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Cosecant Calculator for Degrees or Radians

Written by:
PK

On this page is a cosecant calculator. Input an angle's measurement, choose your units, and run the calculator to see the cosecant.

Cosecant Calculator for Angles or Radians

Using the Cosecant Calculator

To use the tool to find the cosecant, enter the measurement of the angle in either degrees or radians, choose the units, and compute.

  • Angle - measurement of the angle, in degrees or radians
  • Degrees or Radians? - choose your units in the menu

Once happy, click the "Compute Cosecant" button.

  • Cosecant - the cosecant, or ratio of the hypotenuse over the opposite side's measurement

What is the cosecant?

For a given angle in a right triangle, cosecant is the ratio of the longest side (the hypotenuse) to the opposite side. Cosecant is the reciprocal of the sine; sine is the ratio of the opposite side's length to the hypotenuse.

Right triangle to illustrate trigonometry functions
Right Triangle Diagram (CC By-SA 3.0 Wikimedia)

Trigonometric functions like the cosecant can also be used to find the ratio between sides of a unit circle (a circle with radius 1).

Unit Circle to illustrate trigonometry.
Unit circle diagram (CC By-SA 3.0 Wikimedia)

Cosecant as a formula

As a trigonometry formula, cosecant is usually abbreviated as "csc", as in the following equation:

\csc(\theta)

As the reciprocal of sine, it's equivalent to:

\csc(\theta)=\frac{1}{\sin(\theta)}

If you already have the result of a calculation, to find the angle use the arccosecant or inverse cosecant function.

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