Secant Calculator

This secant calculator works out the secant of any angle you enter, in degrees or radians, without needing a scientific calculator to hand. Secant is one of the six trigonometric functions, defined as the reciprocal of cosine, so sec(x) = 1 / cos(x), describing a fixed ratio in a right triangle or a length on the unit circle for a given angle. It comes up in geometry, trigonometry study, physics, engineering, surveying and navigation. You type the angle into the single input field and choose degrees or radians from the dropdown. The calculator converts your figure to radians behind the scenes, since that is what the underlying maths requires, then returns the secant value instantly, along with the same angle shown in both radians and degrees so you can check what you entered. Because secant is the reciprocal of cosine, it is undefined wherever cosine equals zero, at 90 and 270 degrees and every equivalent angle, and the calculator flags this rather than showing a false number. It is also periodic, repeating every 360 degrees (2 pi radians), so equivalent angles give the same result. Use it to check homework, verify hand calculations, or get a quick trig value mid-problem, and see the worked example and formula notes below for the maths spelled out step by step.

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Angle

Angle unit

1.154701

Angle (radians)0.523599 rad

Angle (degrees)30 deg

The formula

Secant is the reciprocal of cosine, sec(x) = 1 / cos(x). It is undefined wherever cosine is zero, that is at 90, 270 degrees and so on.

Worked example

Secant of 60 degrees is 1 / cos 60 = 1 / 0.5 = 2. Enter 60 degrees to confirm.

Frequently asked questions

How do I find the secant of an angle?

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

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 secant 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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