sign based on the quadrant. This makes it easy to evaluate trig functions at 150°, 210°, 330° etc. by reusing the values you know for 30°.
tan θ = sin θ / cos θ. At 90° and 270° (and their equivalents), cos θ = 0, making the denominator zero and the ratio undefined. The function approaches ±∞ from either side — the graph has vertical asymptotes at those points.
Multiply degrees by π/180. Common angles: 30° = π/6, 45° = π/4, 60° = π/3, 90° = π/2, 180° = π, 360° = 2π. To go back, multiply radians by 180/π.
Also known as
TG we-Calculate Editorial Team. (2026). Trig Degree Calculator — All 6 Functions, Radians & Reference Angle [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/trig-degree-calculator
TG we-Calculate Editorial Team. "Trig Degree Calculator — All 6 Functions, Radians & Reference Angle." TG we-Calculate. 2026. https://we-calculate.com/calculator/trig-degree-calculator.
TG we-Calculate Editorial Team, "Trig Degree Calculator — All 6 Functions, Radians & Reference Angle," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/trig-degree-calculator
@misc{wecalculate_trig_degree_calculator, title = {Trig Degree Calculator — All 6 Functions, Radians & Reference Angle}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/trig-degree-calculator}}, year = {2026}, note = {TG we-Calculate} }
Did this calculator help you?