Math formulas

Trigonometry formulas

Measure angles in degrees and radians and use trigonometric relationships in right triangles and on the unit circle.

Formulas and calculators

Convert an angle between degrees, radians, gons and turns, reduce it to one full turn, and read the exact multiple of π.

α[rad] = α[°] × π / 180

Calculated quantities

α - angle · β - converted angle · α₀ - normalised angle · k - whole turns

α[rad] = α[°] × π / 180

When to use it: One full turn equals 360° and 2π rad, so a single degree is π/180 radians. The radian is the coherent derived SI unit of plane angle and has dimension one.
Calculated quantities: α - angle (rad) · β - converted angle (rad) · α₀ - normalised angle (rad) · k - whole turns (1)
Worked example: Sixty degrees in radians: Express the angle 60° in radians and give the exact multiple of π.

One full turn is 360° = 2π rad = 400 gon = 1 turn; every conversion on this page follows from that single definition.
The radian is the coherent derived SI unit of plane angle and has dimension one, so the symbol rad may be written or omitted; the degree and the gon are units accepted for use with the SI, not SI units.
The radian measures a plane angle. It must not be mixed with the steradian, which is the SI unit of solid angle.
Normalisation reduces an angle to the half-open range 0 ≤ α₀ < 360°, so 360° becomes 0° and −90° becomes 270°.
The result is shown as an exact multiple of π only when the angle is a rational multiple of π; otherwise the decimal value is used.

Multiplying by 180/π when converting degrees to radians; that factor converts radians to degrees.
Leaving a calculator in degree mode while the argument of a trigonometric function is given in radians.
Confusing the radian, which measures a plane angle, with the steradian, which measures a solid angle.
Treating one gon as one degree; a gon equals 0.9°, because a full turn has 400 gons.
Normalising −90° to 90° instead of 270° by dropping the sign instead of adding a full turn.