Enter an angle and select its unit (degrees or radians) to calculate the cosecant (csc) of that angle. You'll get the csc value along with the corresponding sine value and secant value at the same angle — all computed from the formula csc(x) = 1 / sin(x). Also try the Law of Sines Calculator.
csc(α)
--
sin(α)
--
sec(α)
--
Angle in Degrees
--
Angle in Radians
--
The cosecant (csc) is a trigonometric function defined as the reciprocal of the sine function: csc(x) = 1 / sin(x). In a right triangle, it equals the length of the hypotenuse divided by the length of the side opposite the angle. See also our find cot(x) with Cotangent Calculator (cot).
Cosecant is the reciprocal of sine, not the inverse. csc(x) = 1 / sin(x), meaning it flips the sine value. The inverse sine (arcsin or sin⁻¹) is a different function that returns the angle when given a sine value.
The cosecant function is undefined wherever sine equals zero — that is, at x = nπ (or x = 0°, 180°, 360°, etc.) for any integer n. Its range is all real numbers except those between -1 and 1, written as (-∞, -1] ∪ [1, ∞).
No. Cosecant is an odd function, meaning csc(-x) = -csc(x). So the cosecant of a negative angle is the negative of the cosecant of the corresponding positive angle. You might also find our calculate Cofunction Result, Original Function Value & Complementary Angle (Degrees) — Cofunction useful.
Yes, for common angles. For example, csc(30°) = 1 / sin(30°) = 1 / 0.5 = 2, and csc(90°) = 1 / sin(90°) = 1 / 1 = 1. For other angles, you would use the sine value and take its reciprocal.
Most basic calculators do not have a dedicated csc button. To find csc(x), first calculate sin(x), then take its reciprocal by pressing the 1/x or x⁻¹ button. Scientific calculators may have a csc function directly.
Cosecant (csc) is the reciprocal of sine: csc(x) = 1 / sin(x). Secant (sec) is the reciprocal of cosine: sec(x) = 1 / cos(x). They are related but correspond to different sides of a right triangle.
Multiply degrees by π/180 to convert to radians. For example, 45° × (π/180) ≈ 0.7854 radians. You can then use csc(0.7854) = 1 / sin(0.7854) ≈ 1.4142. This calculator handles the conversion automatically.