Cosecant Calculator

This calculator works out the cosecant of any angle, saving you from digging out a scientific calculator or misremembering the reciprocal rule. Cosecant, written csc(x), is one of the six trigonometric functions and is simply the reciprocal of sine, csc(x) = 1 / sin(x), so it turns up wherever sine does, in geometry, physics, engineering, surveying and navigation problems that involve angles and ratios. You enter a single angle and choose whether it is in degrees or radians from the dropdown. The calculator converts internally to radians, since that is the unit the underlying maths needs, and returns the cosecant value front and centre, with the same angle shown in both radians and degrees underneath so you can double-check what was actually calculated. Because sine repeats every 360 degrees (2 pi radians), the same cosecant value comes back for any equivalent angle, and the result is shown as undefined wherever sine is zero, at 0, 180 and 360 degrees and their multiples, since dividing by zero has no answer. A worked example below confirms the maths using a 30 degree angle, and the assumptions section explains the rounding applied to the displayed figures. Use it to check homework, verify a manual calculation, or get a quick trig value while working through a larger problem.

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Angle

Angle unit

Angle (radians)

Angle (degrees)

The formula

Cosecant is the reciprocal of sine, csc(x) = 1 / sin(x). It is undefined wherever sine is zero, that is at 0, 180, 360 degrees and so on.

Worked example

Cosecant of 30 degrees is 1 / sin 30 = 1 / 0.5 = 2. Enter 30 degrees to confirm.

Frequently asked questions

How do I find the cosecant of an angle?

Enter the angle and pick degrees or radians. The calculator converts to radians and evaluates the cosecant.

Degrees or radians?

Either. Choose the unit in the dropdown. The angle is shown in both units beside the result so you can check.

Why is the result the same every 360 degrees?

The trig functions are periodic. Sine and cosine repeat every 360 degrees (2 pi radians), so equivalent angles give the same value.

Who this calculator is for

This calculator is for students, engineers, surveyors and anyone who needs the cosecant of an angle.

What this calculator assumes

You enter a single angle in the chosen unit.
The angle is converted to radians for the calculation.
Results are rounded for display.

Formula and sources

Related calculators

Trig Calculator: all six trig functions at once.
Degrees to Radians Calculator: convert angle units.
Right Angle Triangle Calculator: solve a right triangle.

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